From 35fa85802fc276c4e46ce202d82c07e456009b5f Mon Sep 17 00:00:00 2001 From: corolth1 Date: Fri, 15 Mar 2024 19:35:21 -0400 Subject: [PATCH] Tree for 0.1.0 --- .gitignore | 65 + LICENSE.txt | 21 + README.md | 202 +++ dev/build-docs.sh | 13 + dev/codeqc.sh | 19 + dev/environment.yml | 26 + dev/run-doctests.sh | 18 + dev/run-unittests.sh | 12 + docs/AUTHORS.md | 8 + docs/CHANGELOG.md | 7 + docs/Makefile | 20 + docs/conf.py | 70 + docs/devnotes.md | 102 ++ docs/index.rst | 36 + docs/loss.rst | 9 + docs/metrics.rst | 9 + docs/notebooks/helpers_introduction.py | 42 + docs/notebooks/helpers_momentum.py | 183 +++ docs/notebooks/introduction.ipynb | 1179 +++++++++++++++ docs/notebooks/momentum.ipynb | 494 +++++++ docs/source/benchmark_auc.png | Bin 0 -> 46054 bytes docs/source/benchmark_auc_se.png | Bin 0 -> 53672 bytes docs/source/benchmark_brier_score.png | Bin 0 -> 35803 bytes docs/source/benchmark_cox.png | Bin 0 -> 90190 bytes docs/source/benchmark_harrell_cindex.png | Bin 0 -> 16055 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+ tests/benchmark_data/benchmark_cox.json | 1 + tests/benchmark_data/benchmark_ipcw.json | 1 + .../benchmark_kaplan_meier.json | 1 + tests/benchmark_data/benchmark_weibull.json | 1 + tests/benchmark_script/test_auc.R | 208 +++ tests/benchmark_script/test_brier_score.R | 171 +++ tests/benchmark_script/test_cindex.R | 184 +++ tests/benchmark_script/test_cox.R | 152 ++ tests/benchmark_script/test_ipcw.R | 54 + tests/benchmark_script/test_kaplan_meier.R | 41 + tests/benchmark_script/test_weibull.R | 89 ++ tests/test_auc.py | 346 +++++ tests/test_brier_score.py | 284 ++++ tests/test_cindex.py | 295 ++++ tests/test_cox.py | 134 ++ tests/test_ipcw.py | 111 ++ tests/test_kaplan_meier.py | 222 +++ tests/test_mnist.py | 155 ++ tests/test_train.py | 91 ++ tests/test_weibull.py | 274 ++++ tests/utils.py | 673 +++++++++ 70 files changed, 10707 insertions(+) create mode 100644 .gitignore create mode 100644 LICENSE.txt create mode 100644 README.md create mode 100755 dev/build-docs.sh create mode 100755 dev/codeqc.sh create mode 100644 dev/environment.yml create mode 100755 dev/run-doctests.sh create mode 100755 dev/run-unittests.sh create mode 100644 docs/AUTHORS.md create mode 100644 docs/CHANGELOG.md create mode 100644 docs/Makefile create mode 100644 docs/conf.py create mode 100644 docs/devnotes.md create mode 100644 docs/index.rst create mode 100644 docs/loss.rst create mode 100644 docs/metrics.rst create mode 100644 docs/notebooks/helpers_introduction.py create mode 100644 docs/notebooks/helpers_momentum.py create mode 100644 docs/notebooks/introduction.ipynb create mode 100644 docs/notebooks/momentum.ipynb create mode 100644 docs/source/benchmark_auc.png create mode 100644 docs/source/benchmark_auc_se.png create mode 100644 docs/source/benchmark_brier_score.png create mode 100644 docs/source/benchmark_cox.png create mode 100644 docs/source/benchmark_harrell_cindex.png create mode 100644 docs/source/benchmark_uno_cindex.png create mode 100644 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tests/test_kaplan_meier.py create mode 100644 tests/test_mnist.py create mode 100644 tests/test_train.py create mode 100644 tests/test_weibull.py create mode 100644 tests/utils.py diff --git a/.gitignore b/.gitignore new file mode 100644 index 0000000..3695f31 --- /dev/null +++ b/.gitignore @@ -0,0 +1,65 @@ +# Temporary and binary files +*~ +*.py[cod] +*.so +*.cfg +!.isort.cfg +!setup.cfg +*.orig +*.log +*.pot +__pycache__/* +.cache/* +.*.swp +**/.ipynb_checkpoints/* +*/.ipynb_checkpoints/* +**/lightning_logs/* +**/checkpoints/* +.DS_Store + +# Project files +.ropeproject +.project +.pydevproject +.settings +.idea +.vscode +tags + +# Package files +*.egg +*.eggs/ +.installed.cfg +*.egg-info + +# Unittest and coverage +htmlcov/* +.coverage +.coverage.* +.tox +junit*.xml +coverage.xml +.pytest_cache/ + +# Build and docs folder/files +build/* +dist/* +sdist/* +docs/api/* +docs/_rst/* +docs/_build/* +docs/_autosummary/* +cover/* +MANIFEST + +# Per-project virtualenvs +.venv*/ +.conda*/ +.python-version + + +# Data +*.gz +*-ubyte +MNIST/** + diff --git a/LICENSE.txt b/LICENSE.txt new file mode 100644 index 0000000..41f2c3c --- /dev/null +++ b/LICENSE.txt @@ -0,0 +1,21 @@ +The MIT License (MIT) + +Copyright (c) 2023 Novartis Pharmaceuticals Corporation + +Permission is hereby granted, free of charge, to any person obtaining a copy +of this software and associated documentation files (the "Software"), to deal +in the Software without restriction, including without limitation the rights +to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +copies of the Software, and to permit persons to whom the Software is +furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in all +copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE +SOFTWARE. diff --git a/README.md b/README.md new file mode 100644 index 0000000..a017aca --- /dev/null +++ b/README.md @@ -0,0 +1,202 @@ +# Survival analysis made easy + +`torchsurv` is a statistical package that serves as a companion tool for survival modeling on PyTorch. Its core functionalities include the computation of common survival models’ log-likelihood and predictive performance metrics. `torchsurv` requires minimal input specifications and does not impose parameter forms allowing to rapidly define, evaluate, and optimize deep survival models. + +## TL;DR + +Our idea is to **keep things simple**. You are free to use any model architecture you want! Our code has 100% PyTorch backend and behaves like any other functions (losses or metrics) you may be familiar with. + +Our functions are designed to support you, not to make you jump through hoops. Here's a pseudo code illustrating how easy is it to use `torchsurv` to fit and evaluate a Cox proportional hazards model: + +```python +from torchsurv.loss import cox +from torchsurv.metrics.cindex import ConcordanceIndex + +# Pseudo training loop +for data in dataloader: + x, event, time = data + estimate = model(x) # shape = torch.Size([64, 1]), if batch size is 64 + loss = cox.neg_partial_log_likelihood(estimate, event, time) + loss.backward() # native torch backend + +# You can check model performance using our evaluation metrics, e.g, the concordance index with +cindex = ConcordanceIndex() +cindex(estimate, event, time) +cindex.p_value(method="noether", alternative="two_sided") + +# You can even compare the metrics between two models (e.g., vs. model B) +cindex.compare(cindexB) +``` + +## Installation + +First, install the package: + +```bash +pip install torchsurv +``` +or for local installation (from package root) + +```bash +pip install -e . +``` + +If you use Conda, you can install requirements into a conda environment +using the `environment.yml` file included in the `dev` subfolder of the source repository. + +## Getting started + +We recommend starting with the [introductory guide](notebooks/introduction), where you'll find an overview of the package's functionalities. + +## Usage + +### Survival data + +We simulate a random batch of 64 sujects. Each subject is associated with a binary event status (= ```True``` if event occured), a time-to-event or censoring and 16 covariates. + +```python +>>> import torch +>>> _ = torch.manual_seed(52) +>>> n = 64 +>>> x = torch.randn((n, 16)) +>>> event = torch.randint(low=0, high=2, size=(n,)).bool() +>>> time = torch.randint(low=1, high=100, size=(n,)).float() +``` + +### Cox proportional hazards model + +The user is expected to have defined a model that outputs the estimated *log relative hazard* for each subject. For illustrative purposes, we define a simple linear model that generates a linear combination of the covariates. + +```python +>>> from torch import nn +>>> model_cox = nn.Sequential(nn.Linear(16, 1)) +>>> log_hz = model_cox(x) +>>> print(log_hz.shape) +torch.Size([64, 1]) +``` + +Given the estimated log relative hazard and the survival data, we calculate the current loss for the batch with: + +```python +>>> from torchsurv.loss.cox import neg_partial_log_likelihood +>>> loss = neg_partial_log_likelihood(log_hz, event, time) +>>> print(loss) +tensor(4.1723, grad_fn=) +``` +We obtain the concordance index for this batch with: + +```python +>>> from torchsurv.metrics.cindex import ConcordanceIndex +>>> with torch.no_grad(): +>>> log_hz = model_cox(x) +>>> cindex = ConcordanceIndex() +>>> print(cindex(log_hz, event, time)) +tensor(0.4872) +``` + +We obtain the Area Under the Receiver Operating Characteristic Curve (AUC) at a new time $t = 50$ for this batch with: + +```python +>>> from torchsurv.metrics.auc import Auc +>>> new_time = torch.tensor(50.) +>>> auc = Auc() +>>> print(auc(log_hz, event, time, new_time=50)) +tensor([0.4737]) +``` + +### Weibull accelerated failure time (AFT) model + +The user is expected to have defined a model that outputs for each subject the estimated *log scale* and optionally the *log shape* of the Weibull distribution that the event density follows. In case the model has a single output, `torchsurv` assume that the shape is equal to 1, resulting in the event density to be an exponential distribution solely parametrized by the scale. + +For illustrative purposes, we define a simple linear model that estimate two linear combinations of the covariates (log scale and log shape parameters). +```python +>>> from torch import nn +>>> model = nn.Sequential(nn.Linear(16, 2)) +>>> log_params = model(x) +>>> print(log_params.shape) +torch.Size([64, 2]) +``` + +Given the estimated log scale and log shape and the survival data, we calculate the current loss for the batch with: + +```python +>>> from torchsurv.loss.weibull import neg_log_likelihood +>>> loss = neg_log_likelihood(log_params, event, time) +>>> print(loss) +tensor(731.9636, grad_fn=) +``` + +To evaluate the predictive performance of the model, we calculate subject-specific log hazard and survival function evaluated at all times with: + +```python +>>> from torchsurv.loss.weibull import log_hazard +>>> from torchsurv.loss.weibull import survival_function +>>> with torch.no_grad(): +>>> log_params = model(x) +>>> log_hz = log_hazard(log_params, time) +>>> print(log_hz.shape) +torch.Size([64, 64]) +>>> surv = survival_function(log_params, time) +>>> print(surv.shape) +torch.Size([64, 64]) +``` + +We obtain the concordance index for this batch with: + +```python +>>> from torchsurv.metrics.cindex import ConcordanceIndex +>>> cindex = ConcordanceIndex() +>>> print(cindex(log_hz, event, time)) +tensor(0.4062) +``` + +We obtain the AUC at a new time $t =50$ for this batch with: + +```python +>>> from torchsurv.metrics.auc import Auc +>>> new_time = torch.tensor(50.) +>>> log_hz_t = log_hazard(log_params, time=new_time) +>>> auc = Auc() +>>> print(auc(log_hz_t, event, time, new_time=new_time)) +tensor([0.3509]) +``` + +We obtain the integrated brier-score with: + +```python +>>> from torchsurv.metrics.brier_score import BrierScore +>>> brier_score = BrierScore() +>>> bs = brier_score(surv, event, time) +>>> print(brier_score.integral()) +tensor(0.4447) +``` + +## Contributing + +We value contributions from the community to enhance and improve this project. If you'd like to contribute, please consider the following: + +1. Create Issues: If you encounter bugs, have feature requests, or want to suggest improvements, please create an issue in the GitHub repository. Make sure to provide detailed information about the problem, including code for reproducibility, or enhancement you're proposing. + +2. Fork and Pull Requests: If you're willing to address an existing issue or contribute a new feature, fork the repository, create a new branch, make your changes, and then submit a pull request. Please ensure your code follows our coding conventions and include tests for any new functionality. + +By contributing to this project, you agree to license your contributions under the same license as this project. + + +## Contact + +If you have any questions, suggestions, or feedback, feel free to reach out to [us](AUTHORS). + +## Cite + +If you use this project in academic work or publications, we appreciate citing it using the following BibTeX entry: + +```bibtex +@misc{projectname, + title={Project Name}, + author={Your Name}, + year={2024}, + publisher={GitHub}, + howpublished={\url{https://github.com/your_username/your_repo}}, +} +``` + diff --git a/dev/build-docs.sh b/dev/build-docs.sh new file mode 100755 index 0000000..fe18867 --- /dev/null +++ b/dev/build-docs.sh @@ -0,0 +1,13 @@ +#!/bin/bash +# build & preview the documentation locally + +DIR="$( cd "$( dirname "${BASH_SOURCE[0]}" )" >/dev/null 2>&1 && pwd )" + +set -e +cd "${DIR}/../docs" +make html +cd _build/html + +if [ "$1" == "serve" ]; then + python -m http.server --bind 127.0.0.1 8000 +fi \ No newline at end of file diff --git a/dev/codeqc.sh b/dev/codeqc.sh new file mode 100755 index 0000000..7dccfb2 --- /dev/null +++ b/dev/codeqc.sh @@ -0,0 +1,19 @@ +#!/bin/bash + +DIR="$( cd "$( dirname "${BASH_SOURCE[0]}" )" >/dev/null 2>&1 && pwd )" + +set -e + +cd "${DIR}/.." + +if [ "$1" == "check" ]; then + CHECK="--check" +else + CHECK="" +fi + +export PYTHONPATH=${DIR}/../src + +isort --profile black ${CHECK} src tests +black ${CHECK} src tests +# pylint src tests \ No newline at end of file diff --git a/dev/environment.yml b/dev/environment.yml new file mode 100644 index 0000000..091120e --- /dev/null +++ b/dev/environment.yml @@ -0,0 +1,26 @@ +name: torchsurv +channels: + - conda-forge + - pytorch +dependencies: + - python=3.10 + - build + - pep517 + - numpy + - pandas + - pytorch + - torchvision + - lightning + - loguru + - scikit-survival + - lifelines + - tox + - black + - pylint + - mypy + - sphinx + - sphinx-book-theme + - sphinxcontrib-bibtex + - myst-parser + - nbsphinx + - ipython diff --git a/dev/run-doctests.sh b/dev/run-doctests.sh new file mode 100755 index 0000000..554d8bb --- /dev/null +++ b/dev/run-doctests.sh @@ -0,0 +1,18 @@ +#!/bin/bash +# Run all unit tests + +DIR="$( cd "$( dirname "${BASH_SOURCE[0]}" )" >/dev/null 2>&1 && pwd )" + +set -e + +cd "${DIR}/.." + +export PYTHONPATH="${DIR}/../src" + +files=$(find src -type f -name "*.py" -exec grep -l 'if __name__ == "__main__"' {} +) + +for f in $files; do + module=$(echo $f | sed 's/\//./g' | sed 's/\.py//g') + echo "Running $f -> $module" + python -m $module +done diff --git a/dev/run-unittests.sh b/dev/run-unittests.sh new file mode 100755 index 0000000..247043b --- /dev/null +++ b/dev/run-unittests.sh @@ -0,0 +1,12 @@ +#!/bin/bash +# Run all unit tests + +DIR="$( cd "$( dirname "${BASH_SOURCE[0]}" )" >/dev/null 2>&1 && pwd )" + +set -e + +cd "${DIR}/.." + +export PYTHONPATH="${DIR}/../src" + +python -m unittest discover -s tests $@ \ No newline at end of file diff --git a/docs/AUTHORS.md b/docs/AUTHORS.md new file mode 100644 index 0000000..0db078e --- /dev/null +++ b/docs/AUTHORS.md @@ -0,0 +1,8 @@ +Contributors +============ + +* Thibaud Coroller +* Mélodie Monod +* Peter Krusche +* Qian Cao + diff --git a/docs/CHANGELOG.md b/docs/CHANGELOG.md new file mode 100644 index 0000000..a73fe41 --- /dev/null +++ b/docs/CHANGELOG.md @@ -0,0 +1,7 @@ +Changelog +========= + +Version 0.1 +----------- + +Initial release of CoxPH and Weibull classes. diff --git a/docs/Makefile b/docs/Makefile new file mode 100644 index 0000000..d4bb2cb --- /dev/null +++ b/docs/Makefile @@ -0,0 +1,20 @@ +# Minimal makefile for Sphinx documentation +# + +# You can set these variables from the command line, and also +# from the environment for the first two. +SPHINXOPTS ?= +SPHINXBUILD ?= sphinx-build +SOURCEDIR = . +BUILDDIR = _build + +# Put it first so that "make" without argument is like "make help". +help: + @$(SPHINXBUILD) -M help "$(SOURCEDIR)" "$(BUILDDIR)" $(SPHINXOPTS) $(O) + +.PHONY: help Makefile + +# Catch-all target: route all unknown targets to Sphinx using the new +# "make mode" option. $(O) is meant as a shortcut for $(SPHINXOPTS). +%: Makefile + @$(SPHINXBUILD) -M $@ "$(SOURCEDIR)" "$(BUILDDIR)" $(SPHINXOPTS) $(O) diff --git a/docs/conf.py b/docs/conf.py new file mode 100644 index 0000000..914830c --- /dev/null +++ b/docs/conf.py @@ -0,0 +1,70 @@ +# Configuration file for the Sphinx documentation builder. +# +# For the full list of built-in configuration values, see the documentation: +# https://www.sphinx-doc.org/en/master/usage/configuration.html + +# -- Project information ----------------------------------------------------- +# https://www.sphinx-doc.org/en/master/usage/configuration.html#project-information + +# import module for docs creation +import os +import sys + +sys.path.append(os.path.abspath(os.path.join(os.path.dirname(__file__), "..", "src" ))) + +project = "torchsurv" +copyright = "2024, Novartis Pharma AG" +# author = 'Novartis Pharma AG' + +# -- General configuration --------------------------------------------------- +# https://www.sphinx-doc.org/en/master/usage/configuration.html#general-configuration + +extensions = [ + "myst_parser", + "sphinx.ext.autodoc", + "sphinx.ext.autosummary", + "sphinx.ext.coverage", + "sphinx.ext.napoleon", + "nbsphinx", + "sphinxcontrib.bibtex", +] + +# templates_path = ['_templates'] +exclude_patterns = ["_build", "Thumbs.db", ".DS_Store"] + +# path to citations +bibtex_bibfiles = ["source/references.bib"] +suppress_warnings = ["bibtex"] + +# -- Options for HTML output ------------------------------------------------- +# https://www.sphinx-doc.org/en/master/usage/configuration.html#options-for-html-output + +html_theme = "sphinx_book_theme" +html_static_path = ["_static"] +html_logo = "source/logo_firecamp.png" + + +# latex_engine = 'xeltex' +latex_elements = { + 'preamble': r''' +\usepackage[T1]{fontenc} +\usepackage[utf8]{inputenc} % The default since 2018 +\DeclareUnicodeCharacter{200B}{{\hskip 0pt}} +\DeclareUnicodeCharacter{2223}{{\hskip 0pt}} +''', + 'printindex': r'\footnotesize\raggedright\printindex', +} +latex_show_urls = 'footnote' + +autodoc_default_options = { + "members": True, + "member-order": "bysource", + "undoc-members": False, + "special-members": "__call__, __init__", + "private-members": False, + "imported-members": True, + "recurse": True, + "collapse": False, +} + +autosummary_generate = True diff --git a/docs/devnotes.md b/docs/devnotes.md new file mode 100644 index 0000000..9349e97 --- /dev/null +++ b/docs/devnotes.md @@ -0,0 +1,102 @@ +# Development notes + +## Set up a development environment via conda + +To use conda to install all package dependencies locally and start development, +run the following commands in the root directory of the repository. + +Create the environment: + +```bash +conda create -y -n torchsurv python=3.10 +conda env update -n torchsurv -f dev/environment.yml +``` + +Activate the environment: + +```bash +conda activate torchsurv +``` + +## Test and develop the package + +To run all unit tests either use `dev/run-unittests.sh` or run the +following command from the repository root directory: + +```bash +PYTHONPATH=src python -m unittest discover -s tests -v +``` + +To run other scripts within the repo, you can run the following +from the top level directory of the repository clone, and then run +scripts from there that import torchsurv. Alternatively you may give +an absolute path to the source directory. + +```bash +export PYTHONPATH=src +``` + +To test building the package, run: + +```bash +python -m build # builds the package as a tarball -> dist +``` + +To get a local installation for testing e.g. other tools that depend on torchsurv +with a local development version of the code: + +```bash +pip install -e # install for development ("editable") +``` + +## Installing a local package build + +To install a specific package build e.g. into a local conda environment / virtualenv: + +```bash +python -mbuild +# ... activate virtualenv +# install the first tarball in dist +pip install "$(set -- dist/*.tar.gz; echo "$1")" +``` + +## Code formatting + +We use `black` for code formatting. To format the code, run the following command: + +```bash +./dev/codeqc.sh +``` + +Code should be properly formatted before merging with `dev` or `main`. + +## Build and test the documentation locally + +We use Sphinx to build the documentation. To build and view the documentation, +run the following script: + +```bash +# just run ./dev/build-docs.sh to build but not start a webserver +./dev/build-docs.sh serve +``` + +You can then access the documentation at `http://localhost:8000` in your web browser. + +When updating toctrees / adding content you may need to clean your local documentation +build: + +```bash +cd docs +make clean +``` + +To build a single PDF of the documentation, run: + +```bash +cd docs +make latexpdf LATEXMKOPTS="-silent -f" +``` + +There are a few errors in the PDF build due to layout issues, +but the PDF can still be used to summarize the package in a single +file. diff --git a/docs/index.rst b/docs/index.rst new file mode 100644 index 0000000..62c0cea --- /dev/null +++ b/docs/index.rst @@ -0,0 +1,36 @@ +Welcome to Torchsurv's documentation! +===================================== + +.. include:: ../README.md + :parser: myst_parser.sphinx_ + +.. toctree:: + :maxdepth: 2 + :caption: API: + + loss + metrics + stats + +.. toctree:: + :maxdepth: 2 + :caption: Tutorials: + + notebooks/introduction + notebooks/momentum + +.. toctree:: + :maxdepth: 2 + :caption: Other: + + devnotes + AUTHORS + CHANGELOG + + +Indices and tables +================== + +* :ref:`genindex` +* :ref:`modindex` +* :ref:`search` diff --git a/docs/loss.rst b/docs/loss.rst new file mode 100644 index 0000000..8d58c99 --- /dev/null +++ b/docs/loss.rst @@ -0,0 +1,9 @@ +Loss +============= + +.. autosummary:: + :toctree: _autosummary + + torchsurv.loss.cox + torchsurv.loss.momentum + torchsurv.loss.weibull diff --git a/docs/metrics.rst b/docs/metrics.rst new file mode 100644 index 0000000..84ab6c6 --- /dev/null +++ b/docs/metrics.rst @@ -0,0 +1,9 @@ +Metrics +======= + +.. autosummary:: + :toctree: _autosummary + + torchsurv.metrics.auc + torchsurv.metrics.cindex + torchsurv.metrics.brier_score diff --git a/docs/notebooks/helpers_introduction.py b/docs/notebooks/helpers_introduction.py new file mode 100644 index 0000000..b54ede3 --- /dev/null +++ b/docs/notebooks/helpers_introduction.py @@ -0,0 +1,42 @@ +import pandas as pd +import matplotlib.pyplot as plt +import torch +from torch.utils.data import Dataset + + +def plot_losses(train_losses, val_losses, title: str = "Cox") -> None: + + train_losses = torch.stack(train_losses) / train_losses[0] + val_losses = torch.stack(val_losses) / val_losses[0] + + plt.plot(train_losses, label="training") + plt.plot(val_losses, label="validation") + plt.legend() + plt.xlabel("Epochs") + plt.ylabel("Normalized loss") + plt.title(title) + plt.yscale("log") + plt.show() + # plt.clf() + + +class Custom_dataset(Dataset): + """ "Custom dataset for the GSBG2 brain cancer dataset""" + + # defining values in the constructor + def __init__(self, df: pd.DataFrame): + self.df = df + + # Getting data size/length + def __len__(self): + return len(self.df) + + # Getting the data samples + def __getitem__(self, idx): + sample = self.df.iloc[idx] + # Targets + event = torch.tensor(sample["cens"]).bool() + time = torch.tensor(sample["time"]).float() + # Predictors + x = torch.tensor(sample.drop(["cens", "time"]).values).float() + return x, (event, time) diff --git a/docs/notebooks/helpers_momentum.py b/docs/notebooks/helpers_momentum.py new file mode 100644 index 0000000..8173a01 --- /dev/null +++ b/docs/notebooks/helpers_momentum.py @@ -0,0 +1,183 @@ +import torch +import pytorch_lightning as L +from torch.utils.data import DataLoader, random_split +from torchvision.datasets import MNIST +from torchvision.transforms import v2 + +from torchsurv.loss.cox import neg_partial_log_likelihood +from torchsurv.loss.momentum import Momentum +from torchsurv.metrics.cindex import ConcordanceIndex + + +class LitMNIST(L.LightningModule): + + def __init__( + self, + backbone, + ): + super().__init__() + + # Set our init args as class attributes + self.data_dir = "." + self.learning_rate = 1e-3 + self.num_workers = 2 + + # Model evaluation + self.cindex = ConcordanceIndex() + + # Momentum + self.model = backbone + + def forward( + self, + x, + ): + return self.model(x) + + # Lightning related behaviors: + + def configure_optimizers(self): + optimizer = torch.optim.Adam(self.parameters(), lr=self.learning_rate) + return optimizer + + def training_step(self, batch, batch_idx): + x, y = batch + y[y == 0] = 10 # Offset 0 to prevent log(0) + log_hz = self(x) + loss = neg_partial_log_likelihood( + log_hz, torch.ones_like(y, device=y.device).bool(), y.float() + ) + self.log("loss", loss, prog_bar=True, on_step=True, on_epoch=True) + return loss + + def validation_step(self, batch, batch_idx): + x, y = batch + y[y == 0] = 10 # Offset 0 to prevent log(0) + log_hz = self(x) + loss = neg_partial_log_likelihood( + log_hz, torch.ones_like(y, device=y.device).bool(), y.float() + ) + cindex = self.cindex( + log_hz, torch.ones_like(y, device=y.device).bool(), y.float() + ) + self.log("val_loss", loss, prog_bar=True, on_step=True, on_epoch=True) + self.log( + "cindex", + cindex, + prog_bar=True, + on_step=True, + on_epoch=True, + ) + return loss + + def test_step(self, batch, batch_idx): + # Here we just reuse the validation_step for testing + return self.validation_step(batch, batch_idx) + + +class LitMomentum(L.LightningModule): + + def __init__(self, backbone): + super().__init__() + # Set our init args as class attributes + self.data_dir = "." + self.learning_rate = 1e-3 + self.num_workers = 2 + + # Model evaluation + self.cindex = ConcordanceIndex() + + # Momentum + self.model = backbone + + # Lightning related behaviors: + + def configure_optimizers(self): + optimizer = torch.optim.Adam(self.parameters(), lr=self.learning_rate) + return optimizer + + def forward(self, x, event, time): + return self.model(x, event, time) + + def training_step(self, batch, batch_idx): + x, y = batch + y[y == 0] = 10 # Offset 0 to prevent log(0) + loss = self(x, torch.ones_like(y, device=y.device).bool(), y.float()) + self.log("loss", loss, prog_bar=True, on_step=True, on_epoch=True) + return loss + + def validation_step(self, batch, batch_idx): + x, y = batch + y[y == 0] = 10 # Offset 0 to prevent log(0) + loss = self(x, torch.ones_like(y, device=y.device).bool(), y.float()) + log_hz_k = self.model.target(x) + cindex = self.cindex( + log_hz_k, torch.ones_like(y, device=y.device).bool(), y.float() + ) + self.log("val_loss", loss, prog_bar=True, on_step=True, on_epoch=True) + self.log( + "cindex", + cindex, + prog_bar=True, + on_step=True, + on_epoch=True, + ) + return loss + + def test_step(self, batch, batch_idx): + # Here we just reuse the validation_step for testing + return self.validation_step(batch, batch_idx) + + +class MNISTDataModule(L.LightningDataModule): + def __init__(self, batch_size: int = 32, transforms=None, num_workers: int = 2): + super().__init__() + self.data_dir = "." + self.batch_size = batch_size + self.num_workers = num_workers + self.transforms = transforms + + #################### + # DATA RELATED HOOKS + #################### + + def prepare_data(self): + # download + MNIST(self.data_dir, train=True, download=True) + MNIST(self.data_dir, train=False, download=True) + + def setup(self, stage=None): + # Assign train/val datasets for use in dataloaders + if stage == "fit" or stage is None: + mnist_full = MNIST(self.data_dir, train=True, transform=self.transforms) + self.mnist_train, self.mnist_val = random_split(mnist_full, [55000, 5000]) + + # Assign test dataset for use in dataloader(s) + if stage == "test" or stage is None: + self.mnist_test = MNIST( + self.data_dir, train=False, transform=self.transforms + ) + + def train_dataloader(self): + return DataLoader( + self.mnist_train, + batch_size=self.batch_size, + num_workers=self.num_workers, + persistent_workers=True, + ) + + def val_dataloader(self): + return DataLoader( + self.mnist_val, + batch_size=self.batch_size, + num_workers=self.num_workers, + persistent_workers=True, + ) + + def test_dataloader(self): + return DataLoader( + self.mnist_test, + batch_size=self.batch_size, + num_workers=self.num_workers, + persistent_workers=True, + ) diff --git a/docs/notebooks/introduction.ipynb b/docs/notebooks/introduction.ipynb new file mode 100644 index 0000000..8512d99 --- /dev/null +++ b/docs/notebooks/introduction.ipynb @@ -0,0 +1,1179 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "ca2213c2-6abc-4340-853a-7ab1e06e68d3", + "metadata": {}, + "source": [ + "# Getting started\n", + "\n", + "In this notebook, we use `torchsurv` to train a model that predicts relative risk of breast cancer recurrence. We use a public data set, the [German Breast Cancer Study Group 2 (GBSG2)](https://paperswithcode.com/dataset/gbsg2). After training the model, we evaluate the predictive performance using evaluation metrics implemented in `torchsurv`.\n", + "\n", + "\n", + "We first load the dataset using the [lifelines](https://lifelines.readthedocs.io/en/latest/) package. The GBSG2 dataset contains features and recurrence free survival time (in days) for 686 women undergoing hormonal treatment. " + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "013dbcb4", + "metadata": {}, + "outputs": [], + "source": [ + "import warnings\n", + "\n", + "warnings.filterwarnings(\"ignore\")" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "2601dd00-7bd2-49d5-9bdf-a84205872890", + "metadata": {}, + "outputs": [], + "source": [ + "import lifelines\n", + "import pandas as pd\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "import torch\n", + "from torch.utils.data import DataLoader\n", + "from sklearn.model_selection import train_test_split\n", + "\n", + "# Our package\n", + "from torchsurv.loss.cox import neg_partial_log_likelihood\n", + "from torchsurv.loss.weibull import neg_log_likelihood, log_hazard, survival_function\n", + "from torchsurv.metrics.brier_score import BrierScore\n", + "from torchsurv.metrics.cindex import ConcordanceIndex\n", + "from torchsurv.metrics.auc import Auc\n", + "\n", + "# local helpers\n", + "from helpers_introduction import Custom_dataset, plot_losses" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "d7a98ea2-100f-43ef-8c45-c786ddcd313e", + "metadata": {}, + "outputs": [], + "source": [ + "# Constant parameters accross models\n", + "EPOCHS = 100\n", + "BATCH_SIZE = 32\n", + "LEARNING_RATE = 1e-2" + ] + }, + { + "cell_type": "markdown", + "id": "38dd4c6e-2934-44f5-88fa-1d9d02032fc3", + "metadata": {}, + "source": [ + "## Dataset overview" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "1df49737-dc02-4d6b-acd7-d03b79f18a29", + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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horThagemenostattsizetgradepnodesprogrecestrectimecens
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" + ], + "text/plain": [ + " horTh age menostat tsize tgrade pnodes progrec estrec time cens\n", + "0 no 70 Post 21 II 3 48 66 1814 1\n", + "1 yes 56 Post 12 II 7 61 77 2018 1\n", + "2 yes 58 Post 35 II 9 52 271 712 1\n", + "3 yes 59 Post 17 II 4 60 29 1807 1\n", + "4 no 73 Post 35 II 1 26 65 772 1" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Load GBSG2 dataset\n", + "df = lifelines.datasets.load_gbsg2()\n", + "df.head(5)" + ] + }, + { + "cell_type": "markdown", + "id": "8f23ce41-c0eb-4c30-83f3-2a2d45dcf097", + "metadata": {}, + "source": [ + "The dataset contains the categorical features: \n", + "\n", + "- `horTh`: hormonal therapy, a factor at two levels (yes and no).\n", + "- `age`: age of the patients in years.\n", + "- `menostat`: menopausal status, a factor at two levels pre (premenopausal) and post (postmenopausal).\n", + "- `tsize`: tumor size (in mm).\n", + "- `tgrade`: tumor grade, a ordered factor at levels I < II < III.\n", + "- `pnodes`: number of positive nodes.\n", + "- `progrec`: progesterone receptor (in fmol).\n", + "- `estrec`: estrogen receptor (in fmol).\n", + "\n", + "Additionally, it contains our survival targets:\n", + "\n", + "- `time`: recurrence free survival time (in days).\n", + "- `cens`: censoring indicator (0- censored, 1- event).\n", + "\n", + "One common approach is to use a [one hot encoder](https://pandas.pydata.org/pandas-docs/stable/reference/api/pandas.get_dummies.html) to convert them into numerical features. We then seperate the dataframes into features `X` and labels `y`. The following code also partitions the labels and features into training and testing cohorts." + ] + }, + { + "cell_type": "markdown", + "id": "34132fea-daa6-46a5-8429-16df73886a51", + "metadata": {}, + "source": [ + "## Data preparation" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "id": "7a5fd9ef-2643-46b7-9c98-05ff919026ea", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + " age tsize pnodes progrec estrec time horTh_yes menostat_Pre \\\n", + "0 70.0 21.0 3.0 48.0 66.0 1814.0 0.0 0.0 \n", + "1 56.0 12.0 7.0 61.0 77.0 2018.0 1.0 0.0 \n", + "2 58.0 35.0 9.0 52.0 271.0 712.0 1.0 0.0 \n", + "3 59.0 17.0 4.0 60.0 29.0 1807.0 1.0 0.0 \n", + "4 73.0 35.0 1.0 26.0 65.0 772.0 0.0 0.0 \n", + "\n", + " tgrade_II tgrade_III event \n", + "0 1.0 0.0 False \n", + "1 1.0 0.0 False \n", + "2 1.0 0.0 False \n", + "3 1.0 0.0 False \n", + "4 1.0 0.0 False " + ] + }, + "execution_count": 32, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "df_onehot = pd.get_dummies(df, columns=[\"horTh\", \"menostat\", \"tgrade\"]).astype(\"float\")\n", + "df_onehot.drop(\n", + " [\"horTh_no\", \"menostat_Post\", \"tgrade_I\"],\n", + " axis=1,\n", + " inplace=True,\n", + ")\n", + "df_onehot.head(5)" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "0f8b7f3b-fb2a-4d74-ac99-8f6390b2f5eb", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(Sample size) Training:336 | Validation:144 |Testing:206\n" + ] + } + ], + "source": [ + "df_train, df_test = train_test_split(df_onehot, test_size=0.3)\n", + "df_train, df_val = train_test_split(df_train, test_size=0.3)\n", + "print(\n", + " f\"(Sample size) Training:{len(df_train)} | Validation:{len(df_val)} |Testing:{len(df_test)}\"\n", + ")" + ] + }, + { + "cell_type": "markdown", + "id": "00ad6603-0dff-4991-992a-081ba9a4fafa", + "metadata": {}, + "source": [ + "Let us setup the dataloaders for training, validation and testing." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "326c03fc-91f1-493b-a9ba-820de17fb2f8", + "metadata": {}, + "outputs": [], + "source": [ + "# Dataloader\n", + "dataloader_train = DataLoader(\n", + " Custom_dataset(df_train), batch_size=BATCH_SIZE, shuffle=True\n", + ")\n", + "dataloader_val = DataLoader(\n", + " Custom_dataset(df_val), batch_size=len(df_val), shuffle=False\n", + ")\n", + "dataloader_test = DataLoader(\n", + " Custom_dataset(df_test), batch_size=len(df_test), shuffle=False\n", + ")" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "570386fb-f0ea-4061-bae2-11b274e7f851", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "x (shape) = torch.Size([32, 9])\n", + "num_features = 9\n", + "event = torch.Size([32])\n", + "time = torch.Size([32])\n" + ] + } + ], + "source": [ + "# Sanity check\n", + "x, (event, time) = next(iter(dataloader_train))\n", + "num_features = x.size(1)\n", + "\n", + "print(f\"x (shape) = {x.shape}\")\n", + "print(f\"num_features = {num_features}\")\n", + "print(f\"event = {event.shape}\")\n", + "print(f\"time = {time.shape}\")" + ] + }, + { + "cell_type": "markdown", + "id": "6b53d40d-d2c4-4dd7-bb85-97d4e946c356", + "metadata": {}, + "source": [ + "## Section 1: Cox proportional hazards model\n", + "\n", + "In this section, we use the [Cox proportional hazards model](../_autosummary/torchsurv.loss.cox.html). Given covariate $x_{i}$, the hazard of patient $i$ has the form\n", + "$$\n", + "\\lambda (t|x_{i}) =\\lambda_{0}(t)\\theta(x_{i})\n", + "$$\n", + "The baseline hazard $\\lambda_{0}(t)$ is identical across subjects (i.e., has no dependency on $i$). The subject-specific risk of event occurence is captured through the relative hazards $\\{\\theta(x_{i})\\}_{i = 1, \\dots, N}$.\n", + "\n", + "We train a multi-layer perceptron (MLP) to model the subject-specific risk of event occurence, i.e., the log relative hazards $\\log\\theta(x_{i})$. Patients with lower recurrence time are assumed to have higher risk of event. " + ] + }, + { + "cell_type": "markdown", + "id": "46343fe0", + "metadata": {}, + "source": [ + "### Section 1.1: MLP model for log relative hazards" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "9c2bd89a-c90a-4795-aab5-b5c21906a0de", + "metadata": {}, + "outputs": [], + "source": [ + "cox_model = torch.nn.Sequential(\n", + " torch.nn.BatchNorm1d(num_features), # Batch normalization\n", + " torch.nn.Linear(num_features, 32),\n", + " torch.nn.ReLU(),\n", + " torch.nn.Dropout(),\n", + " torch.nn.Linear(32, 64),\n", + " torch.nn.ReLU(),\n", + " torch.nn.Dropout(),\n", + " torch.nn.Linear(64, 1), # Estimating log hazards for Cox models\n", + ")" + ] + }, + { + "cell_type": "markdown", + "id": "97c90244", + "metadata": {}, + "source": [ + "### Section 1.2: MLP model training" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "d7889dc1-1cfa-424e-a586-481cbc789581", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch: 000, Training loss: 47.81\n", + "Epoch: 010, Training loss: 44.93\n", + "Epoch: 020, Training loss: 43.78\n", + "Epoch: 030, Training loss: 44.77\n", + "Epoch: 040, Training loss: 43.74\n", + "Epoch: 050, Training loss: 45.28\n", + "Epoch: 060, Training loss: 43.95\n", + "Epoch: 070, Training loss: 46.27\n", + "Epoch: 080, Training loss: 46.49\n", + "Epoch: 090, Training loss: 44.58\n" + ] + } + ], + "source": [ + "torch.manual_seed(42)\n", + "\n", + "# Init optimizer for Cox\n", + "optimizer = torch.optim.Adam(cox_model.parameters(), lr=LEARNING_RATE)\n", + "\n", + "# Initiate empty list to store the loss on the train and validation sets\n", + "train_losses = []\n", + "val_losses = []\n", + "\n", + "# training loop\n", + "for epoch in range(EPOCHS):\n", + " epoch_loss = torch.tensor(0.0)\n", + " for i, batch in enumerate(dataloader_train):\n", + " x, (event, time) = batch\n", + " optimizer.zero_grad()\n", + " log_hz = cox_model(x) # shape = (16, 1)\n", + " loss = neg_partial_log_likelihood(log_hz, event, time, reduction=\"mean\")\n", + " loss.backward()\n", + " optimizer.step()\n", + " epoch_loss += loss.detach()\n", + "\n", + " if epoch % (EPOCHS // 10) == 0:\n", + " print(f\"Epoch: {epoch:03}, Training loss: {epoch_loss:0.2f}\")\n", + "\n", + " # Reccord loss on train and test sets\n", + " epoch_loss /= i + 1\n", + " train_losses.append(epoch_loss)\n", + " with torch.no_grad():\n", + " x, (event, time) = next(iter(dataloader_val))\n", + " val_losses.append(\n", + " neg_partial_log_likelihood(cox_model(x), event, time, reduction=\"mean\")\n", + " )" + ] + }, + { + "cell_type": "markdown", + "id": "0e2bdd8c-f84c-4003-98f4-220ddab518d1", + "metadata": {}, + "source": [ + "We can visualize the training and validation losses." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "21afc248-303a-4156-8d9c-b97be3e0a56b", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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pSE5ORkpKClauXImcnBzMnDnTie8QQRBugSJfBNEsiIuLw969e929DJtwu/g6cuQIUlNTxZ/nzZsHAJg6dSpWrVqF4uJiZGVl6TynX79+2LBhA15++WUsWLAAbdu2xdKlSzF58mSD/ctkMixatAiDBg2Ct7e3+Hj37t2xdetWswZ4S2ubOHEiSkpKsGDBAhQUFKBbt25IT083GYEjCKIZQdWOBEE0ER5luCcYZLgnCA/g8h5g1b3sft/pQNpSty6HaF6Q4f7W5bY13BMEQTQ5OrMdKfJFEITzIPFFEARhDOrzRRBEE0HiiyAIwhg6hnsSXwRBOA8SXwRBEMZQUdqRIIimgcQXQRCEMajVBEHYRZs2bbB06VLxZ0EQsHHjRpPbX758GYIg4NixYw69rrP24wrc3mqCIAjCI5F6vqjJKkHYTUFBAVq0aOHUfU6bNg1lZWU6oi4uLg4FBQWIiIhw6ms1BSS+CIIgjCGtdqTIF0HYTatWrVzyOnK53GWv5SiUdiQIgjAGNVklbkM++ugjxMbGQqVS6Tw+duxYTJ06FVlZWbj//vsRFRWFwMBA9OvXD1u3bjW7T/2046FDh9C7d2/4+voiOTkZmZmZOtsrlUrMmDEDbdu2hZ+fHzp16oT//ve/4u9ff/11rF69Gj/++CMEQYAgCPjjjz+Mph137tyJ/v37w8fHB9HR0fj73/+Oxkbtd3vIkCF47rnnMH/+fISFhaFVq1Z4/fXXbX/jbIQiXwRBEMbQr3ZUqwFBcN96iOaNWu0+Ee/lb/Xf7sMPP4znnnsOO3bswLBhwwAApaWl2Lx5M37++WdUVVVhzJgxWLhwIXx9fbF69WqkpaXh3LlziI+Pt7j/6upq3HfffRg6dCi+/PJLZGdn4/nnn9fZRqVSoXXr1li3bh0iIiKwb98+PPnkk4iOjsaECRPwwgsv4MyZM6ioqMDnn38OAAgLC0N+fr7OfvLy8jBmzBhMmzYNa9aswdmzZ/HEE0/A19dXR2CtXr0a8+bNw8GDB7F//35MmzYNd955J4YPH27Ve2YPJL4IgiCMIRVfaiWgrAcUPu5bD9G8aagB3opxz2v/Xz7gHWDVpmFhYRg1ahS+/vprUXx99913CAsLw7BhwyCXy9GzZ09x+4ULF2LDhg346aef8Mwzz1jc/1dffQWlUonPPvsM/v7+6Nq1K3Jzc/H000+L23h5eeGNN94Qf27bti327duHdevWYcKECQgMDISfnx/q6urMphmXL1+OuLg4LFu2DIIgoHPnzsjPz8dLL72Ef/7zn5DJWPKvR48eeO211wAAHTp0wLJly7Bt27YmFV+UdiQIgjCGVHwB1OuLuG2YPHkyfvjhB9TV1QFggukvf/kL5HI5qqurMX/+fHTp0gWhoaEIDAzE2bNnkZOTY9W+z5w5g549e8Lf3198LCUlxWC7FStWIDk5GS1btkRgYCA+/vhjq19D+lopKSkQJFG/O++8E1VVVcjNzRUf69Gjh87zoqOjUVRUZNNr2QpFvgiCIIyhL74aagCEuWUpxC2Alz+LQLnrtW0gLS0NKpUKv/76K/r164fdu3djyZIlAIAXX3wRmzdvxrvvvovExET4+fnhoYceQn19vVX7tmac9Lp16zB37lwsXrwYKSkpCAoKwn/+8x8cPHjQpv+HWq3WEV7S15c+7uXlpbONIAgGnjdnQ+KLIAjCGAaRLzLdEw4gCFan/tyNn58fxo8fj6+++goXL15Ex44d0bdvXwDA7t27MW3aNIwbNw4AUFVVhcuXL1u97y5duuCLL77AzZs34efnBwA4cOCAzja7d+/GwIEDMWvWLPGxrKwsnW28vb2hVCphji5duuCHH37QEWH79u1DUFAQYmNjrV5zU0BpR4IgCGMo9SNflHYkbh8mT56MX3/9FZ999hkeffRR8fHExESsX78ex44dw/HjxzFp0iSbokSTJk2CTCbDjBkzcPr0aaSnp+Pdd9/V2SYxMRFHjhzB5s2bcf78ebz66qs4fPiwzjZt2rTBiRMncO7cORQXF6OhoQH6zJo1C1evXsWzzz6Ls2fP4scff8Rrr72GefPmiX4vd0HiiyAIwhgU+SJuY4YOHYqwsDCcO3cOkyZNEh9/77330KJFCwwcOBBpaWkYOXIk+vTpY/V+AwMD8fPPP+P06dPo3bs3XnnlFbz99ts628ycORPjx4/HxIkTMWDAAJSUlOhEwQDgiSeeQKdOnURf2N69ew1eKzY2Funp6Th06BB69uyJmTNnYsaMGfjHP/5h47vhfAS1NQlYwqVUVFQgJCQE5eXlCA4OdvdyCOL2ZNubwG7JFfnk74EOTVf9RNxa1NbWIjs7G23btoWvr6+7l0M4EXOfrbXnb4p8EQRBGEOll8agakeCIJwEiS+CIAhjqPTMvNTlniAIJ0HiiyAIwhjU54sgiCaCxBdBEIQxlHppR4p8EQThJEh8EQRBGIOqHQknQDVttx7O+ExJfBEEQRjDwPNFaUfCenjX9JoaEu23Gvwz1e+MbwvU4b6J+eWXX/C3v/0NKpUKL730Eh5//HF3L4kgCGvg1Y7egUB9FXm+CJuQy+UIDQ0VZwT6+/sbjLohmhdqtRo1NTUoKipCaGgo5HK53fsi8dWENDY2Yt68edixYweCg4PRp08fjB8/HmFhNB+OIDwennb0DdGIL4pgELbRqlUrAGjyIc2EawkNDRU/W3sh8dWEHDp0CF27dhVnSI0ZMwabN2/GI4884uaVEQRhES6+fIIB5FHakbAZQRAQHR2NyMhIo+NviOaHl5eXQxEvjtvF165du/Cf//wHGRkZKCgowIYNG/DAAw+Yfc7rr7+ON954Q+exqKgoXLt2zeVrW758Of7zn/+goKAAXbt2xdKlSzFo0CAAQH5+vs7wztatWyMvL8+payQIoongsx19NV2qKfJF2IlcLnfKCZu4dXC74b66uho9e/bEsmXLbHpe165dUVBQIP47efKkyW337t1r9Krj7NmzZgWbpbWtXbsWc+bMwSuvvILMzEwMGjQIo0ePRk5ODgDjFRGU8yeIZoI07QhQqwmCIJyG2yNfo0ePxujRo21+nkKhsCrnqlKpMHv2bHTo0AHffvutePVx/vx5pKamYu7cuZg/f75da1uyZAlmzJghmuiXLl2KzZs348MPP8SiRYsQGxurE+nKzc3FgAEDbPlvEgThLnTSjiDDPUEQTsPtkS97uXDhAmJiYtC2bVv85S9/waVLl4xuJ5PJkJ6ejszMTDz22GNQqVTIysrC0KFDMXbsWJPCyxL19fXIyMjAiBEjdB4fMWIE9u3bBwDo378/Tp06hby8PFRWViI9PR0jR440uc8PPvgAXbp0Qb9+/exaE0EQToRXO/K0I0W+CIJwEs1SfA0YMABr1qzB5s2b8fHHH+PatWsYOHAgSkpKjG4fExOD7du3Y+/evZg0aRKGDh2KYcOGYcWKFXavobi4GEqlElFRUTqPS71nCoUCixcvRmpqKnr37o0XX3wR4eHhJvc5e/ZsnD59GocPH7Z7XQRBOAne54unHcnzRRCEk3B72tEepKnA7t27IyUlBe3bt8fq1asxb948o8+Jj4/HmjVrMHjwYLRr1w6ffvqpU/xX+vtQq9U6j40dOxZjx451+HUIgnAx+mlHqnYkCMJJNMvIlz4BAQHo3r07Lly4YHKbwsJCPPnkk0hLS0NNTQ3mzp3r0GtGRERALpcbGPaLiooMomEEQTRDlHppR4p8EQThJG4J8VVXV4czZ84gOjra6O+Li4sxbNgwJCUlYf369di+fTvWrVuHF154we7X9Pb2Rt++fbFlyxadx7ds2YKBAwfavV+CIDwEsdoxVPNzg+GwbYIgCDtwe9qxqqoKFy9eFH/Ozs7GsWPHEBYWhvj4eCxbtgwbNmzAtm3bxG1eeOEFpKWlIT4+HkVFRVi4cCEqKiowdepUg/2rVCqMGjUKCQkJWLt2LRQKBZKSkrB161akpqYiNjbWZBTM0trmzZuHKVOmIDk5GSkpKVi5ciVycnIwc+ZMJ75DBEG4Be754mlHgFU8+oW6ZTkEQdw6uF18HTlyBKmpqeLP3LM1depUrFq1CsXFxcjKytJ5Tm5uLh555BEUFxejZcuWuOOOO3DgwAEkJCQY7F8mk2HRokUYNGgQvL29xce7d++OrVu3mjXAW1rbxIkTUVJSggULFqCgoADdunVDenq60XUQBNHM4NWOXn6AIAfUSlbxSOKLIAgHEdTGOoESbqWiogIhISEoLy9HcHCw5ScQBOF8/tcbuHEJ+Otm4KuHgboK4JkMICLR3SsjCMJDsfb8fUt4vgiCIJwO93zJvAAvf3afKh4JgnACJL4IgiCMwWc7yuSAt0Z8UcUjQRBOgMQXQRCEMcTIlwLwDmD3KfJFEIQTIPFFEARhDC6+5F6Al0Z8UeSLIAgnQOKLIAjCGDqRL+75IvFFEITjkPgiCIIwhkri+eKG+3pKOxIE4TgkvgiCIIwhrXbkni8SXwRBOAESXwRBEMbgo4RkCkmrCUo7EgThOCS+CIIg9FGpAGj6T0urHSnyRRCEEyDxRRAEoQ9POQKAnCJfBEE4FxJfBEEQ+vC5joButSO1miAIwgmQ+CIIgtBHGvmSKbR9vqjJKkEQToDEF0EQhD4qpfa+zIsiXwRBOBUSXwRBEPrwSkcIgExGni+CIJwKiS+CIAh9pN3tAap2JAjCqZD4IgiC0Ec61xGgyBdBEE6FxBdBEIQ+BpEv8nwRBOE8SHwRBEHoI53rCFC1I0EQToXEF0EQhD7SuY4ARb4IgnAqJL4IgiD0kc51BLSRL2WdbhsKgiAIOyDxRRAEoQ8XWPqeL4AqHgmCcBgSXwRBEPqI1Y4a8aXwBSCw+1TxSBCEg5D4IgiC0Eell3YUBOr1RRCE0yDxRRAEoY9+qwlAK74o8kUQhIOQ+GpifvnlF3Tq1AkdOnTAJ5984u7lEARhDcbElxdVPBIE4RwUljch7KWxsRHz5s3Djh07EBwcjD59+mD8+PEICwtz99IIgjCH0lzki9KOBEE4BkW+mpBDhw6ha9euiI2NRVBQEMaMGYPNmze7e1kEQVjCbOSLxBdBEI7hdvG1a9cupKWlISYmBoIgYOPGjTY9f9GiRRAEAXPmzHHL2pYvX462bdvC19cXffv2xe7du8Xf5efnIzY2Vvy5devWyMvLc/o6CYJwMvqzHQFqtEoQhNNwu/iqrq5Gz549sWzZMpufe/jwYaxcuRI9evQwu93evXvR0NBg8PjZs2dx7do1u9e2du1azJkzB6+88goyMzMxaNAgjB49Gjk5OQAAtVpt8BxBEMyulSAID0B/vBBAI4YIgnAabhdfo0ePxsKFCzF+/HibnldVVYXJkyfj448/RosWLUxup1KpMHv2bEyaNAlKpbYz9fnz55Gamoo1a9bYvbYlS5ZgxowZePzxx5GUlISlS5ciLi4OH374IQAgNjZWJ9KVm5uL6Ohom/6fBEG4AaPVjhT5IgjCObhdfNnL7Nmzce+99+Kee+4xu51MJkN6ejoyMzPx2GOPQaVSISsrC0OHDsXYsWMxf/58u16/vr4eGRkZGDFihM7jI0aMwL59+wAA/fv3x6lTp5CXl4fKykqkp6dj5MiRJvf5wQcfoEuXLujXr59dayIIwknoz3YEtJ4vajVBEISDNMtqx2+//RZHjx7F4cOHrdo+JiYG27dvx913341JkyZh//79GDZsGFasWGH3GoqLi6FUKhEVFaXzeFRUlJjKVCgUWLx4MVJTU6FSqTB//nyEh4eb3Ofs2bMxe/ZsVFRUICQkxO61EQThIPqzHQFqskoQhNNoduLr6tWreP755/H777/D19fX6ufFx8djzZo1GDx4MNq1a4dPP/3UKf4r/X2o1Wqdx8aOHYuxY8c6/DoEQbgQo54vinwRBOEcml3aMSMjA0VFRejbty8UCgUUCgV27tyJ//3vf1AoFDq+LimFhYV48sknkZaWhpqaGsydO9ehdUREREAulxsY9ouKigyiYQRBNDP4YG2qdiQIoglodpGvYcOG4eTJkzqPTZ8+HZ07d8ZLL70EuVxu8Jzi4mIMGzYMSUlJ+O6773DhwgUMGTIEPj4+ePfdd+1ah7e3N/r27YstW7Zg3Lhx4uNbtmzB/fffb9c+CYLwEPRnOwJU7UgQhNNwu/iqqqrCxYsXxZ+zs7Nx7NgxhIWFIT4+HsuWLcOGDRuwbds2AEBQUBC6deums4+AgACEh4cbPA6wasdRo0YhISEBa9euhUKhQFJSErZu3YrU1FTExsaajIJZWtu8efMwZcoUJCcnIyUlBStXrkROTg5mzpzpjLeGIAh3QdWOBEE0IW4XX0eOHEFqaqr487x58wAAU6dOxapVq1BcXIysrCy79y+TybBo0SIMGjQI3t7e4uPdu3fH1q1bzRrgLa1t4sSJKCkpwYIFC1BQUIBu3bohPT0dCQkJdq+XIAgPwFyHe/J8EQThIILaWCdQwq3wasfy8nIEBwe7ezkEcfuxYxGw899A8gzgviXssXO/Ad/8BYjpAzy5w73rIwjCI7H2/N3sDPcEQRBNDkW+CIJoQkh8EQRB6GN0tiPv80XiiyAIxyDxRRAEoY/ZPl9U7UgQhGOQ+CIIgtCHqh0JgmhCSHwRBEHoY3S2oybt2HgTUKlcvyaCIG4ZSHwRBEHoY3S2o7/2PpnuCYJwABJfBEEQ+vDxQlLPl8IPgGZuK4kvgiAcgMQXQRCEPsaqHWUyrem+nkz3DlGRD/z2ElB80fK2BHELQuKLIAhCH2OzHQFt6pEiX45x7Gvg4Arg0Ep3r4Qg3AKJL4IgCH2MVTsCFPlyFnWV7JbeR+I2hcQXQRCEPqLnSz/yxRutkmhwCGW95rbOvesgCDdB4osgCEIfY9WOAI0YchaNdbq3BHGbQeKLIAhCH1NpR2q06hx4xIuLXIK4zSDxRRAEoY+xakdA22iVRgw5RiOlHYnbGxJfBEEQ+hib7QhQ5MtZcNHFRRhB3GaQ+CIIgtDHUrUjRb4cQ4x8kfgibk9IfBEEQehjbLYjIKl2pMiXQ4ieL0o7ErcnJL4IgiD0oWrHpoVHvijtSNymkPgiCILQx9hsR0Di+aK0o0OIkS8SX8TtCYkvgiAIfUxVOyr82G1jrWvXc6vRSOKLuL0h8UUQBKGPqdmOXr7stuGma9dzq8HTutRklbhNIfFFEAShj6lqR4p8OQdKOxK3OSS+CIIg9DE121GMfJH4cghqNUHc5pD4IgiC0MdUtaMY+aK0o0MoabYjcXtD4osgCEIfk01WKfLlFHjkS63URhkJ4jaCxBdBEIQ+XBCYrHakyJdDSJurUuqRuA0h8UUQBKGPqdmOFPlyHLVaN91I4ou4DXFYfFVUVGDjxo04c+aMM9Zzy/HLL7+gU6dO6NChAz755BN3L4cgCGsw1WqCIl+Oo2oEoNb+TF3uidsQm8XXhAkTsGzZMgDAzZs3kZycjAkTJqBHjx744YcfnL7A5kxjYyPmzZuH7du34+jRo3j77bdx48YNdy+LIAhLmJrtSJEvx9E32dN8R+I2xGbxtWvXLgwaNAgAsGHDBqjVapSVleF///sfFi5c6PQFNmcOHTqErl27IjY2FkFBQRgzZgw2b97s7mURBGEOlQpQq9h9c5EvtRqEHeinGSntSNyG2Cy+ysvLERYWBgDYtGkTHnzwQfj7++Pee+/FhQsXbF7Arl27kJaWhpiYGAiCgI0bN1p8zocffogePXogODgYwcHBSElJwW+//WbzaztjbcuXL0fbtm3h6+uLvn37Yvfu3eLv8vPzERsbK/7cunVr5OXlOX2dBEE4ER71Akx7vgBqk2Av+u8bpR2J2xCbxVdcXBz279+P6upqbNq0CSNGjAAAlJaWwtfX18KzDamurkbPnj3FVKY1tG7dGv/+979x5MgRHDlyBEOHDsX999+PP//80+j2e/fuRUNDg8HjZ8+exbVr1+xe29q1azFnzhy88soryMzMxKBBgzB69Gjk5OQAANRGrowFQbDmv0gQhLuQii9T1Y4A+b7sRT/NSGlH4jbEZvE1Z84cTJ48Ga1bt0ZMTAyGDBkCgEWJunfvbvMCRo8ejYULF2L8+PFWPyctLQ1jxoxBx44d0bFjR/zrX/9CYGAgDhw4YLCtSqXC7NmzMWnSJCiV2n4y58+fR2pqKtasWWP32pYsWYIZM2bg8ccfR1JSEpYuXYq4uDh8+OGHAIDY2FidSFdubi6io6Ot/n8SBOEGdCJfemlHuRcgaA6b5PuyD/1Il9LwwpggbnVsFl+zZs3C/v378dlnn2HPnj2Qydgu2rVr5xbPl1KpxLfffovq6mqkpKQY/F4mkyE9PR2ZmZl47LHHoFKpkJWVhaFDh2Ls2LGYP3++Xa9bX1+PjIwMMfLHGTFiBPbt2wcA6N+/P06dOoW8vDxUVlYiPT0dI0eONLnPDz74AF26dEG/fv3sWhNBEE7AnPgSBMDLn92nyJd96Ee6KH1L3IYoLG9iSHJyMpKTkwEw8XPy5EkMHDgQLVq0cOrizHHy5EmkpKSgtrYWgYGB2LBhA7p06WJ025iYGGzfvh133303Jk2ahP3792PYsGFYsWKF3a9fXFwMpVKJqKgoncejoqLEVKZCocDixYuRmpoKlUqF+fPnIzw83OQ+Z8+ejdmzZ6OiogIhISF2r40gCAcQxZdg6PkCAIUvUF9FkS97MYh8kfgibj/sSjt++umnAJjwGjx4MPr06YO4uDj88ccfzl6fSTp16oRjx47hwIEDePrppzF16lScPn3a5Pbx8fFYs2YN1q5dC4VCgU8//dQp/iv9fajVap3Hxo4di/Pnz+PixYt48sknHX49giCaGFOjhThe1OvLIQw8X5R2JG4/bBZf33//PXr27AkA+Pnnn5GdnY2zZ8+KxnNX4e3tjcTERCQnJ2PRokXo2bMn/vvf/5rcvrCwEE8++STS0tJQU1ODuXPnOvT6ERERkMvlBob9oqIig2gYQRDNCFNDtTkK6vXlEAbVjhT5Im4/bBZfxcXFaNWqFQAgPT0dDz/8MDp27IgZM2bg5MmTTl+gtajVatTVGf8SFxcXY9iwYUhKSsL69euxfft2rFu3Di+88ILdr+ft7Y2+fftiy5YtOo9v2bIFAwcOtHu/BEG4GR750q905PB2ExT5sg/q80UQtnu+oqKicPr0aURHR2PTpk1Yvnw5AKCmpgZyuRF/hAWqqqpw8eJF8efs7GwcO3YMYWFhiI+Px7Jly7BhwwZs27ZN3Ob//u//MHr0aMTFxaGyshLffvst/vjjD2zatMlg/yqVCqNGjUJCQoKYckxKSsLWrVuRmpqK2NhYk1EwS2ubN28epkyZguTkZKSkpGDlypXIycnBzJkzbX4fCILwEPhQbWN+L0DbboIiX/Zh0OGexBdx+2Gz+Jo+fTomTJiA6OhoCIKA4cOHAwAOHjyIzp0727yAI0eOIDU1Vfx53rx5AICpU6di1apVKC4uRlZWls5zCgsLMWXKFBQUFCAkJAQ9evTApk2bxLVIkclkWLRoEQYNGgRvb2/x8e7du2Pr1q1mDfCW1jZx4kSUlJRgwYIFKCgoQLdu3ZCeno6EhASb3weCIDwEU3MdOWLki8SXXeiLLUo7ErchgtpYJ1ALfP/997h69SoefvhhtG7dGgCwevVqhIaG4v7773f6Im83eLVjeXk5goOD3b0cgri9KDgOfHQ3EBQD/O2M4e+/mgBc2AyMXQb0meL69TV3Mr8Cfpyl/Xn0O8CAp9y3HoJwItaev+1qNfHQQw8ZPDZ16lR7dkUQBOFZWKx2pMiXQxhUO1Lakbj9sNlwDwA7d+5EWloaEhMT0aFDB4wdO1ZnpiFBEESzRcnFlyXPFxnu7UK/zxelHYnbEJvF15dffol77rkH/v7+eO655/DMM8/Az88Pw4YNw9dff90UayQIgnAdVlc7UuTLLgyqHanPF3H7YXPa8V//+hfeeecdnQrB559/HkuWLMGbb76JSZMmOXWBBEEQLsVS2pEiX45Bg7UJwvbI16VLl5CWlmbw+NixY5Gdne2URREEQbgNsdrRRNqRR75IfNmHQdqRPF/E7YfN4isuLk6n5xZn27ZtiIuLc8qiCIIg3IbY58tE2lFB44Ucggz3BGF72vFvf/sbnnvuORw7dgwDBw6EIAjYs2cPVq1aZXa8D0EQRLPA2mpHarJqHzRYmyBsF19PP/00WrVqhcWLF2PdunUAgKSkJKxdu5Z6fBEE0fyxONuRIl8OwcWWVwDQUE1pR+K2xK4+X+PGjcO4ceOcvRaCIAj3I1Y7UuSrSeBiyyeQiS9KOxK3IXb1+SIIgrhlET1fFPlqEnjkyydI8zOJL+L2w6rIV4sWLSAIglU7vHHjhkMLIgiCcCvWznakyJd9NOqJL2qyStyGWCW+li5d2sTLIAiC8BBEwz1VOzYJPNLlHaj7M0HcRlglvmhuI0EQtw0qC+OFKPLlGGLkSzN0mMQXcRtCni+CIAgpSis73NN4IfvgYovSjsRtDIkvgiAIKVb3+aK0o12IkS+edqTZjsTtB4kvgiAIKZYGaytosLZDGFQ7UuSLuP0g8UUQBCHF4mxHGqztEI2UdiQIEl8EQRBSLPb50kS+1EpKmdkDj3R588gXvYfE7YdV1Y7jx4+3eofr16+3ezEEQRBux1KrCR75Alj0y1R6kjCOfuSL0o7EbYhVka+QkBDxX3BwMLZt24YjR46Iv8/IyMC2bdsQEhLSZAslCIJwCRZnO/pq75Pvy3YMPF8U+SJuP6yKfH3++efi/ZdeegkTJkzAihUrIJczT4RSqcSsWbMQHBzcNKskCIJwFZb6fAkCE2CNteT7sgfpbEeAPF/EbYnNnq/PPvsML7zwgii8AEAul2PevHn47LPPnLo4giAIl8M9X+bSiVTxaD/Gqh3VavethyDcgM3iq7GxEWfOnDF4/MyZM1CpVE5ZFEEQhNuwNNsRoIpHe1GrJeOFgrSP82ijq9dCEG7CqrSjlOnTp+Ovf/0rLl68iDvuuAMAcODAAfz73//G9OnTnb5AgiAIl2KpySpAkS97kY4S8pGIr8Y61xYunPwe2Px/wIQvgPgBrntdgtBgs/h699130apVK7z33nsoKCgAAERHR2P+/Pn429/+5vQFEgRBuBRrxBdFvuxDR3wFGn/cFVzYAlQVAtk7SXwRbsFm8SWTyTB//nzMnz8fFRUVAEBGe4Igbh0szXYEKPJlL40SkeXlDwgyQK1yvfhqqNHckngm3INdTVYbGxuxdetWfPPNNxAEAQCQn5+Pqqoqpy6OIAjC5VgV+fJnt3Tytg1uthfkrJpU7s1+dnXFIxdfJJ4JN2Fz5OvKlSsYNWoUcnJyUFdXh+HDhyMoKAjvvPMOamtrsWLFiqZYJ0EQhGuwNNsR0A7XppO3bXCRpfBht3If9h66PPKlEc1chBGEi7E58vX8888jOTkZpaWl8PPTdnoeN24ctm3b5tTFEQRBuBxLfb4AbdrREyNfteXAwY+AykJ3r8QQLrJ4xEvhrfu4qxDTjiSeCfdgc+Rrz5492Lt3L7y9vXUeT0hIQF5entMWRhAE4RZsMdx7YuQr80tWyVd6BRj1lrtXo4tB5MtNacd6Lr4o8kW4B5sjXyqVCkql0uDx3NxcBAUFGXkGQRBEM8LSbEfAsyNfVUWaW0+OfOmJL3elHT1RPBO3BTaLr+HDh2Pp0qXiz4IgoKqqCq+99hrGjBnjzLXdEvzyyy/o1KkTOnTogE8++cTdyyEIwhKWZjsCnh354sKivtq96zCGGPniaUeNCHO5+NK8N54ononbApvTju+99x5SU1PRpUsX1NbWYtKkSbhw4QIiIiLwzTffNMUamy2NjY2YN28eduzYgeDgYPTp0wfjx49HWFiYu5dGEIQp+Hih5ur54sKi3gOrz3m1oxj50kQXG91luPfAz4+4LbBZfMXExODYsWP45ptvcPToUahUKsyYMQOTJ0/WMeATwKFDh9C1a1fExsYCAMaMGYPNmzfjkUcecfPKCIIwiVXVjh4c+eJ+Jk8UX1xk8cgXF2FKF3q+1Grq80W4Hbv6fPn5+eGvf/0rli1bhuXLl+Pxxx+3W3jt2rULaWlpiImJgSAI2Lhxo9ntFy1ahH79+iEoKAiRkZF44IEHcO7cObte2xnrWr58Odq2bQtfX1/07dsXu3fvFn+Xn58vCi8AaN26NRUlEISnY81sRzHy5YHiy5PTjvqRL3ekHaWCq5HEF+EebBZfcrkcqampuHHjhs7jhYWFkMvNhOlNUF1djZ49e2LZsmVWbb9z507Mnj0bBw4cwJYtW9DY2IgRI0agutr0gWbv3r1oaGgwePzs2bO4du2a3etau3Yt5syZg1deeQWZmZkYNGgQRo8ejZycHACA2sjgVt6UliAID8WmakcPPHnztGNdc4h8uSHtKBVfFPki3ITN4kutVqOurg7Jyck4deqUwe9sZfTo0Vi4cCHGjx9v1fabNm3CtGnT0LVrV/Ts2ROff/45cnJykJGRYXR7lUqF2bNnY9KkSTpVmufPn0dqairWrFlj97qWLFmCGTNm4PHHH0dSUhKWLl2KuLg4fPjhhwCA2NhYnUhXbm4uoqOjrfp/EgThJkTPF0W+nI6B58sdkS9JewkSX4SbsFl8CYKAH374AWlpaRg4cCB+/PFHnd+5mvLycgAwaWKXyWRIT09HZmYmHnvsMahUKmRlZWHo0KEYO3Ys5s+fb9fr1tfXIyMjAyNGjNB5fMSIEdi3bx8AoH///jh16hTy8vJQWVmJ9PR0jBw50uQ+P/jgA3Tp0gX9+vWza00EQTgBm6odPfDkLXq+Kpm/yZMw6POliXy50vNF4ovwAOyKfMnlcvz3v//Fu+++i4kTJ2LhwoV2Rb0cRa1WY968ebjrrrvQrVs3k9vFxMRg+/bt2Lt3LyZNmoShQ4di2LBhDo1CKi4uhlKpRFRUlM7jUVFRYipToVBg8eLFSE1NRe/evfHiiy8iPDzc5D5nz56N06dP4/Dhw3aviyAIB7Em7ejRkS9NxEut8ryCAIMO9xoR5tK0o0R8KesAlcp1r00QGmyudpTy5JNPomPHjnjooYewc+dOZ63Jap555hmcOHECe/bssbhtfHw81qxZg8GDB6Ndu3b49NNPnRKp09+HWq3WeWzs2LEYO3asw69DEISLsKna0QMjJ9JoTl2Vdq2egLHZjoD7DPcA+wy9A1z3+gQBOyJfCQkJOsb6IUOG4MCBA8jNzXXqwizx7LPP4qeffsKOHTvQunVri9sXFhbiySefRFpaGmpqajB37lyHXj8iIgJyudzAsF9UVGQQDSMIohlh02xHD4ssAdq0I+B57Sb0I19i2tGF4qteb6SQJ36GxC2PzeIrOzvbIHWWmJiIzMxMXLp0yWkLM4VarcYzzzyD9evXY/v27Wjbtq3F5xQXF2PYsGFISkoSn7du3Tq88MILdq/D29sbffv2xZYtW3Qe37JlCwYOHGj3fgmCcDO2VDt62mxAaQ8rwPNM9/qRLzHt6CbPl7GfCcIFOJR2lOLr64uEhASbn1dVVYWLFy+KP2dnZ+PYsWMICwtDfHw8li1bhg0bNmDbtm0AmC/q66+/xo8//oigoCAx8hQSEmK015hKpcKoUaOQkJCAtWvXQqFQICkpCVu3bkVqaipiY2ONRsEsrQsA5s2bhylTpiA5ORkpKSlYuXIlcnJyMHPmTJvfB4IgPARbZjt6oqdKLZm963GRL17t6K17665qR8DzPkPitsAq8RUWFobz588jIiICLVq0MOuV0u//ZYkjR44gNTVV/HnevHkAgKlTp2LVqlUoLi5GVlaW+HvexmHIkCE6+/n8888xbdo0g/3LZDIsWrQIgwYNgre3t/h49+7dsXXrVpMGeEvrAoCJEyeipKQECxYsQEFBAbp164b09HS7RChBEB6C0pbIl4eduPUjXZ4mvsQ+X24crE2RL8IDsEp8vffeewgKCgIAnaHazmDIkCFmKyVff/11vP766+LP9lRVDh8+3OjjvXr1sntdnFmzZmHWrFk2r4kgCA/FFs+Xpxnu9c3kntZo1VSHe5emHfXeI08T0MRtgVXia+rUqUbvEwRB3HLYUu2orGdNWc0JNVeiH8XxOM+Xfod7HvkynEDSZBgY7inyRbgeq8RXRUWF1TsMDg62ezEEQRBux5bZjgDzDHlKqwID8eVpkS/9akcuvtxouCfPF+EGrBJfoaGhFnti8f5W0hE+BEEQzQqVijUnBazzfAEsbeUp4ks/quNx4kvPcO8RaUeKfBGuxyrxtWPHjqZeB0EQhPuRVgqaE18yOauGVDV4lu+rQS/N6GmeL5OGexemHfXfI/J8EW7AKvE1ePDgpl4HQRCE+5GKAHPiC2DRr7oGzzp560d1PM3zZTBY2x1pR4p8Ee7H7j5fNTU1yMnJQX29bolwjx49HF4UQRCEW+Bme8Cy+FL4AnUVnhX5Mkg7epj40jfc81tXznbUf4/I80W4AZvF1/Xr1zF9+nT89ttvRn9Pni+CIJotUvFlrtoRALw8cMSQgeG+0j3rMIVB5Msdsx0175GXP7vvSZ8fcdtg83ihOXPmoLS0FAcOHICfnx82bdqE1atXo0OHDvjpp5+aYo0EQRCuQSq+BAuHR4UHDtdutq0m3JB29Nc02Ka0I+EGbI58bd++HT/++CP69esHmUyGhIQEDB8+HMHBwVi0aBHuvffeplgnQRBE0yOd62ihwtsjI188peYbCtSWeZ7h3qDJqhsN9/5hQPlVSjsSbsHmyFd1dTUiIyMBsLFD169fB8DG9Rw9etS5qyMIgnAl1sx15Hhy5CuQHaM9L/KlN1ibR77c0WqCIl+EG7FZfHXq1Annzp0DwMbzfPTRR8jLy8OKFSsQHR3t9AUSBEG4DKUVDVY5nhj5EsVXFLv1OM+XfpNVd3i+9MWXB31+xG2DzWnHOXPmoKCgAADw2muvYeTIkfjqq6/g7e0tDpwmCIJolqg0BUPWjAvy5MhXQEt26+mRLzHt6MpqR8174hfGbinyRbgBm8XX5MmTxfu9e/fG5cuXcfbsWcTHxyMiIsKpiyMIgnAp1sx15Hhi5KteL+3ocZ4vE+OF3Jl2JM8X4Qbs7vPF8ff3R58+fZyxFoIgCPdizVxHTnOIfDXe9KzB36Y8X66KfKmUWtO/P498edDnR9w22Cy+1Go1vv/+e+zYsQNFRUVQqVQ6v1+/fr3TFkcQBOFSpNWOlvDEyJe+4R5gaTbfYPesR4pKpRW3YrWjiz1f0hSj6Pki8UW4HpsN988//zymTJmC7OxsBAYGIiQkROcfQRBEs0X0fFkjvvzZrSdFvnja0S8MEDTRLk8Zri0VWPp9vlSNTJw1NaLQEgC/UL3HCMJ12Bz5+vLLL7F+/XqMGTOmKdZDEAThPmypdlR4YuRLIyS8/QHvQKCu3HNM99JGqvqzHfnvZX5Nuwb+Xnj5e6Z4Jm4bbI58hYSEoF27dk2xFoIgCPdiT9rRk07eDRJx4RPI7td5SLsJ6fxGLrp42hFwTeqRi1MvP/ZP+hhBuBCbxdfrr7+ON954Azdv0h8sQRC3GGK1ow2Ge0+KfNVL5hZ6B2ge87DIl8wLkMm09zmuGK4tjQwqSHwR7sPmtOPDDz+Mb775BpGRkWjTpg28vHRLsqnLPUEQzZZmH/nikR2p+PIQz5d+pSPARJjMixnxXTHfURoZpMgX4UZsFl/Tpk1DRkYGHn30UURFRUGwNP+MIAiiuWCL+PLEyBcXF9zzBXhQ5EuvxxdH4QPUN7gv7aisY2Z/mc2JIIKwG5vF16+//orNmzfjrrvuaor1EARBuA9bZjuKkS8PEV/KBu36vaTiy4MjX4C2oa1L0o48LRugFV8Ai17ySCFBuACbpX5cXByCgz2gZwxBEISzEasdbRgv5ClpK2mES8dw7yHiS4x86Qlbcb6jC9KOoifOT/v5AZ4VvSRuC2wWX4sXL8b8+fNx+fLlJlgOQRCEG7Gpz5eHRb54VEemYH20PM5wz8WXfuSLd7lvaPo18PfI25+lGflaaL4j4WJsTjs++uijqKmpQfv27eHv729guL9x44bTFkcQBOFSbJnt6GmRL6nZHpCkHT2l1YSJtKPChfMdGyTVoAAT0Mo6zxHQxG2DzeJr6dKlTbAMgiAID8CW2Y6eFvmSNhAFmo/hXu7CEUNSwz3A3qvacop8ES7HJvHV0NCAP/74A6+++io1WiUI4tZDNNw3Q8+XtIcV4HmeL0uGe5eIL73IlydOKSBuC2zyfHl5eWHDhg1NtRaCIAj3Inq+mmG1Y4N+5MtTPV9GWk0Arkk71uunHTW3FPkiXIzNhvtx48Zh48aNTbAUgiAIN2PTbEdJ5Eutbro1WYu+sPAO0jzu4Z4v0XDvjrSjhwlo4rbBZs9XYmIi3nzzTezbtw99+/ZFQIBub5TnnnvOaYsjCIJwKfZ0uIeaCQd9UeFq9IWFx0W+NOLLwPPlSvHFqx017w1Fvgg3YbP4+uSTTxAaGoqMjAxkZGTo/E4QBBJfBEE0X+yZ7Qgw4eN28cW72wfo3nqK+OJNVA2qHV2YdmyQ9PkCyPNFuA2bxVd2dnZTrIMgCML92NLnS+4FCDJArfKMtJV+qwlPM9yLkS8P6PMler40IsyT5nMStwUODbNSq9VQe4LXgSAIwhnY0mpCEDyr4lFsNcHTjp42XohHvkylHd1huPegz4+4rbBLfK1Zswbdu3eHn58f/Pz80KNHD3zxxRfOXhtBEIRrsWW2I+BZhm19P5NUfHnCRbKpyJdLm6zq+eIo7Ui4CZvF15IlS/D0009jzJgxWLduHdauXYtRo0Zh5syZeO+995pijc2aX375BZ06dUKHDh3wySefuHs5BEGYw5Y+X4Ak8uUBhm1ThntVo2vM7JYQqx1NNVl15XghMtwT7sVmz9f777+PDz/8EI899pj42P3334+uXbvi9ddfx9y5c526wOZMY2Mj5s2bhx07diA4OBh9+vTB+PHjERYW5u6lEQRhDKUN1Y6ANvLlCZETMe2oF/kCmO/L3QUBFmc7usFw70mRy1uFojPsMw1v7+6VeDQ2R74KCgowcOBAg8cHDhyIgoICpyzqVuHQoUPo2rUrYmNjERQUhDFjxmDz5s3uXhbhKajVQJ2H9GAiGLbMdgS0kS9PMGxLh0YDrGKTp9U8wfdlcbajK/t8UZPVJqG+Bvh4GPDpcG3xCmEUm8VXYmIi1q1bZ/D42rVr0aFDB5sXsGvXLqSlpSEmJgaCIFjVwNWe59iDNa+zfPlytG3bFr6+vujbty92794t/i4/Px+xsbHiz61bt0ZeXl6TrNXtVOSTadVWfnoWeKcdUJLl7pUQHFv6fAGeFfnSTzsCnmW6Nznb0Q19vmi8UNNQXcRantSUADfL3L0aj8Zm8fXGG2/gn//8J0aNGoU333wTCxcuxKhRo/DGG29gwYIFNi+guroaPXv2xLJly5rsOXv37kVDg6Gf4OzZs7h27Zrdr7N27VrMmTMHr7zyCjIzMzFo0CCMHj0aOTk5AGC0ElQQBKvW3KwozwOWdge+nujulTQvcg6wE07BMXevhOCI1Y7Wer48KG2ln3YEPKvXl8kO99zz1cRpx8Z6rbgW044e5Nm7Fagt196vKXbfOpoBNnu+HnzwQRw8eBDvvfceNm7cCLVajS5duuDQoUPo3bu3zQsYPXo0Ro8e3WTPUalUmD17Njp06IBvv/0Wcjk7qJ4/fx6pqamYO3cu5s+fb9frLFmyBDNmzMDjjz8OAFi6dCk2b96MDz/8EIsWLUJsbKxOpCs3NxcDBgyw9r/ZfLh+hh3UCv9090qaF/zgVHPDvesgtNgy2xHwrFYFzTXy5aq0o1RgiYZ7njb2APF8KyAVX9XFQMtO7luLh2Oz+AKAvn374ssvv3T2WpoEmUyG9PR03H333XjsscfwxRdfIDs7G0OHDsXYsWNNCi9L1NfXIyMjA3//+991Hh8xYgT27dsHAOjfvz9OnTqFvLw8BAcHIz09Hf/85z9N7vODDz7ABx98AKWymeXKq0vYbW0Z8zHditE9Z6NsBG6WsvskvjwHW9OOnhT5Ejvc+2sf86RGq+6e7cjFl0yh9fR5kni+FdCJfJW4bx3NALvEV3MjJiYG27dvx913341JkyZh//79GDZsGFasWGH3PouLi6FUKhEVFaXzeFRUlJjKVCgUWLx4MVJTU6FSqTB//nyEh4eb3Ofs2bMxe/ZsVFRUICQkxO61uRz+JVM1svSGT6D57Qmt8ALoIOVJ2DJYG/Csk7fYQNRD044WO9w3tfjSM9sDntUk91aA0o5WY7X4kslkFv1KgiCgsbHR4UU1BfHx8VizZg0GDx6Mdu3a4dNPP3WK/0p/H2q1WuexsWPHYuzYsQ6/jkcj/ZLdLCXxZQ3S94zEl+dgy2xHwMMiXx6edjTV4Z5HwlwV+ZKKL08Sz7cCOmlHOq6Zw2rxtWHDBpO/27dvH95//32PHjVUWFiIJ598EmlpaTh8+DDmzp2L999/3+79RUREQC6XGxj2i4qKDKJhtzxS8VBbBiDOXStpPlRLBSulHT0GW2Y7Ap518tYfrA14lviyFPlq6g739Xo9vqT3PaFVyK0ApR2txmrxdf/99xs8dvbsWbz88sv4+eefMXnyZLz55ptOXZyzKC4uxrBhw5CUlITvvvsOFy5cwJAhQ+Dj44N3333Xrn16e3ujb9++2LJlC8aNGyc+vmXLFqPv1S2NjpAoc9symhUU+fJMbJntCHh+5MujPF/ccK9XzOBqzxdFvpoOSjtajV2er/z8fLz22mtYvXo1Ro4ciWPHjqFbt252LaCqqgoXL14Uf87OzsaxY8cQFhaG+Ph4LFu2DBs2bMC2bdusfo4UlUqFUaNGISEhAWvXroVCoUBSUhK2bt2K1NRUxMbGmuzKb+l15s2bhylTpiA5ORkpKSlYuXIlcnJyMHPmTLvei2aL1DBeW+a2ZTQrpIKLDPeeg82zHT3k5K2UjBCSigtP9HwZNFl1VdpR8xl5k+erydCvdiRMYpP4Ki8vx1tvvYX3338fvXr1wrZt2zBo0CCHFnDkyBGkpqaKP8+bNw8AMHXqVKxatQrFxcXIysqy6TlSZDIZFi1ahEGDBsHbW+s16N69O7Zu3WrWAG/pdSZOnIiSkhIsWLAABQUF6NatG9LT05GQkGDju9DMkQoJqZHcHgr/ZOmH2D6O7cfTqSbx5ZGIacdm1uerQSKuPDbtaGq8kEbouqrVhLG0I4kv50BpR6uxWny98847ePvtt9GqVSt88803TkutDRkyxKxX7PXXX8frr79u03P0GT58uNHHe/Xq5dDaAGDWrFmYNWuW1Wu5JalxUtpRpQRWp7F9zNp/a/eIkb5nDdWswzbvlk64j+Za7chfX5Dp9tHyJPFlynDvqiarDUaqQfnnp6wDVCpAZnPfcUIKiS+rsVp8/f3vf4efnx8SExOxevVqrF692uh269evd9riiGaASqkb7XIk7XizVPuF3fkO8NCnDi3No9EPyd+8AXjFuGcthBabZzt6SORL2t1eWoHNPV+elHbUj3y5Ou1oLPIFMNO9NGpI2I6++KK+jyaxWnw99thjt+ZoHMIxbpYBapXuz/ZSfV17/9QPwN0vApGd7d+fJ6N/VVhTAgST+HI7Ns925IOZPSTyJRUTgFZMeJLh3iDy5eS0481S4NpJoM0g3RO/KFCNeL4AFn0m8eUYUvHVWEt9H81gtfjS91IRBABDEeGI50snGqQGdr0DPPSZ/fvzZIyJL8L9iOLLSs+Xl4dEvnhKTWomBzwr7Wiy1YST047pLwInvwMmfw90kFhOjBnuZTL2+so6zXto2gNMWIH+xXdNMYkvE1CCm3AM/XJiR9KOPPIVFM1uT60His7Yvz9PhgtN7yB2S6Z7z8DWakdPqZYzFtUBPEd8qVTa99bkeKEG57xW4Wl2W3Ra93FjhnvAcwR0c0fZCNRXsvv8e0EXlSYh8UU4hkHkq8z+fXFBEtcfSEoDoAZ2vm3//jwVtVr7vkV0YLd0kPIMbE47esiJ29joHMBzWk1Io1omB2s7KfJVkctuy/N0HzfW5wuQCOgaEA5QV6G9H9aW3VKXe5OQ+CIcg4sG31B264zIV0BLYLBmYPmfG7VXsrcKdRXaZp68opMiX56BrdWO4onb3eLLRNrRU5qsSoWVQeRLknZ0dEpKXZXWd1ShL75MCFQvD/kMmzv8ffcKAIJasfvUaNUkJL4Ix+DRqvBEduuQ50sjvvwjgFbdgKSxuCWjX2LKMVCbYqURQ54B7/Nl7WxHMfLlbsO9iagOTzs2VLPUn7uQVjLqR76klaU88mgvFfmS+3riS0zN6qcdKfLlFLj48g0B/DXeOYrom4TEF+EYPGLDxVdtuf0HeTHyFcFuh2iiX6c33lrRL35A8g+jg5SnYWvakbeacHfUpN6C+ALcKy545Evubdh6QBoJczT1yFOOgJG0Izfc61U0ivMdKfLlEDriS3MMpy73JiHxRTgGDyuHt2e3apXWdGnzvjQCJKAlu43qCnR5gN0/tNLuJXoc/IDkH8EEGEDiy1OwdbajpwxmbjBhuPfyY41XAfea7k11t9d/zNFeX9LIV3WRbvsKU+04yPPlHIxGvkh8mYLEF+EYXDQEx2qjAPaa7qWeL07ne9ltyUXD7Zsr/IAUECE5SFHa0SOwudrRV/s8pYMpM0cw1kYBYFEmseLRjaZ7HtHS7/EFaNp6aKJhjoov/WhXpUSMmROogPujl80dqfgKoOOaJUh8EY4hptDCtaZ7e31fxsRXSGt2W37Vvn16IuJ7RuLL47B1tqN+h3R3YSrtCEgardoZkXYGpnp8AUwg8tSjw2lHPfElFWMmDfce4ttr7lDa0SZIfBGOwUuJAyIAv1B2356Kx8Z67ZeXe74AICSO3Zbnudcw7Ez4ASkgHPBrwe5T2tEzsLnaUTKP052RE1OGe8Az2k2Y6m7PkTtpxJC++JKmIU0JVE+ZUtDcobSjTZD4IhxDah4XI19lduxH8yUV5Nr9AKwaUJAzL07VNQcW6kFIo4X8IMWHaxPuxdbZjoIgme/oxpO3qVYTgGc0WjUX+QK077ez0o4BkexWasA31WTVU4ommjs6aUfNBTRdVJqExBdhPw03tT4K/whtFMeeyFe1xAclk/xZyhXamYfluYbPA5jXZvdiNs+tOSA13PuGMHEJULsJd6NWA2qedrR68po2clJbYX67psRUGwXAM8SXpciX09KOmkhXXH/dnwHTvjgx8kWGe4cwlnasLXfe5IJbDBJfhP3wqxqZF+ATpE072uP5Mub34vDUY1mO8eee+QnYtgD46TnbX9cd1EhStYIgqXgk8eVWpD2mrPV8AUBER3arP87GlYh+JiODoT2h0arFyJcTRgzVVQJ1GgHQuh+75ZEwtdp0atZTphQ0d6Tiyy8UYhEFHdeMQuKLsB8xghPORIQjaUdp5EufUO77MmG6v36O3RYcMx99KLvq3ugEp0YS+QKo15enoCO+rEw7AkB0T3abf8ypy7EJs2lHT/B88WpHS+LLgcgXj3L5hGgnR/C0Y2MtAE33fJOeL4p8OYRUfMnkkotK8n0Zg8QXYT/SCA7gYNrRisiXqbTjjUvsVq0Crh4yvk3xBeD9vsC3k2xfm7OplvjkgOYnviry3T+upinQEV82pB1jerHbguNOXY5NmDXce0CrCbHPl6m0I5/v6IDnix8fQmJZ6xtAK8ikZnryfDUN/LjvG8JuqeLRLCS+CPvh4WQuIsS0Y5nt+zIrvjTtJspMRL64+AKAK3uNb3PmZ3ZVfXm3ew8GUp+cvmhtDp6vkizgv72A76e7eyXOR5ryskV88cjXtRPuq8g122qCiy83tpqQdrg3hhj5ckB8caEVHKMVX9XX2Wtz4Sn3MUwp03gh5yCNfAHN76LSxZD4IuxHP33mSJ8vaQpTH0tpRx3xtc/4Nlnbtfcv77F9fc5CxycXzO43p15fOfuZiL247daLfvEeX4CNnq9OLHpSVwGUZjt/XdZgqpIP0Hq+PCHyZbHVhCNpR42/KziWXRDyiFZFvmmzPUDjhZyFvvgKIPFlDhJfhP1IWyYAjvX5Eru+G4t8xbNbY2nHm6W6EaO8DMN+PXVVQM4B7c+Xd9u+Pmch9bbxGXfNacTQ9bPsVq1k7/WthHSuo/78QXPIFWwUFsB8h+5A9HwZMdyLTVbdWe1owXDvjLSjVHwJgrZKuiLPdHd7QBL5oj5fdqNs1FbT8otwSjuahcQXYT/60SoxfVZmx77MpR01KYS6CsN986hXYBTrCaZqAHKP6G5zebdmZp/mhJq9y/b1OYsaIxG+5hT5KjqrvX/1oPvW0RTYOtdRSnQvdusu35dVaUcPmO1o0XDviOdLI7748YKnHsvzTM91BCSzHUl82U2dpJCJ0o5WQeKLsB99wz2/4nG24d47QPtF1k893tCkecLaAwkD2X1939fFbey223gAAlB8Hqh0U8PWar1oofR+czhI8cpSQDeaeCtg61xHKdz35Yj4yjkA/Py87RcvKqU2Xefp4sui58sZaUdNxIt7RSvyzBckUOTLcfgx3zuQRYIBSaNVinwZg8QXYT81elV7YtqxXNc/Yw3mWk0ApiseeeQrrB2QcCe7byC+trLbbg8C0T3YfXf5vvQFKwD42Zh2zM1g1Zuupq4KKJf0Wss9fOuMfAJsn+soRdpuQq227/X/+DeQsQo4/q1tz5MaxZtrqwmxyaozDPca0SVNO5qLDIqeLxJfdqPv9wIo7WgBEl+E/UgHRAO6Y4H4l9Ea6qu1JxBjkS/AdMWjKL7aasXX1cPag/iNS8wELVMAbQaxfwCQvdP69TkT/SIFQBv5sqbasaIA+HwU8Mkw295jZ1CsiXr5h7Mr3LoK4PoZ166hKbF1rqOUyC4sYlZbZroZsCW4Wd9WLx0XFhB0Z01yPKLJqrWRLzvFV22FNvXFRZe03YQ5w73YaoLEl90YFV/UPNocJL4I+9E33Cu8tR22bUk98pSjwte4YRgAQrnpXu/ExsVXeHvWWNE/nF3BcuMzTznGDQB8g4G2d7Ofs91kujdW1WnLQSovg52gasuBjNXOX585uN8rsgsQ25fdv5VSj7bOdZSi8AaiurD79qQeVUptVDf/qG3PlabUjBUKeEKfL6ubrNopvnjUyzdEKzZFz1euhbQjDdZ2GGPii9KOZiHxRdiHSqUVCzoptFB2a4tvhfugAlqarjIzlXYsyWK3Ye3Yc+NT2M889chbTLQfym7jU9gsxdJs033DmhIx7WhEfNVXWZ5td+2E9v7BFdaPY8k/Bnw+Rrflhq3wSseWnYH4O9h9a033ajX77OxNyXFqK4AfZwOXmiByKa12tAdHfF8VedrXL7lo2/fHXHd7wEM8X5aqHR2c7cg72fOUI6A13ut4vowY7r0o8uUwRiNfEi+ro9/7WxASX4R91JZphxBzzxJgX68v0Wxvwu8FGE871pZrr6patGW3ou9rH0s98srGxGGa9QUDMb3ZfXe0nNBP1QJsHAofrm0p+lUgEV8VecCfGy2/Zn0N8P1fmSDd975Ny9WBm+0jO7NIImC9+DqwHHivK3Birf2vDwCZX7J/P8427yu01XMISMSXHZ4vQCK+jtn+XP1UpS37MFfJB0g8Xx48WNtZkS+ecgS0ka+aEu3xyFzkS1l3a3kYXYk5z5eq0fUWiWYAiS/CPriI8AnWPaDa0+vLXKUjx1ijVV7pGNCSiSoAaKMRXzkHWEPQ+ip2EGjVU/u8ttz35QbxZaywQCazvtcXj3y114jJff+zfFW5bQFwQxMhvHrYPmECaP1dLTuzwcWCDCi9DFQWWn7u8W/Y7an19r02h0c0y68C5zcb36b4IvBuB+DHZ2zbtyPVjgAQrRH19pjuS6/o/pxnQ+qRpxONDdUGtGk4Zb1jhnZHsHqwtp3r028zAbDWN7yNRMlFdmtMfEl9cmS6tw9j4svLVxt1bQ6V3C6GxBdhH/p+L449vb6sEV+80WpVoTY1Ia105ER1Y4KwroIJEwBon8oEDof7vi7vdn043JjhHrCu4rG6RFtOf98SdmK5dsJ8BO/yHuDgh+y+zIuNmCk6bfu666u10ZmWSUzsRmoai1614PuqLASunWT3c/azhoz2oFaz53MOf2x8u51vs/fxzw22RTIcTTtGdWERzJpioLLAtueWXdF9bVt8X+ZSaoD2BAi4L/plKfLltLSjRHwJglaMFXPxZSztKHmM5jvahzHxBTSvBtIuhsQXYR+mxgHZ0+vLUpsJQDMuRHOQ5L4vY+JLJtf6kXiLicR7dPcVdwcTIuVXXTsORtmoTX/ov2/WVDxe03iJwtoBLdoAvSezn02lEuuqWHoOAPpM1Ub87DHJ85Sjf4TWrxbXX7M/C6lHqc+srkLXt2YLxefZQVzuDUBg++UnVU5JFnDqe3a/vkp39JQlHKl2BNhJvGVndj//mG3P5ZGvdkPYbV6m9c81190eYAUEPOL01UPAF+OAbycDG2baFmFzBIuRL0200VoPoz5i2jFW93GehuSRL2O+OJlcG3mj+Y72YVJ8UbsJU5D4IuzDWL8qQGK4t8HzZSoaJEUQDFOP0garUnizVQ4323O8/YHWyey+K1OPorAStFeEHGuuELnfq5WmV9kds9i+Lvyu23mes/U1lhYMiQNGLGSiE3BMfHFxAVhvus/apvuzvT3W+NzOuAFAhxHs/pFPdbfZvRhQS6JdtnineDpWbqf4AoCYXprXtdF0z6OKSWMBCCySU1Vk3XPN9bDiRHRgt3kZTLSe/YWlgje/Yts67cVitaODsx3L9RqscrgBn6cTTb1HNN/RMUyJL0cqHlWqW9qDR+KLsA9TaUfRcF9m/b6sSTsChhWP3McU1lZ3O266B4BW3YHASMN98X5fTWW6v3HJMCLE3zO/FoamblF8mRGtPGLEG8WGtwc638vu71+mu+2lP4DDn7D7Y99nacJ4R8SXxu8VKRFf3HRfcNx0pZhKpY18db6P3ToqvhIGAv2fYPczv9J6nm5kaxuUxiZr12YtjqYdAfsrHnnaMaobENGR3bc2KmXJcA8A034BJn8PTFgDjPuIiXGANcp1RQsKS32+uChz1HDPC3M4IXqRMFPiSxwxRJEvu+DHe4PIlwPTO76bCrybaJ2ntBlC4ouwD/3u9pymMtwDhhWPxtKOAJuzxw+y3Jiuj9jva5fzfV8Ntaytw2cjtV4nwHx61ZqDlBj5khQPDHyW3Z5YC2x7E1j7KPB+MkstAUDyDOZ5A1i0T5CzqIqtbTaMRb5C47XzNE0JhYJj7P/kEwzcNZc9Zq/vi/u94lPY59qiDVBXDpzUpBn3LGEVuO2HAX2nal7fFvHlYNoRsE98NdZpxUNovLaHmrXNVvnQaFNpR4AJ/g7DgS73Az3/AqQ8w3yUqgbX9GqzGPnSpB3tKQioLWdeRsBI5EvvZ0uRL/J8aVGrWWsXazCZdtQc12xNO17eA5z5iR07Lm6x7bn6qNUeGUEj8UXYh7GWCYCdhnsrPF+AbtqxroqZ7wHDyJfCm0WEZAqg6zjj+2rdj6U6qgqBfBv8NdZw4luN4VqtFQaA8aHaHEuG+7oqrW+FR74AFn2KTWYRg93vAmd+BkousNRb637A8AXabb0DtM+1dSi2tMcXRxC0vi9Tpnve5Lbt3azFh0+Ifb6vshz2ucsU7DVlMiYsAWa8L8sBjn3Nfh78kjY1W3DcuLhWNgIbZwM739E+5ozIV6vuAASgMt/6tGF5LgA1EwYBEUBsH/a4tab7eguGe2MIgqTq14FB8yol84798W/z21nscO9A2lFssBpqKECD9SJhpt4jL4p8GfDLXODtNuw7Ykm8WEw72hj5kv49XT1k23P1OfAh8GYEkLXDsf04GRJfhH1YMtxbK77UahsiX7zLvcQo7xemFXxSxi4D5p7WenD08fIF4jVps4+HAp/fCxz+1HFjqEoF7JOkAP9crz35m3rPpI+ZMtwXnQagBgJb6aZRBQEY8w6QOBzoPQUY+RYwZQMw7ywwY4u2zQDHHt9XfY3WEC4VXzr7MyHmuN8r8R6WauV+PFtTj1c0Ua/ontoTbO9HWZuAaydZHzNVI9B2MPtcI5PMj/u5shc49iWw4y3tkHVxtqMD4ss7QJs2tDb6VXqZ3YYmsM8zRiO+8o5aF5U1173dHNLor73kHmbesT8Wme85Z23kyx7Dvej3ijX8nX7ky1QjWmd6vgpPO95SxV7UauCbScDyFMeGvNeWs4sZtRLY8S/g64fN9yC0FPmyRXxd2adrB3FEfKlUzJKhVjIR5kGQ+CLsw6ThXiOErE071pZpIw6WIl/StKOplCPHyxcIijK/v2Gva3xLauDKHuDXecC7HYFf/2bd2o1xfhOLPPmEsL5LZTnalJyxiQAcSwcpfiCVRr04sX2BR78H7l8GpMxmBQbB0canBdjj+yo+D0DN1hioJ5C5gM09ZHh1XFuuPXDyJrdt7fTa8f5efIIBwFLe3R7SvP5hdjt4PrtV+DABBhg/CV36Q3NHzaKFgOPVjhxbm61ycdgigd226saE480bWi+YOSxVO5qC+x4LjtnfBLPwT+39X+cBVdeNbydGvpqgwz1vM6Hv7zL2mEXPlxP6fK17DPh+umPTJOwlaxtw7ld2sfbZaODcJvv2c/pHFoUMiGTvzcWtwIpBQO4Rw22VDdrUt3S+L2BftePOt9kt94heP2NbJkVK7iFte56sbdppKh4AiS/CPkyl0GwdL8S/DD7Bpq+KOTztWJEHFF9g902JL2to3ReY8Tsw5xQw/E3mFVMrmVHd3tFDvO1D8nSg0yh2/0/NVbC5qk5L1Y48TdfKiPiyBS6+iv60/oRrLOXIadWDndBuljLRKeXSTvZ+RnTUzuZscxe7vWKj74v7vaTFFADQ/3Ht/YQ7tfsHtCLIWIpTFF9gJxrAOWlH6ete3mvd9lxg8fdI4QNEaXqoWWO6t8Zwb4yQWCA8kaWoeTGDrUh7xtWUAL/ONR6tEyNfTZh2NBb58g3VFVwW044Oiq+yHO33gIt6V8KPP74hTBB9+whw8CPb93NcM4nijqeBx7eyivKKXOCzUdrfcaS+MJ9g3d/ZWu2Yc5B9N2UKFsXnx3djog8AcjOA7f8y/bmd+kF7X9UInN5g3TpcAIkvwj54FMdU2rG+0roUgjWjhThBMayrurJe61kKb2/+OdYQGgfc+Rzw1E7tyf1cuu37yT0C5OxjUYsBM4Gu49njvNmnNWlHU9WO3GxvLPJlC0GtmFFdrdJGiywhiq9Ohr+Te2kN4vs/0D3x8j5r0qKHqG7sxFBfqe1bZomq65roG7TikRPTm0VwBBkw5GXd35kyv98s1fX5XdnLPhtxsLaD4qvTaLaeSzt0x0GZgqd0QxO0j9ni+xI73NuYdgS00S97U4+FGvGV8gw7YZ75WdfnyGnKPl/m0o6CoPu4qSkAfL6jox3upa1rzv3mWqN3wQkmXAQ58OQfQJ/H2Pf8t/nAby9ZP9miLIdlAiAAPSawSOyTf7BiDVUDsOkl3e85z3J4Bxl+d8TjmoWxaZxdGg9mz0dYJNjSGLOfnmHPMdbrUKXUpsJ5/7wT31m3DhdA4ouwnYZabadsA/ElyflbE1mx1u8FsC92kMbDwa/UHYl8GYO3bjj7i+3P5R31e0xgab/Ee9gBqSKPhb/51Z/RtCMfrl1pmHpRNmgjDI5GvgDLPi19eA+xlknGf3/nHAACcHS1tr2FWq1NuyRKxJdMrhW41vq+eNQrsothdS0A/OVr4Jkj2pQmJ7oXu9UXX9m7AaiBiE7s/VSrgLO/Oi/yFd5eK7x3/cfy9jzy1UIivkTflxXFIPZ6vgDHfF9qNYugAkCPicDdmpRv+gtaHx2HVzFykaWPQ2lHI6OFpEgfNxn50rx3jka+pO9jZQFQ4ORiHnPwdjNdx7HjYtr/gHveYI8dXAGsnWLd/+/EOnbb5i6t1cM3GBj/iSYdXqqbDjfl9wK054f6Kt1K0uoS1hBZKuJyM9gFmyAHBmmsH2JBj5Fj1Y1L2uPiwRWG/7fLe4DqImaFSfsfAIEVBumP8nITJL6agF9++QWdOnVChw4d8Mknn7h7Oc6Hp8ZkCsMvnFyhDT1bk3q0RXwB2tQjF3/OFl+dxrDby3utv1oD2IGApxl4+wcvX6CzZn9/bjAdLQQ0w7U1X0f9171+jkX7fEJY1MpRRN/XfvPbia9vJvIFAB3uAYZrDvK/vcSqiorPs8IIuY9hqpCnBq0VX1xoS/1eUnyDjUdAo7qy97SqUFcM8JRj+1R2NQ+wsnZniS8AuPsF7X6Lzpjf1lzkq+CY5YgFP+mYMpObg0e+Ck/ZXmxSWcBOvIKc/W0MmseijbVlwM/P655YeeTLYpNVO1pNcPGlb67nSCNfpnxxfL6jI60m1Gqtl5FfJJ61I4JuD+W52hTbQM1MU0EA7poDPLyKvb/nfgW+GG/+uKxWs7Y1AGtJIkXhLfFRSiK65sSXb4j2+8QvPksvA8sHAO/3Af7XC9j0MhOtfyzSvi6vYOeRr7wMw++B9L2tKQEyv9T9PX8/ktLYhQ2/ODtlJDLrBkh8OZnGxkbMmzcP27dvx9GjR/H222/jxg0bTuLNAWmDVWOmbltGDFnbZoLDG61ynC2+wtqy1JhaaXpwszH2L2cRlMTh2gMUIEk9btS2HjD2f5XJtO0m9CseRb9Xd+Pvt61w8ZWXYTnN03BTW40XaSLyBQADn2OpArWSNUc8tJI9njDQUBTY6vviZnv9yQWW8PZn0S1AN/p1SVNy3m6IVnxd2qn9W7R3sLaUyCRNt3oAu941vV19tfakxD1fAFu3lz+7yCi+YPy50n0AplNq5ghsqZ3RaWsRBE85hicyUSX3Ah5YwdpJnN8E/K83sP4p4NDH2qkDFtOONoovtVqSdmxtfJtgWyJfDrSauHGJCUG5NzDkJfaYLfaFxjr705QHV7CLhzaDWCpeStdxwJT17KI4Zx/rQVhhYvZofia7cFL4av9+pXDbwzUrxZcg6BYT1ZYDX0/UXnSXXgYOLAdWp7F+XoJMG/UCmM/UJ5h9D/Rn0p79ld1GdWe3+5dpjyfKBnbhAwDdHmS33R9mt8bS4m6AxJeTOXToELp27YrY2FgEBQVhzJgx2LzZhpN4c8BcvyoA8NN8Ca0ZMcS/hOZGC0kJlYgv3xDjbSYcxdbUY80N7VXXnc/p/q79ULbOqmssBA6Yft9MVTw6y+/FiejEBHJDjW4TWGPwSke/Fuajk4IA3LeU9RarLdemH/XnagK2+b5qy1lUBrBdfAGGvq/SK+wkKWjSnxEdWDpV1aD9vPWnD9jL3S+y2z/XG86g5PBKR98QbbEKwCLIfO2Wmq1aGqxtCbHfl43ii6cco7poH4vqAoz6N3t/S7NZz7v0F7S/d/Zg7dpybaWdycgXf1zQRrj0ET1fDkS+eMqxdT8mXAQ5Ewx8DJo5Lu8BFncCPhlme2VfbQWQsZrd51F3fdrcBUxPBwKj2Of22Qjjf5M86tX5XhZR1oc3eLY28gVoj+2VhcB301gkPSiaWQUmfgn0mqzdpvcU3Si2TK4dBSdNPVYXa3sLPvQpu3AtvQyc0RTPXPqDnX8CIrXR3aSxTBgXnQaunTK+VhdC4kuPXbt2IS0tDTExMRAEARs3bjTYZvny5Wjbti18fX3Rt29f7N6tPWjl5+cjNlZ7pdW6dWvk5eW5Yumuw1z6DLCt15fog7Iy7SgdHxLWzjmRIH24+Lq4TdvA0hR1VaysvPEmO1nyLzpH4Q10TtN9zJTQNFXx6KxKR45Mpg3nW2o5IXa2T7L8Xnv5AhO/0o00SP1e4uvLgQQrU49XD7GoSYs2pk+u5uCClYuv7J3stnWy9uTSRXOFz039zkg78tfuOJqtf/di49sYSzlyeCGDJdO9I2lHwH7fF4988cgZp98MYH4WMPkH5gNrN4R5H9sOBrwDDXYDQNt81dbIF6909Gth+v/Pjxle/qb/hp0R+eLvX9u72XeZXyyc+8388y5uBb58UFMIchT4dpJt6c+ja1jj4ohOLPJuilbdgb9uZsfNshwmwKSNR5UN2qhQj78Y34etkS9Ae1zb9HfmA/XyBx75ll34JKUBDywHXjgPPJMB3GvkeyKa7iX9vs5vYt+rVj1YynvAU+zxvf9l0VCecuz6gPZiyi9UOxP2pPuN9yS+9KiurkbPnj2xbNkyo79fu3Yt5syZg1deeQWZmZkYNGgQRo8ejZwcdgWrNlJmLTSFQLATldIJ1Tem5jpyjPX6UjYC301nPbSk75HNaUdJasbZKUdOqx7sdRpvalNUxrhZysb4XPqDpXxGv2P84N5N0mXfO1B7la2PscoglUobnXJW5AuQDMW2IL64X8mU30ufoCjgkW9YqiCqu/H2FID1vi/R72VH1AuQRL40Jwvu9+LVT4BhesWUKdweBmuiXyfWGo+AGDPbc3j66PJe8xcBjlQ7AiwCKMhYiwQuZqzBWOSL49eCeQGHvgI89iPw8lVg6k+mxY+94ou3CZGmbPXhx4kAE8crwHHPl9TvxS/AuH/UXOrx7K/AN4+wiFubQex7c2UvsP4J66oTlQ3a5qEps9mFlTnC2jIBFt2THce/GMfGkikbmTCqKWYXh+2HGn9+VFewCQ4F2p5ulsQXP7bfyGLPffATw+bXMjkQkWj8u9e6H7uVRr6434tfKPd7gvUjKzgOXPhdm5Lktg+ONPXo5pFDJL70GD16NBYuXIjx48cb/f2SJUswY8YMPP7440hKSsLSpUsRFxeHDz9kX4DY2FidSFdubi6io6PNvmZdXR0qKip0/jkbVUM99n/yN5xYkga1o3905lomAMZ7fV3exdIvhz/Rdj0H7DfcA6z3TFMgCJLU46/Gt6kqAlbdx6oYfUPZiUW/DQKn7WCtn8vUewZoRatUfJVdZle1ch9t53RnIG22aizV01gHXNiq9b2Z83vpE90TmHMSeHyL6ZOt6PvaZz5CysWZPSlHQDPuB0B5DquwuqSJfEnFV1RXXSHvrMgXwKJX7YcxL9ye9wx/z9OOxiJf8SlMlFw/A3w40HRkSuzzZaf48gvVilRrU4/KRuC6JlIYaUR86WPpApSnHVWN1p8U846ykVoAkGIi3QawNNaDn7JqPVM4Ol7o+ll2LFP4adNkvNjmyj7jxTsnv2cViMp65j18dD2r3JV7M7/Sb/MtTzg4uob13wpoySpOrSEwkgmwvtMBqNl7uPo+5hsDgO4PmW634hOk/a7w6Je1aUcAGPGm9thqLa2TAQgsrVhZyC5EeCU131dAOGutAQAbn2bHzOBYbdSM03EkE7gVuZYvPJsYEl82UF9fj4yMDIwYMULn8REjRmDfPnaF3r9/f5w6dQp5eXmorKxEeno6Ro4caXa/ixYtQkhIiPgvLi7O7Pb2cOXin+h7dRV6Ve/Bjm+XOLYzU93tOWLaUeL5kjYc3P4vycgdG8WXftqxqeBf6nO/GZrCy3JYs8HCU8xDMT1de8A1htyLhdcB8+LL2IghHrGJTHJuRCamDzvIVxUCb8Wy7tU/PsP65Xw3DXinPfDVg9roBk+BWYtfqHkPUlQ39vnVVwE/P2f8JHPsGyZuIWhTY7biG6L9Ozn+Nbuy9wpg8zA5gqA13gPO83xxeNf9Y19rzeEc6WghfUJi2ck4KIb5p1anAT89x8SqsoG1ADm1Xtubyl7xBdieeryRxSoYvQKMr91WpDMfrWm02nAT2PAUE2tdHmCCwRzdH9JOYzCGo+OFuGiNv0MrJFu0YSlZtZJFY6QcXQP88Dj7XY+/AA9+xiwKbQcB41cCENiFKheXxrj0B6suBpjXy1RE3RhefkDaUuChz1hKOGe/VtBYEnH6qUee4TAlvnjlbvIM1g/OVnxDtAI/9xDLRjTeZNmJqG7a7VJmM58dPz91HWcYCfTy0x6LeUsNN0HiywaKi4uhVCoRFaU7tiYqKgrXrrFSdoVCgcWLFyM1NRW9e/fGiy++iPBwMydcAC+//DLKy8vFf1ev2tld3Qxtk3rjz6TnAQD9z/0Hew6Z6BhsDRYN96Hsln8pVUrgjMS8nn+U5eyVjZKRO1aKL+8A7ZWUMxqsmiI+hUWibt7QvULKPwZ8OpKdfELigem/abuRm6PfDHaiMhXOBwwN98oG7QHRmSlHgB2o75rHhLKqgR1IM78Afv8Ha4tRX8lMscl/Bab9al5c2oNMpukbpGCpoyOf6f6+8E822BcAhvzdeFrOWnhUZ/9ydtvmTkPjtzT16IxqRynxd7DUnqqBvcdSzKUdAaDDcGD2AfY5AKyX2tLuwL+iWbn+99PZ43JvFpWwlzYS8ZV3lFUorn8K+PAu3VmlHD5WKDLJcqrLGnTElxWpx20LmEcvMAq47z3HvZ9i2lHSK6q+Bjj+rW4Hd1NwL6F+rzke/eIRdLUa2LEI+OlZAGqg7zTggQ91I01dxzELAwBsXwhsfV3bJ41z7RSLmqkaWGrNXOTPHN0eZM2leU+8lkmG1ZL6iEPrrYx89ZrEZs3et8T+z0ns93VIknIco7u/FglAN0nGSnpfCk89nt5o+L66ECfG128f9D1carVa57GxY8di7FgjZbom8PHxgY+PhdE6TqD3hFdwefFWtKk+Dt9fn8HF+E1IbBWqu1HNDebz8Q9n4WnfUHZwvZHNjKEXt2l9UJY8XzydlHuYVfr5hAB9prCS4O3/0jSSVAMQjDfPNMXIt1j/o1gnCwIpcgUzSx//mgnHNnexdhEbZrKrrpadWZrAVGNHfaJ7An/PMd89nb8HJVnsoHv0C1YlCWibbjqT1JeZsCnLYV6JayfYZx/Rkc1Vi+ntnBOrKVr3Be55nQm+TS+zFEGrbuxgvnYKe5/bD9M277SX6J5MUFZq/EzSlCMnpjcT0+U5zk07cvpOZ16ezK/Y/4e/r6Vm0o4c3xAmMLo9xKKEJZoqNe9A9ncYmcSu5m2JfOgTfwf7f5fnAB+n6v5uRxYblyXtkcXL/o35vexBKr4snRCzd7H2BAAwdpltxw5T6DdZVauBjTPZhUHicGDyd6aFg0qlTY+3Haz7u05jWKPdi9tYcc5vL7GB7gBrqTD0VeP7HfAku8jd+TZLV1/6g12sRCSy0WdfPcRSawl3AeNWOPY9DW/Pxqyd+ZldZFkSSAaRLwviC2BNpx0hbgCQ8TmL0PG5vsbSl3fOYZ9ZREfTx8y2d7MLy/BEdl6SZlNcCIkvG4iIiIBcLhejXJyioiKDaJhHIpMjZtpq3FyegmScwYefvYaWc99FiJ/mSv/UeuCXObqd6WWapqn6vadCE0z7cPT7fPGUY6dR7ICTsRooPKmNdviH2Zbq6TmR/WtqOt/LxNfZX5mg/OMt9njicFbebO5gYwxLY2u4mM07wv4BLCLYZ6phw0NnIQjsirFFgrbqz5XcMZudTC/8zqI4T+wAfpzNIovBrYHxHzsuAHnki2NMfAkC0OsRdrIzZ962l6T72MVHeQ6LkrRPZWn5Os13TeplNEWbO4GZe9lJL6gVe3+cJY59AoGOo1i7Dd9QdhKOTdakSnNY+l2a2jNV6WgvMhk71qgazUe+asuBDU+z+32nAR1HmN7WFrz0Il/Hvtaa+S9uYQUTpr6DhSfZsc47SBtB4sT0Zmnjynxg5WAmnAUZq+rj0UxTpP4fi6r/9Bzrv/XRIHaxcuQzZnhvmQT85SvLM3GtQeFjOXXL4e0mSrKYoLRGfDkKj3zxkWi+ocaLcFp1A2YfZL83JSJlcuDZDNsH0TsZSjvagLe3N/r27YstW7boPL5lyxYMHGinIdjFeLdsi8YRTET8te5LvL16PZQ3K9gB7fvp7IsUEKkVUKpGJrxkClaNM+w14KndwHPHTJf+i4b7UnYFyZvdJaUxoZUyi/3MDcjWphxdTfuhzEBbnqMVXnfMBiatbZoDjdTD1vZu1pl67mlg2Kv293DydGQy1pgzKJqlkVYOYWJd5gVMWGO+Qs1aWknEV0BL0wbxu18Ent4H9H7U8dfUx8sP6KFJd/DUIzfbB7S0/kTg5ctORKHxzo9KPvQ5+3t76TLw6A8sMsovcvRL881VOtqLQvM3/tlIIP1FlnJvrGfFLad/Aja/Anw6gpmlW7QBRvzLea/NI1+NN1lk5TdNtJUL901/1zZJ1of7vRIGGl5gCQKb9Qkw4eXlD/zlG8vCi9PlfvY32fZuVgzw23xtn6xHv9ftDecqAluy14eapZ9dIb7C2uka9zuONH0xG9bOcjTUzcILoMiXAVVVVbh4Udt8Ljs7G8eOHUNYWBji4+Mxb948TJkyBcnJyUhJScHKlSuRk5ODmTNnunHVthF0x3RUnPkFwTnbMC3/DZQvfQNhdXma7sIvMIOw3Isd+GqKmQcpNMF40z1jSPt8XTvJTjIKP+2A5Ttmscoa/qX1VPHl7c/6VJ39hYnPe5cAfac23eu17AQ8vp0dUJvSz+ZpBISz8vPVaazdAQCMWsTSks7af0gcG3fUboiZdgde1vn37KX3FGaiPvMLS++b6/HlDhTehmn07g9r0mZb2Zr9w1i0Q5x64ETxdcdM5i8rv8omJBxayap89Q34Cj9g3EcsWucsuOerrop53eqrmE9vygbgk3tYtDH9RWDCasPniv29Bhn+DmDeoyOfMvEweZ3txSshscCUH5ldY9sCJuAmf++2dBkA5vuqLGDviyvElyCw1OM5jXfO1opJD4TElx5HjhxBaqrW8zBv3jwAwNSpU7Fq1SpMnDgRJSUlWLBgAQoKCtCtWzekp6cjIcFDDqDWIAgIfvhD1L3fHx3r84A6oMKnFYInfa6bSlR4s+iWrc0tpX2+eMqxwz3aJoh+oaw6Z/tC9rO1Pb7cweD57Is/4GmW9mlqnCU4mhtt7gJSXwG2v8nGFPV73Pn7P/6NtveSO4juyXqfFZ5kkSSeXnOkmKCpadlJu+bTPzLvF5/1GRDp3O/u0H+wIpDsnaw31rlNmqkQAhN58QPYUPi2dzvuIdKHR76qi7T+1HErWDru/mXAylRm0D7zs7ZaDmBFQ7wXnamK3DZ3scKc8ETmo7UHmYxNz+j+MEub2bsfZ9GqO3BhM5u+wNtzNHUULq4/E19yH+2FfDOGxJceQ4YMMdooVcqsWbMwa9YsF62oiQiKgs+DH6H+uxn4ta4nXiufhmevtMITzjgP8C9hQ42207B+l/cBM1n12c0bnhv5AtgJc+KXlrcjHOfuF5jwCo5x/uSCUYtY1ZX+BAJXIgis4OS3+ayYgvda85TIlym6P6QRjN8z8VXYBClHjrc/S9N1Gs2M7CUXWEVjU5/Y9YsV7l2s9f5F9wTufB7Ys4Q1iW5zF4vu37jEjm/1lexnPmPQGPb2qdPH2aLTXrjpXtoXzsfKzIi9dL6XDd/uMdG5UU83QeLrdqbTKHi/kov8P7JQsfkc/pV+BgE+Ckwa4KDh2CcEgABAzYzTMgXL0etsE8Qa7v36N+MGaOL2xNrqUVvxa2F/rzBn0v1hVt3JTdpA0xj8nUm3B4Gtr7FqzfI8baWjs8z2ppDJrJ+s4CjSHmndH9b68ziDX2JRr5ILwJr7maWCtwkBWAFFU1YGexq83URFLrv1CXZ+fzx9IjoAL11xbr9DN3Ib/bUQRhEEzBrSHjMHM4/RKxtP4sdjDs6ilMl08/9tBxu/cu39KPB/+bdE/p4grMI/jLXxAJi3CfDstCPAKjHjBwJQsykVTRn5chd+LVgqLbIrMMZIY1MvX5Z+hMDaspRdYUUhbTQViGNMzO68VWnRRnORraEp/V5SvHybXuS5CIp8ERAEAS+N6oTqukZ8ceAK/rbuOLrFhqB9SwdCu36h2iv7pDTT290iXySCsJo+U5iI4Xh62hEAuj8I5OxjXcErNBdnzjTbuxuZnFVxq5Smq+ji72ANUa+dZOb6NoNuifSXXQgCE6tXNP3NXCW+biEo8kUAYALsjbFdcVdiBBpVanx1IMexHfKKRwgU2SIIKW2HsOpLAIAgue/BdBnH7APXTmgmMAimh6Y3VwTBci++Xo8Ao95inrTbVXhxpFM3SHzZDIkvQkQmEzBjUFsAwPcZV3GzXmn/zniaMT7F/ZU5BOFJyGRAr8nsfnCM4agjTyQgXHc0Vlg7bfUycXvSisSXI5D4InQY3KElWrfwQ0VtI345kW//jnjDUFPztQjidqbfDNbvydpmm55Ad4kJ/VbyexH20UpS3Uniy2ZIfBE6yGSCWO341UEHUo+p/wAmfsUm2Xso+WU38dXBK6htcCDCRxD2EBgJPLGdtddoLnQao+1C39SVjgQAQKky3/bIrbTsxHpuASS+7IDEF2HAhOQ4eMkFHLtahlN55ZafYIyAcDbPzoPLr9/dfA6vbDiFn445EOFrxiz5/Rz+uuowiU/COnwCgT6PARCADsPdvZpbnm8O5aDba5ux92Kxu5diHLkXG+oOkPiyA889MxJuIyLQB6O6sWZ+DkW/moh//3YWj6w84JgnDUBuKRuie/F6lTOW1axQqdT4aNclbD9bhAOXSty9HKK5MGoRMP8SG7xNNClbThfiZoMSm05dc/dSTMNHKoUnuncdzRASX4RRJmtSjz8ey0NlbYObV6Olqq4RH+++hP2XSnDo8g2H9lVczWbG5ZbWOGNpzYrrVXWoa1QBADJzyty7GKL5IJNbHlrsgew4V4QzBRXuXoZNXL3Bjkun8u3MPriC1H+w9Hm3h9y9kmYHiS/CKAPahiExMhA19Ups9KC03OHLN0QfxFkHD6Y3qtlsvas3bjq8ruYGP7ADQObVMvcthCCamKs3ajD988N4Ys0Rdy/FatRqNXI039EzBRVoVKrcvCITePmywhEPtpd4KvSOEUYRBEGMfn114IrFeZeu4kCWNkV29lql3ftpUKpQVsMieldtjHzVNSqbvU8qRyK+juWUQuXJxl4X0uCpJznCbq6UsL/13NKbzeZ7e71SG5mubVDhUnG1m1dEOBsSX4RJxvduDV8vGc5eq8R3R3LxxYEr+PsPJ5D2/h4MX7LTfjO+A+yTiC9H0gilNfXi/bKaBqtTq0qVGmPf34sR7+1qNgdyY0jFV0VtIx3cAaw9nIOO//gNm04VuHsphBMprKgV7xeU15rZ0nPQvyB0x7GWaFpIfBEmCfH3QlqPGADA/B9O4NWNp/Dt4as4mVeOC0VVmPLpQZwvtD/6ZCvlNxvwp8T/kHW9yu5IBU85cqxNPZ4pqMC5wkrk3KjB0Suldr22JyAVXwCQmdN8/y/OYv3RPKjVwPvbL3pMpJdwnMJKifgqax4WA/3v56m85uVXawryym4iZdE2LP79nLuX4hRIfBFmefLudgjx80JEoA+GdGqJ2antsWxSb/RoHYLSmgZM+vggLrmoWvBQ9g2o1EDbiAAE+SjQoFTj0nX7IjYlVbriy1rT/cFsrcnf1irBgvKbNns3cktr8MWBK6hvdG46jHu+YkNZ36ajt7npvr5RhWMa79uf+RU4nkuRhluFooo68X5ecxFfJWyd/t5s9u2fnmy6dxG/nSxAQXkt1h/Nc/dSnAKJL8IsHaKCcOyfw3HkH/dg1fT+eHFkZ9zXIwZr/tofnVsFobiqDpM/Oahj4G4q9mWxfjcp7cPRqVUQAODsNfuuCEv0I1+l1h2UD0oE14FL1ldbHs0pRcqi7XhlwymrnwMAb6WfwasbT+F/2y7Y9DxL8Ejf2F4ssnm7R75O5ZeLHhuA+RyJWwNp2jG/rHmlHYd2ZqPZTudX3Pa+zCOX2TEqr+wmqusa3bwaxyHxRVhEEASDx0L9vfHl4wOQGBmIgvJaPPLxAeQ38VXlfo3fa2D7cHSOZuLrTIF9ac+Sqjqdn60RjyqVWqe9xbGrZVb3GtunaZR4+Ipt7TFOaCIwq/ZdRnmNc1p+1DYocU1zQhrbk4mv84WVqLoFDmj2ckTzubZuwSKBP5/Id9r7TbgXXc9XM4l8aY5HqZ0i4a2QobKu0SAVeTuhVqtxRGLzsDfj4UmQ+CLsJiLQB189PgAJ4f7ILb2J577JbLLXulFdL1Y33tEuHJ1bBQOwP/LFPV/eCvYVsCbteL6oEmU1DfDzkiMq2Af1SpXVEaMzmrXn3rhp9ciQqrpGsRFsVV0jPt2bbdXzLMH3GeijQOdWQYgN9YNKDZzILXPK/psjhzVX1VPuSEDnVkGobVBhfWaum1dFOIPCZph25BeDbVsGIEkT5ffofl9NTM6NGhRLLpgvXned17ipIPFFOERUsC++nDEAggAcuVLaZFeW3F/VMSoQEYE+SNJEvs7aGfkq1ni+usUwEZdrRdrxoCbNmNymBQa2jwAA7LfS98V7ktUrVVa/R+c0go0HHj/fm43ym45HY/iBvXULPwiCgF7xoQDc32xVrVbjUPYNs1WkarUav/95DUWVzksfqdVqMfLVr20YJt+RAIBNd3CW8b5BqXLqmj2JS9erPPb/plarddbW1NF5Z1DXqI1Mx4f5o2ssG91zO5vuecqRc6Gw+U8lIfFFOExcmD96x4UCAHacvd4kr6FNOTLR0zGKia9rFbUoq6k3+TxT3NB0t++pWffVGzUWT7QHs9kaBrQNwx3tWJdva0z3tQ1KZEtaOeSUWJc+4OLrrsQIdIgMRGVtI1bvu2zVc83B0xfxYf4AIH527hZfq/ZdxoSP9putZvrlRAGe/CID/7DRO2eOrOvVKK1pgI9Chm4xIXigVwz8veW4WFSFQ9mOTVHgzPrqKAa8tQ2vbjyFCg+aGOEo+WU3MeZ/u/HoJwfNbrdqbza+2H/ZNYuSUFrTgAal9ntdUF5r8nv+x7ki7Lng/jmKeaU3oVYDfl5yhAd4o1sME1+3s+mepxyDfBUAgItFJL4IAoDWGLr9bGGT7J+b7e9oFw4ACPL1Ev059jRb5WnHHq3Zga26XolSMx4fHpUBgP5tw8V1WOP7ulhUBWmm8bLV4otd6SZFB+PZYR0AAJ/uyXZ43NNVffEV3wIAcOxqqdtaLKjVanytmSP6+2nTf0PbzxYBAA5dvuG0tfKoV6+4UHgrZAjy9cL9mkIEZ8w2rW9UYef561CrgS8OXMGwxTvx8/H8W6Kdxd6LxahtUOF8YRWKKoxHvworavH6z6fx6o9/6qSOXAH3ewX6sJN2Tb3SaPS4vKYBT6w5gumrDhm0oXE1vPgnPswfgiCgWyyLzp/KK78l/mbsIUPjlR3XOxYAiS+CEBnaOQoAsOdisUPNR89dq8RxvXE3RRW1yLpeDUGAGHECoPV92dFslbeaiA7xQ2SQDwDzpvus69UorqqHj0KGnnEhiA/zR3SILxqUahy14PvSF4dXblhnFuXP6xQVhHu7R6N9ywCU32zAmv2OVeKJka9wJr66xgTDSy6guKreqvRrU3C6oAIXNAfUKyU1Rj8LtVqNvZrChbKaBqeNheJ+r35ttH9bk/qz1OOmU9cMijNs5XRBBeobVQjyUaBdRACuV9bh2W8yMe3zw81+rmiGxAT9Z77x7+EJSdsOU9s0FVx8tW7hh4hAbwDGfV8Xr1eiQalGg1KN3ReaJnpvLfz7Gae5OOoYFQSFTEBpTYNbm8Sq1Wp8uicbO84VufR1y2sacF6TZpyQHAcAuHKjxuntd1wNiS/CKSRFByE6xBe1DSqrfVD61DYo8fCKfXhg+V58ISn15/vrEh2MUH9vndcE7It88VYTEYHe4kHOnPDgKcfe8aHwUcghCIIY/bKUeuTi0NeLfd2uFFs+4arVarGBbadWQZDLBDw7lEW/Pt59yaHKRP2Du6+XHF01qQ1LQrKp2Jip27uHRzqlXCyqQlGlVgidyCtzymsfuaL18nG6tw5Bz9YhqFeq8H2GY8Z73ow3uU0L/DZnEObc0wHechl2nr+Oh1fsd4lf6lReOXaed76oOCyp/jXVhf1knlR8OZY6O5VXjnWHr1odAeI9vqKCfRGj6WlXYKTdRFaR9oJox1nni4vLxdWoqbfuO3tV/H6y9fp6yZEYGQjAvZ3uj+eW481fTuPZrzNdKnyOXmXfnzbh/ugaE4wgHwWUKjUulzTvikcSX4RTEAQBqTz1eMa+g9fxq2WoqG2EWg28uvEUPvwjC4DW75WiETscHvk6Y6P4alCqxNRDWIAP4jTpS3MzHrnZfkBb7Rqs9X2d04iouzu0BMCu2ixxvbIOpTUNkAkQD7z39YhG24gAlNU04As7o19qtVp7cG/hLz7e242me6VKjR81w9t5imXPRcP3lEe9OCfMNEItrqqz6gRRVFGLKyU1EASgT0ILnd9N0sw2/WxvNjadKrC6SlUfLmj7xLeAj0KOOfd0xG9zBqFdywAUlNfiqS8ymnRUlUqlxrTPD2Ha54ecmq65UV2PLEnJv6mo1qk850S+1Go1Zn6Zgfk/nMAfVgpJHvmKCvZBdIgvACDfSMFLlqRR9M7z1+3+rI1xOr8CQxf/gemfH7ZKNOrbAgCgGzfduzhyKIUL56q6RpdepGVoItN9E8IgCALaa46Hzd10T+KLcBrDRN9XkV3eBN60NDyARbfe3nQW72w6K0a+Bibqii/eaPX8tUqbGhCWaqJeMgEI9fMSI0Cm0o5qtVprtpekPa31ffFeZCO7tgIAXCmptvj+8Ghem4gA+HqxLtcKuQyzUxMBAJ/uuWTXCeJGdT2qNWvlnjlA6/vK1Ev5uoL9WSUoqqxDiJ8XXh6dBID1RdP/TPdqRHi7lgEATLfGyLpehTve2oZ7rJg/yo28nVsFI9jXS+d3aT1jEBPii8KKOsz88iiGvLsDn+3JtjnqyAWtVNy1bxmIT6f2Q4ifFzJzyvB/6082mZ8n63oViqvqoVYDe5yYUuMpR7mMleOaaoWgE/lyIHJzuqBCjE5be4HHI6XSyJextKNURJbWNOC4E9uu7MsqhkrNpmPstsLQr18QA2irsh15/xxFWlm+qwmiqKbQj0zzi1FTFxJKlbpZeONIfBFOY2D7CPgoZMgruynm6G2BC5w5wzvi76M7AwCW/5GFKyU1kMsEHU8OwMLQPgoZbjYobWpAyNtMhAV4QyYTRBFiqsv9lZIaFFbUwUsuoE+89gRqje+ruKoOxVV1EARgWFIkBIGZfourzJt6eaVjZ43A5NzfKwZBvgoUV9WL43Bsgf8fWwX7iqIO0FY8ns4vd/nA8A2alOO9PaLRr00Y/L3lKJH0dQOARqUKBzTia+bd7QGw0ntjovv3PwvRqFIj50YNxi/fhy/2XzZ5MOZps35tWhj8zt9bgR+fuQvPpCYi1N8LV2/cxIJfTiNl0TarfS+FFbXIK7sJmaCtrOW0jQjAB5P6QC4TsD4zDx/tumTVPm1FKqilg+kdhRcqjNJcVOSW3jRoTFtYUYvrlXViu5TLJTV2F4xskwiuP85bd4HHI1+Rwb6ICTGdduQj0lpq/J9/nHOeuJA2gn5/+wWL6zYqvsTIl/vE1znJ93GXi3xxDUrt2K9kzcVLBx75KjLMeNyorsfAf2/Dgx/u8/iGuiS+CKfh5y3HwPYsGrTNxqrHukaleCWd0i4MMwe3x8IHuokH7W6xIQjSi0wo5DKx5YQtzVZ5NVN4ADvQ8vRbrgkBx6sce7YO1REs1vi++AErIcwfof7e4gngigW/gtZsH6zzuJdchrs7svTlH3YYX40d2AFuSPZBg1Lt0pL2m/VKbDpVAAAY3zsW3goZBrRlIluaZjyZV47KukYE+ypwf+8Y+HrJUFXXiEvFhu8jf15MiC/qlSq8+uOfePabTKMnfd4/KFlP2HNaBvnghZGdsP/vw7DwgW5oE+6PytpGfHvIuipI7vfqGBUkVtxJuatDBF5L6wKARXq3mqn0tBepSD+YfcNpY2q4cE3tHCn6k/T/dnjksUNkoJj2MzWV4tlvMnHf+7tNirOtZ7TvzdUbN3Xat5iikEe+gnzEyJd+r6/6RpVoBZiawgot7PlumeK0pCDo8OVSs2PJymsaUFnLIqutJbaApOhgCAJrGHu90vkVo5k5pbhnyU58sOOi0d+r1WqckRxjT+VVuKRy9XR+BWobVAjx80L7lkx0mYt8bT1TiMKKOhzNKcPYZXvd5mG1BhJfhFPhLSdsNa2eyGWz9SICvcUv2aN3JGDpxF5oFeyLKZrGl/rwyJAtY4ZKND2+wjTpTdFwX3bT6InpgJGUI8eS70sUUZp1JmgqDK9YaDdxrrBC53lShnbSpndt5aqe2Z4jCIJbfF9bzhSiul6J1i380FdzZXtnIuvltldiuucRm5T24fBRaAsETuqZ7msblOIIqNV/7Y9/3JsEhUzALycKMHbZXp0DdlVdoygWjEW+pPh5y/HoHQlYNL4HAOu9S6LfK8H0/qfckYDJA+KhVgPPf5uJy2ZERX2jCidyy2wSUNLq4fKbDTpiwF5qG5RiOrFfmxZiLyr9yAzfpltsiPiZGRP3BeU38fPxfJzKq8BGjf9PyrXyWpzILYcgaL/z1kSnikTPly9iQjWeLz3xlXOjBkqVGgHecrGa7kRuuVNETn2jChc1ERpuy3h/u+k5rfziqGWQD/y8tRd6AZpKWcD5/b4OXirBo58cxMWiKny+13iUOL+8FpW1jVDIBHSMYsdnV/RE47aAvgktINOkt7n4ulRcbWC94EUl3nIZrlfW4S8rD2D9Uc+cVEHii3Aq3HSfcaVU9FZZA08pDWgbrjNL8v5esTjwf8PwUN/WRp/XOdr2MUO8zUS4pvQ8OsQXcpmA+kYVrhu5mjNmtudY8n3xSkdeHKAVX6ZPsEqVWjST6qcdAWBwp5YQBCYACk30VjIFb/DKIxVSuPhad+SqSwalA9oqx3G9Y8XP/a4OTHwdvHRDNM3zA/1dGmHG+7Ppm+6PXC5FfaMKrYJ9kRgZiMcHtcPap1IQE+KL7OJqPLRinxhhPZZTBpUaiA31Q3SI4fthjC7R2okI1kwbOKoRsn3jTYsvQRDw+tiuSE5ogep6Jb42E1Vb/Ps5jF22F89+k4kGpeWCgpv1SvECgP8t7XdC6vFEbjkalGq0DPJhXdi5J0lPlPLIV/fYEJPbALon8q+NTBbgkfTecaEY34f1erJUvalSqY16vgor69Aoee+42b5dy0BEBvuiuybFZ011aINShY2ZeSa/hxeKWAuLYF8FFjzQDV5yAfuySsSUrT6mItMAJOLVNvHMi2zqGg2PT7vOX8fUzw+JPtDiqjqjVd/8OJYYGSi2FWqK6ll9eH+vvpKLl9YtmN2kvlGlc5xqVKrEv6NPpiZjeJco1DeqMG/dcSxKP+NyO4UlSHwRTqV1C390bhUEldo2X8BBTWrPWHTJHPyEYku7CW3akYkvhVwmpkT0RUduaQ3yym5CLhN0DgAcS74vXunYWYx8satXcxWPl0uqUdeogp+X3OhBOCLQBz1ahwKwPT1i7uCe1oP5yc4XVmHM/3bj1xMFNu3bVkqq6sQD+P29YsXHO0UFISLQGzcblMjMKUVtgxIZmvd2oAXxtfsi29+diRGimOub0AI/P3sXesaFoqymAZM/OYCtpwvN+r1MEeLvhVjNSfyMhQhSfaNKjPyYi3wBLJ38+KB2AICfj+cbjWw1KFX4TtP24teTBXj6S8tVkqfyy6FUMZHERYupVjA365VWi3n+3iUntIAgCJIROOYiX8FGtwF0U8xnCioMPleejr2nSxSGaCK/By6VmP3/l1TXQ6lSQxBYS5mWgT7wkgtQSkQZoBVf7TWFHEM6WZ/Wf/u3s5iz9hj++aPxiQs8It8lJhixoX54sA+7iPzfduPpPV5xHdfC8GJA2mzVGq6V1+KDHRcxbPFODHpnB/ot3Iq//3CCFQCo1NhyuhCPrz6C2gYVUju1RJLmwsJY0Y1UwN/dkX0Hd1+47rQUtjHY2C9t5Isjlwlo19Iw9Xg8txzlNxsQ4ueFge3D8dGjffGMpkDpo12X0O9fW/F/G04iM8d9zaSlkPginA6Pfm2zsiKpvlElVrTc0c4wumQOLmpybtSg2soqNG3a0Ud8rLWJdhM86tU9NgQBRjw7Ut+Xfm8qpUqtNc5rDmwJGtFjrss9f07HqEAx1K6PvalH/v8zJr7iwvyR/twg9I4PRWVtI2Z/fRQvrz9psYO/vfxygrVv6NE6REwlAOw95WOk9l4s1olm8dRL99hQACwFI41i8JP4IE30jBMe6INvnhiA1E4tUdugwpNfHME3mgiTKb+XKbpoRMRpCxGIP/PLUd+oQliAN9qEG77f+gzp1BJBPgoUlNeKYlPKrvPXcaO6HkG+CvgoZNh6pghPrDli9vM5pom89YoLFd/TQ9k3dN4zzhNrjmDQ2ztw0kwLDw6P3PD3jgurS5J+VkWVtSisYGb7LtHBokC7WFSlE4VRq9Via5G2ms/3G0n0r7quUax0HZ4UhQ6RgYgJ8UVdo/meglxIRgT6QCGXQSYT0CrEMPV4SVPpyO0OXNztOn/d6PvEybhyQxx2vy+rxGj1Mf8b6RLN/u+zhiRCLhOw6/x1owUz5i6OuompdvOfz4FLJZj62SEM/Pc2/GfzOdEXWVHbiG8PX8Wkjw9i4L+34+kvM1CvVGF0t1b4aEqy6LU8esXwb49faHSODkZyAiuKKa6qN0hhq9VqLPn9HCZ/cgBjl+3BkP/sQN83t6D3gt+xxUY/Y27pTRRV1kEhE9BTc7HJ0ZrudVuEACxyzj/vF0Z2wrJJvREb6ofK2kZ8fTAH45bvwz1LduLDP7KcMivXXkh8EU6Hexv+OFekc/BqVKqMXnGczCtDbQM7SXWQnIStITzQBy2DfKBWQ2xKagn9tCMgNd3rhtx5usOcKBysMcD/kJGnkwq6oolg+XrJxIMpj3zlmEk7asWXYcqRk9qZveaeC8VWNzxsUKrEk46xgzvABNi6p1Iwa0h7CAI7Cd7/wR6nH6RqG5T4LuMqAOABSdSLw9OLey4Wi94vaTSrXUQAAn0UqG1Q4aImcnGjul5Myei3JQFY9eLKx5LxcN/WUKm1bQj0q2gtYS59JoWnHHvHheqk0k3h6yXHCE3l4E9GfE+8KvThvnH4fFo/+HnJsftCMaavOmSy/QU/wfeKC0VSdDCCfRWoqms0OIEfu1qGPReLUa9U4aNdWWbXqVKpxdQtjxpGBvkiUvM95CdqHqFp3zIQAT4KxIT4ItTfC40qNc5f0540zxVWoriqDn5ecrx5fzf2/z+eL/6fdmv+xhPC/ZEYGQhBEDBYE53aacb3xZvXRgVrL7J4ejlf0ilemnbk71WovxcqahtNtl6pbVDixe9OgB/OKmsbjUZCTxew94A3hI4P9xf/3pcZ8X6Z8mQCQNfYEChkAnJLmT/OGKfyyvHYp4ew8/x1qNTs83nnwR448foIfPPEHZiYHIcgXwWuVdSiUaXGA71i8P4jveGtkGk9nxYiX94KmVhYpZ/d+Ol4Pv63/SL2XizBidxyXC6pQUl1PUprGvD1Qdt6E/IL8q6xITr+N8C46Z6LL3485tzXIwa756fiq8cHYFzvWPh6yZB1vRpLtpxzaj83WyHxRTid3vEtxINX6uI/0O9fW9H51d+Q+MpvmPDRfoOrSV79079NmFUnKX1sTT2W6KUdAe3BThr5KqmqE6/W+Kw/Y4zu3goRgT64VlGL305dEx+XjgfivZD4SJ/SmgaTguacnknfGN1iQhAR6IPqeqVOl3Fz5JfdhEoN+ChkYkm9MbzkMswf1RlfzhiAiEBvnC+scrjLu5QTuWW47/09OJVXAW+FDGk9Dd/bOzWRq+O55fj9T/ae3ikRVDKZdubdiavsBLcvqxhqNft7iAzyNfl/e+ehHmI6omWQj82Cn/u+LBnXrTHb6zNW83eWfrJA53tSWdsg/i2O6x2LgYkR+GJGfwT6KHDg0g38ddVhoykgLr56x4VCLtNGafUjRqs0ERwA+O3UNQNTupQLRVWoqG2En5dcTFUBknYIeex9OZnLbrmHShAEiXDVij/u0+nfNgx3JoajfcsA1NQrRQHKqxyHdY4Sjw+DO7ILPHO+o0Le3V7ytxCrV/GoVquRpTmBt49kF0ZymSCewE0VDr235TwuFVcjMshHbIFwUG8Iu1qt1kk7cmantodMALaeKTJIIZoTXyF+Xpil+bt9ZcNJg1YKNfWNeO7bTNQrVRjUIQI7XhiC72YOxIR+cQj29UJK+3C8/VAPHH7lHqx4tC/eeagHFk/oBYWcyQDeRke/3Uxtg1JsxcE/b15xLe33VX6zAW/+cgYAMHlAPD6dmox1T6VgxaN9ALCIqzU+RY5YiWzk+yOKL826SqrqxL5/+uILYMeLOxMj8N7EXjj8yj14+8HueHpIolh05Q5IfBFORy4TMLobu4K/euMmrlfWobaBfekOXy7FN4ev6mzPKwXvsNHvxeEHhK8P5uBv647jr6sO44EP9mLKpweNChzR8xWoFSDcgC6dF7ghMw8NSpYWk55k9PFRyMVqzE/3ZIvRPf1KR4AN+I3QvG6OidSj1idm+jVlMgGpmqt/a1OP0pSGNSL3zsQIcaTRT8fyLGxtmfpGFZb8fg7jlu/DxaIqRAT6YOWUvkaFYGyoH9qE+0OpUosNMHkVJIf73viYIX4S199OH0Fg6YhvnrgD3zwxwGRq1xT8RHqxqNJs1JGnb3hEwRoGtg9HWIA3SqrrdXpy/XbqGuoaVWjfMkAUncltwvDV4wPg7y3HoewbBhW3RZWsx5ggsHFJAKsWBXRN90UVtfj1JPP3JWje89X7L5tcIxf7veND4SXXnkL0hZXU76XdxtA0vueitphCEAQ80p9NFvjmUA6UKrX4931Pl0jxOXcmhkMhE5BdXG2yeEXa44ujX/FYUl2PitpGCALQRhOVBoBUTepxh5HIWmZOKT7ezXqyvTWuO4YlMQP6oWzd9z+/vBblNxvgJRfQIVJ7DGjXMhD39WAim0/xAJhNIbfUfGT62aGJ6Nk6BBW1jfjbuuM6gnvBz6dx6Xo1ooJ98N+/9BZTuPr4eskxqlsrTEiOEy8KAe38S/12MxeLqqBSAy38vcQ5uHxaR8aVUtHusfj3cyiuqkO7lgH4Z1oXDEuKQv+2YRjRpRVC/LxQXa+0mDLllFTVibYVY+KLXzBlFVVp0tbaC6+oYOMXXpwgXy9M7BePecM7WrWWpoLEF9Ek/PO+rvhyxgCseyoF6c8Nwu75qfjHvax7+ZLfz4miqEGpElMYA2z0e3H4Qf9kXjl+OJqL7WeLcOxqGXZfKDbaN4n3p5Fe9fCeOjzypVar8a1GJE7sF2dxDZPviIe3QobjV8vEiId+pSOHVzwam012s14pPm4u8gVovXXWNvzUn+loDWO6R0MuE3A8t9xsCwR9jl0tw7eHcvDJ7kv437YLWJR+Bvd/sBf/234RSpUaaT1jsGXu3aK/xhhSEZUYGWhwUOWm+5O55VCr1WL38Ls6mBdfnJT24UiMNP8eGyM21A8hfl5oUKqNNnoEWOuEgvJa1lxVz69iDi+5DGO6a1KPktQSrwod36e1jnDuGReKcb1ZGutbvYsa7vfqEBko9sjjvi/uowOArw7moEGpRt+EFnj1XtZz7JuDOSY9lBnirErdiyUurHjkS1rpqN1GYxrXnNzrGpWir5J/buP7tIa3XIaTeeVYs/8yblTXI9hXoZMeDvL1Ejuem4p+iZEvY2lHTaNVHvVq3cJPp4ff3R1ZRfGZggpck6QoaxuUePH7E1CpWQTyni5MYAAssiMVQ9zvlRjJUnVSZqWyRsHppwrE1FlB+U00qtTwlstMCggvuQzvTewFPy859mWV4DNNxDL9ZAG+PXwVggC8N7GXXREdQRDQK04z6ULSbuaM5DjG//baRAQgPswfDUo19meV4ERumTiPd+H93eCj0L6XMpkgXlhbU2lb26DEE2uO4FpFLeLC/MQom5SE8ADIZQKq6hpxraJWTD+bO554GiS+iCbBz1uOuzpEoH/bMHSJCUZcmD+mDWyDxMhAlNY0iH6Hk3nlqKlXItTfC53MeJzMMbpbNJ4f1gFP3t0OL43qjLcf7C5GhS5KZrYBLPrCmxhGGPF8FZTXolGpwtGcUlwsqoKflxxjjaTF9IkI9MEDmpTRp3vYAVGMYEXr/r+4+DLWlf9CUSXUapYSNZcaBDTGUpmAS9d1r/7VajXWHs7BN4d0S/Z5VM/UVbUxWgb5iP6On0z4TPQ5kVuG8cv34u/rT2Lhr2ewZMt5fLTrEs4UVKCFvxeWTeqN9x/pjRYWThB3ScTXne0NhXkPjen+TEElLhZVIa/sJrzkgmgcbioEQRBTj6Z8X0evlAFgJyxjhRrmSNNERTafuoa6RiUKym+KaUJjf4t/6cciRZtOXdNp7yL1e3E6RgUiPIBVkh7PLUNdoxJfHWTm9ul3tsHQzpFoE+6PitpGk/2RTFWJcmF1vrAS+WU3ca2iFoKgfZxtw4TY2YJKKFVqZOaU4WaDEhGB3uL3PyzAG6M0kfN//3YWALvQkEbZAG3q0VS/L2mPL45+2jFLz2zPCQvwFkXzU18cwcwvMjDn20xM//ywGLXlzXG7x4bAz0uO0poGneMNF19J0YbHtc6tgnFPUhTUamDFThb94t/P2BZ+OhEpfdq1DMSr97HXfmfTOWw/W4i//3ACAPD04PaiwLaHPgns/ywVX6LfS+//wase/zhfhH9sPAW1mtkzBhqJPPO5vJbEl0qlxt/WHcfRnDKE+Hnh82n9jX5/vBUy8Th6vrBK9J4ZSzl6KiS+CJehkMvE6NeqfZeRXVwtXvX2bxNmc/qH462QYe7wjvi/MUl4ekh7TOwXL14B6Q9fLa1hJye5TNCZ5RcZ5ANvhQxKlRoF5bX49hCLItzbI9qgs74p/npXWwDsJHi+sFJspGoQ+Qpj6QBjkSRjqUpTBPt6idEA7k2pa1Ri3rrjeOmHk3h5/Ukdr5Y5P4k5eBuIH4/lWSzRVqnUePXHP6HSpADG9ozBI/3j8PhdbTF/VCdsnnu3mHKxREr7cHHCgbFUYlyYH0L9vVCvVImCt098C/h72yZ27MFSxaPW7xVq8777tQlDq2BfVNY14o9z1/HjsXyo1cwTZeyz6xYbjC7RwahXqrBRkh7m8wmlY42k1bn7s0rw64kCFFfVoVWwL0Z2bQWZTMD0O9nf8Wd7Lxv4yK6V1yK3lI1L6q3Xu6x1CxYRbFSp8YPm765dRIDOybNtRAD8vOS42aBEdnGVTqpY+v3nqcc6TXTuHk1qTwpvCbEvq9hoy4lCI4Z7scu9xi91SWwzYej74wLweG45Nv15DRuP5Ysi+F/juiHUn108eCtk4ud8UJL65RGjLiYsC7M10a+NmXnILa2x6fv5SP84DOsciXqlCn9ddQQVtY3oFReKuQ6m0nprIl/Stjm8h2KS3nGMpx6/OXQVJ3LLEeSjwCua47s+XJAduXLDaL8xztubz+LXkwXwkgv4aEpfnSpofXjq8cdjeSiuqkeAt9xoOyBPhcQX4VKGdIrE4I4t0aBUY1H6GYnfy76Uoyk6iNUwumkhacpRerCXyQS0lvRv+kXT4+ovVqQcOZ1bBeOuxAio1MA/NrC+P5FBPgYpgDYRmkarRiJf1pjtpfCqx+3nrqO8pgGPfXpIrIoDgH/++KeY1jBXxm6OkV2j4K1gFUKWTObrjlzF8atlCPRRYM2M/vjfI72xaHwP/OO+Lpg1JNGkEd4Yof7emDawDVLahWNQB8MrWkEQxJTWD5oozV0W/F7OwpLpXhRfZpqrmkImE3Bfj2gArOeXtBGtMQRBwF/6s7/Tbw9dhVqthkqlFgsReunNlOS+r31Zxfh872UAwJSUBDGy9FDf1gjyVSC7uNogpc0r0JKigw3GJQmCtghi7RF28SJNOQLsoodHgv7Mr9Dxe0m5o12Y6FlSyLTVjVI6twpCq2Bf1DaojBad8LSj9G8uWuP5KqtpQE19o6TS0dAf9dc722LlFGZMf/OBbvjHvUl4UdO6YKSmKpXDGzAfkJju+d+G1GwvpXd8C9yZGI5GlRord12SfD8tN/wVBAFvP9RDjN4H+ijwv7/0NogO2kqP1iGQCSwDUFB+U6doQD/yNTCRRd55xeALIzuZ/H53iAxERKA3ahtUOH7VuO/r64M5+Ggn89K981APi+cELsx45efAxAiD9K4n03xWStwy/OPeJMhlAn4/XSj2ZbK1uaolEjUjMHJu1OhcFes3WJUSq+n19eHOLNxsUKJ9ywCbr6T+elcbABBH3BgTUVz8GDMKn5NUSFoDH+d04FIJxn+4FwezbyDQR4HVf+2PuxIjcLNBiWe+PopayfBxW8VXkK+X2D7EXOqxrKYeb29iaaI593SwSWiZ4rW0rvjmyTsMSs053PfVoGQnAGv9Xo7CT6hn8g2He9c1KvGnxvdkj/gCIFaAbjp1DWevVcJbLsOY7tEmt7+/Zyx8FDKcK6zE8dxyZF2vQmUdq0jU/1vi4utg9g2czCuHt0Kmc5ER4KMQI0+fSaogr96owVqNr8xUew6eVuTG8W564ku6DfcKAYafmyAImDyArWFgYoROlFq6zWBxzqlu6rFRqRIvtKRpx2BfLwRpRGN+Wa3JtCPAIlojujJj+pQ7EvD4oHaYnZpoNHI7QOL7UqvVqKxtEL9vpiJfADBbU7347eGromC39vsZEciM9R2jArFkQk+xktoRAnwUYqT+WE4ZrlfV4UZ1PWQCdIoGACb4+PGxW2wwHjUxAg5gn9UAE/0QAeYjfFXTqHbuPR0xrrfxiSZS+Hr4d785pRwBEl+EG+gQFSQeWBtVaoT4eRmEtB2lZaAPQvy8oFJrmygC2h5fxgypPNzP/Q4T+8XZ3PpiSMdInatoY1WSvKqqsKLOoEGmLWlHgJ004sL8UN+oQtb1asSE+OL7p1MwuGNLLJnYExGB3jh7rRJ//+GEWOTQ2kj3bEtwr9HPx4x3XweAd38/h9KaBnSMCsTUgW1sfg174M1WASDIV2EQaWkqEiMD4S2XobKu0WAcy6m8CtQrWd+6BDtPiD1ahyAh3B+Nmvd6WFIkQvxMp79D/L1Ecbb2cI7Yq6l7bIjYSoDTLiJA7MkFAPf3jNGp/AWAqQPbQC4TsPdiCb46eAWPrz6Mu/+zQ1vUYCLC2FUvymPs8+DbrM/Mg0rNOssbG+80bWAbvP1gd/x7fHeT/29T3eiLq+qhVrNIm/6FFk89Xi6uRq6mwMaY+LKFnnGh8FaweYLZxdXi95j1NjPtbUxpF47e8aGob1SJ1a1xLaz/m7kzMQK/zx0s9odzBrw692hOKc5qol5tIgKMXgA9P6wDBnWIwJIJvcz61ACI3lFjvq//brsApUqN+3pE47lhiVatUz8lSeKLIKxgzj0dEezLrkD7OeD3MoUgaAfASivSSoy0meBID3oKmYDxfSxffekj9cwAxiNYof5eCNL836Wm+5KqOvFq3VyDVSmCIGBkF3bg7RoTjA2z7xSvXCODfLF4Qi8AEIcVRwR622wAB5jhOchHgXwT3ddP5ZWLxu0F93dzOP1hLT3jtCf3ge3DDYRGU+Ell6FjK/b3xRtpcngaxN6+dQD7XNMkERZTKUcpvCr3p2P54gmul5E2F2yCgDalM+3ONgbbxIb6iZ6nVzacwtYzRVCr2eSAT6cmY1iS8aoyHtVirwOxq70UHg3j1ZamhJxCLsPEfvGiWDLGwMQIyGUCsq5X64wGE9tMBPkYHFt46nFfVglUaibapcU39uDrJRfTu4eyb2g725tIOXIEQRB7znFs9WQ6Gx6tzcwp007oMHExyPrNDbDqeMVN95k5ZTrZiD/zy7Hr/HXIZQJeGtXZ6u+M9CK3XcsAt79vtkLii3ALYQHeePW+LvBRyPBwsu0ixxp4GwGp6b5EI26MpR2lw6aHd4kS+3HZyoN9YtHCn0UppOKAIwiCGP2Sph65QGoT7m+TQPr/9u49Kspy3wP4950ZGAYE5CKXAUFUBO8pqKF4QQpF0yx0l1e0ixtT83Lstq2tWW5c63TcrtZKSo/bTmoHc3nJzEJI83q2GkpimGZ5V0RLuYiCMs/5Y5gXRgYaYXhngO9nLdaSd16Gh5/A/Hie3/N75j3ZCR9P6o1NKTE1tqgP7tQGfx3cXn6/vr+gqndf//Khnl/GInvjbqfRPfU2r9+rS4CHi/z/pFS9l4lc91Wt6P52aTm+qKx3qmsZxhpjeumhVknwbaW1agt9vzBvtPNxxZ3yCrnw/uF6LxPT8z3e3tssYaouZVAHOKtVcNdqMLV/O3z3H4Ox7sV+iO/sX+sLZJivG1wrZ0jCKk8heFi4fytoqiVEsRbq+azlqXOSDy3/vlrLCUs9vkxMydz+yh1yHdq0qneSXJ1p6fFw9eSrjiVHk6GRfmbJjS2WDxvCNPN14kohTlS2C6mr56C1wnzdEODhgvJq7YUAyHVeI7sHPtLvJ1dnjTyL39RmvQAmX2RH46Lb4uf3htcoXrWVqvO/qma+6qr5qj7zZU1vr9q4Omvwv9Mfx9qpfWrtI2X6BWvaEXnl9l38167TACAfsGwtN60Gw7sF1rrLb0FChPwiHOZjufGiNZ6Wu6/ny52qTXVexy/ehpuzutbdTo1FkiS8MqQD+oV5W72L0lYstZvYcPgiSssr0DnQw6wjf3109HPHppQYfPHXx60qJJYkCc9Vtp0wLSnWlnw9/ZgeaRN746MJvWt9vu7Bnjj45lAcXhiPxaO7WrU0ZyyoN8altiVgrUaN8MqZErVKanC9Z9VRQ1VLj9eLTd3tLTfwBarOBWzokqOJqej+8G+/y8X2dTVnNpEkSe5c7+PmbLG+TUlhvm7GXcQPDMjMM54uUdvM16OQJMlsswdgrCM0NfidPujRfu8BxqRLo5LkHdlNSePvySaqgy3+4qxNuLzsWG3mqzL58rawzBDu3wr+HsazIi3trnsUkQEedf61aDpo+cIfdyCEwDvbTqK0vALRoV6YUFnsbCtOahU+mRyF1ft+k3fF1Uf/Dj7wbeWMmyXlWPd/F/BLQTG2Hr8in14w78lOf9pdujG8EBsmt/lQkmlJzfRCW/agAp8eOg8AmD4ozCbf249asJ8UFYQPdhnPrPNz1yLQ0/L/hyRJSKyjgN/kz3rNWRIX0QbZF27JXeIt6ar3wKlrRXisbesGJxtDItrgPzNO49Cvv6PsQQW0GrXFHl8mD8fE0k7H+ugd2hoalYSrhfeQX/n5/2zZ0eSp7oHIL7xrs0SwISRJQq+2rbHn9A35Z9uaJNIaMe19sPX4FXlZ/L/3/4YKg8DAcF+LmzP+zOLRXTH/yU4Wy0gcHZMvarZMu2Eu/F4q/1KuWnas+cPq6qzBvtfj5ELdxmTq9XXh91LsOHENu38ugJNaQuqz3W1e/wYYX4TermzMWF8atQojuwfif/7vApbsyJOvdw70wEuxYXi2d9P767MhTLMB1wrv4Y875cg6dR03io09s5SehTPxc3dBfKQfduVdx2NWHuhtaymDO2B4t0B0qCOpGd1Tjy9zrsgbbxqiS6AH/Ny1KCguw9FztxAb7isvO1bv8WXycA2ZrRIeV2cNugd74vjF2zAI425Aa4vnVSoJ0wd1sMk4bKFXiJd8tFIrrUaeLWwo08zXicuFxt2zlUv0KYPr97U7qVVNMvECuOzY6J555hl4eXlh7Nix9h5Ki+PvoYW7VoMKg8D5m8blvapzHS0X2Go1arNjRhqLaRfc6fxivPvVTwCAV4Z0lJdjHNXYKON5cCoJGNE9oPL4qFgkRQXb5YXentxdnOT/x7yrRVi9z1i78kJsO8U2HFjy2rAI9O/gg5frsYxjCxq1Ch396q6jGtSpDX5ZOqJem1oeZt5ywrj0KPf4sjDz9XAi0dHPNjNfQNXSI2BMzhvjDyklVD+PNMKGX0dbb1cEe+nwwCAwd2MO7t03oHuQp9kGkJaCyVcje/XVV/HZZ5/ZexgtkiRJcr8vU92XqdWEpZovJYVW1l4VFJfhZkk5Ovq1ks97c2Tdgz3x7ZyBOPjmUKycGIW+YfXf0dccmOq+0vaexS8FJWil1eB5Gy8bP6pwf3d8/vLjtfbiao5MGwhMRffX61h29PdwkU9OUKskhHjbMvmqirm1S46OqGfb1nKMbFHvVZ0p0TIV3f91cPsW+TuEyVcji4uLg7u7Y89mNGdy0f31EpQ9qEBx5WHBlpYdleTnroWLU9WPX+qz3c0Oo3Vk4f7uFvsytUSmnlUHzxprWMb3bWv3gumWKDbc2HLibEEJLt8qRYGp4N7CsqOzRoU2lUtVId6uNu2KHt3OC6ZJImt2OjoqDxcn+XdnpI2/jphqs1wh3q5I7PbntYfNkUMmX8XFxZg7dy5CQ0Oh0+nQv39/HD161KafY9++fRg1ahT0ej0kScK2bdss3rdy5UqEhYXBxcUFUVFR2L9/v03HQY3LVPd1tqBEXnLUqCR46Oxb7qhSVbWbmNgvpEXNUjQn1Wc31CoJUwcoX/hPxpYTvSuXyjLzrss/6/61nLJgqvuqqy6tPtxdnDC4Uxs4a1SKtlxpDAsSIjCsq7/Fw9wbIqZ9VUuYlwe1b/T6WkflkAX3L730Ek6ePIl169ZBr9dj/fr1eOKJJ5CXl4egoJpFvQcPHkTfvn3h5GT+F+fPP/+M1q1bIyCgZiuDO3fuoGfPnpg2bRqSkpIsjmPjxo2YO3cuVq5ciQEDBuCTTz5BYmIi8vLyEBJiXFqIiopCWVlZjY/dtWsX9Hr7FN1SlerLjtW72zvCNPdbIzrj+9MFmN/Aw3DJfroEVu3QeqpHoM0Kk+nRDYnww9Hzt/DFD8ZzPp3VKrR2tTwLqW/tgpxLQPtG2F340cTeKLn3wGK9WVOS0DXApp3zTQI8XTC+b1tcvnUX46Iap8djU+Bwydfdu3exefNmfPnllxg0aBAAYPHixdi2bRvS0tLw/vvvm91vMBgwc+ZMhIeHIz09HWq1cenmzJkziIuLw7x58/D666/X+DyJiYlITEyscyzLly/Hiy++iJdeegkAsGLFCmRkZCAtLQ2pqakAgOzs7AZ/zdR4TJ2Xz928g4JiYx2IpaOF7GFwpzZNsjkgVfH30CLE2xVXbt/Fy4/Yn41sa3AnY8uJU5WtP/w8tLX+kfVMr2CcuV4iH2BuS67Omlp77pFR6rM97D0Eu3O4ZccHDx6goqICLi7mfzXodDocOHCgxv0qlQo7d+7E8ePHMWXKFBgMBvz6668YOnQoRo8ebTHxskZ5eTmys7ORkJBgdj0hIQGHDh2q13P+mY8++ghdunRBnz59GuX5WyK9pwvcnNW4XyFw7MJtAKh353qih0mShPUv9sPWV/rXq08R2U5XvYdZX7K6es492cUfWfMHo0dwawVGRlSTwyVf7u7uiImJwXvvvYerV6+ioqIC69evx+HDh3Ht2jWLH6PX67F7924cPHgQEyZMwNChQxEfH4+PP/643uO4efMmKioq4O/vb3bd398f+fn5Vj/PsGHDMG7cOOzcuRPBwcF11q7NnDkTeXl5Nq9va8kkSZIPYD18zlgU7SgzX9Q8hPi48kXcAVRvOQFYLrYnchQOl3wBwLp16yCEQFBQELRaLT788ENMmDBBXlK0JCQkBJ999hk2btwIjUaDNWvW2KSu5+HnEEI80vNmZGTgxo0bKC0txeXLlzmrZQemI35yLt0GUHuPLyJq2oZEVCVffrUU2xM5AodMvjp06IC9e/eipKQEly5dwpEjR3D//n2EhdW+k+j69euYPn06Ro0ahdLSUsybN69BY/D19YVara4xy1VQUFBjNowcm+mYofsVxgPv7N3ji4gax8CObeRWD/Y46orIWg6ZfJm4ubkhMDAQt27dQkZGBp5++mmL9928eRPx8fHo3LkztmzZgt27d+OLL77AggUL6v25nZ2dERUVhczMTLPrmZmZ6N+/f72fl5Rn6ldj0lSPoyCiunm6OiG6sm2L6fQBIkfkkFsyMjIyIIRAREQEzp49i9deew0RERGYNm1ajXsNBgOGDx+O0NBQecmxc+fOyMrKQlxcHIKCgizOgpWUlODs2bPy++fOnUNOTg68vb3lNhLz58/H5MmTER0djZiYGKxatQoXL15ESkpK433xZHOmXl8mrPkiar4+GNsTe88UYFgjtEkgshWHTL4KCwvx1ltv4fLly/D29kZSUhKWLl1ao48XYNztmJqaioEDB8LZuepFtXv37sjKyoKPj+VGdz/88APi4uLk9+fPnw8ASE5OxqeffgoAeO655/D7779jyZIluHbtGrp164adO3ciNDTUhl8tNbYgLx1cnFS4d98AAPBlzRdRsxXi44rJMe3sPQyiOklCCGHvQZC5oqIieHp6orCwEB4eTfeICkcy8sP9+Omqsf/PngVDEOZr287WRERE1r5+O3TNF5GtVK/74rIjERHZE5MvahHCKzvdO6kleLg45Go7ERG1EEy+qEUwzXw5yrmORETUcnEKgFqExzv4IMLfHXGRfvYeChERtXBMvqhF8HBxQsa8QfYeBhEREZcdiYiIiJTE5IuIiIhIQUy+iIiIiBTE5IuIiIhIQUy+iIiIiBTE5IuIiIhIQUy+iIiIiBTE5IuIiIhIQUy+iIiIiBTE5IuIiIhIQUy+iIiIiBTE5IuIiIhIQUy+iIiIiBTE5IuIiIhIQRp7D4BqEkIAAIqKiuw8EiIiIrKW6XXb9DpeGyZfDqi4uBgA0LZtWzuPhIiIiB5VcXExPD09a31cEn+WnpHiDAYDrl69Cnd3d0iSZLPnLSoqQtu2bXHp0iV4eHjY7HmpJsZaOYy1chhr5TDWyrJVvIUQKC4uhl6vh0pVe2UXZ74ckEqlQnBwcKM9v4eHB3+YFcJYK4exVg5jrRzGWlm2iHddM14mLLgnIiIiUhCTLyIiIiIFMflqQbRaLRYtWgStVmvvoTR7jLVyGGvlMNbKYayVpXS8WXBPREREpCDOfBEREREpiMkXERERkYKYfBEREREpiMkXERERkYKYfLUQK1euRFhYGFxcXBAVFYX9+/fbe0hNXmpqKvr06QN3d3f4+flhzJgxOH36tNk9QggsXrwYer0eOp0OQ4YMwU8//WSnETcfqampkCQJc+fOla8x1rZz5coVTJo0CT4+PnB1dcVjjz2G7Oxs+XHG2nYePHiAt99+G2FhYdDpdGjfvj2WLFkCg8Eg38N418++ffswatQo6PV6SJKEbdu2mT1uTVzLysowe/Zs+Pr6ws3NDaNHj8bly5cbPjhBzV56erpwcnISq1evFnl5eWLOnDnCzc1NXLhwwd5Da9KGDRsm1q5dK06ePClycnLEyJEjRUhIiCgpKZHvWbZsmXB3dxebN28Wubm54rnnnhOBgYGiqKjIjiNv2o4cOSLatWsnevToIebMmSNfZ6xt448//hChoaFi6tSp4vDhw+LcuXMiKytLnD17Vr6Hsbad999/X/j4+IgdO3aIc+fOiU2bNolWrVqJFStWyPcw3vWzc+dOsXDhQrF582YBQGzdutXscWvimpKSIoKCgkRmZqY4duyYiIuLEz179hQPHjxo0NiYfLUAffv2FSkpKWbXIiMjxZtvvmmnETVPBQUFAoDYu3evEEIIg8EgAgICxLJly+R77t27Jzw9PcXHH39sr2E2acXFxSI8PFxkZmaKwYMHy8kXY207b7zxhoiNja31ccbatkaOHCleeOEFs2vPPvusmDRpkhCC8baVh5Mva+J6+/Zt4eTkJNLT0+V7rly5IlQqlfj2228bNB4uOzZz5eXlyM7ORkJCgtn1hIQEHDp0yE6jap4KCwsBAN7e3gCAc+fOIT8/3yz2Wq0WgwcPZuzraebMmRg5ciSeeOIJs+uMte1s374d0dHRGDduHPz8/NCrVy+sXr1afpyxtq3Y2Fh89913OHPmDADgxx9/xIEDBzBixAgAjHdjsSau2dnZuH//vtk9er0e3bp1a3DsebB2M3fz5k1UVFTA39/f7Lq/vz/y8/PtNKrmRwiB+fPnIzY2Ft26dQMAOb6WYn/hwgXFx9jUpaen49ixYzh69GiNxxhr2/ntt9+QlpaG+fPn429/+xuOHDmCV199FVqtFlOmTGGsbeyNN95AYWEhIiMjoVarUVFRgaVLl2L8+PEA+L3dWKyJa35+PpydneHl5VXjnoa+fjL5aiEkSTJ7XwhR4xrV36xZs3DixAkcOHCgxmOMfcNdunQJc+bMwa5du+Di4lLrfYx1wxkMBkRHR+Mf//gHAKBXr1746aefkJaWhilTpsj3Mda2sXHjRqxfvx6ff/45unbtipycHMydOxd6vR7JycnyfYx346hPXG0Rey47NnO+vr5Qq9U1svSCgoIaGT/Vz+zZs7F9+3bs2bMHwcHB8vWAgAAAYOxtIDs7GwUFBYiKioJGo4FGo8HevXvx4YcfQqPRyPFkrBsuMDAQXbp0MbvWuXNnXLx4EQC/r23ttddew5tvvonnn38e3bt3x+TJkzFv3jykpqYCYLwbizVxDQgIQHl5OW7dulXrPfXF5KuZc3Z2RlRUFDIzM82uZ2Zmon///nYaVfMghMCsWbOwZcsW7N69G2FhYWaPh4WFISAgwCz25eXl2Lt3L2P/iOLj45Gbm4ucnBz5LTo6GhMnTkROTg7at2/PWNvIgAEDarRMOXPmDEJDQwHw+9rWSktLoVKZvxSr1Wq51QTj3TisiWtUVBScnJzM7rl27RpOnjzZ8Ng3qFyfmgRTq4k1a9aIvLw8MXfuXOHm5ibOnz9v76E1aTNmzBCenp7i+++/F9euXZPfSktL5XuWLVsmPD09xZYtW0Rubq4YP348t4jbSPXdjkIw1rZy5MgRodFoxNKlS8Uvv/wiNmzYIFxdXcX69evlexhr20lOThZBQUFyq4ktW7YIX19f8frrr8v3MN71U1xcLI4fPy6OHz8uAIjly5eL48ePy22WrIlrSkqKCA4OFllZWeLYsWNi6NChbDVB1vvoo49EaGiocHZ2Fr1795bbIVD9AbD4tnbtWvkeg8EgFi1aJAICAoRWqxWDBg0Subm59ht0M/Jw8sVY285XX30lunXrJrRarYiMjBSrVq0ye5yxtp2ioiIxZ84cERISIlxcXET79u3FwoULRVlZmXwP410/e/bssfg7Ojk5WQhhXVzv3r0rZs2aJby9vYVOpxNPPfWUuHjxYoPHJgkhRMPmzoiIiIjIWqz5IiIiIlIQky8iIiIiBTH5IiIiIlIQky8iIiIiBTH5IiIiIlIQky8iIiIiBTH5IiIiIlIQky8iIgckSRK2bdtm72EQUSNg8kVE9JCpU6dCkqQab8OHD7f30IioGdDYewBERI5o+PDhWLt2rdk1rVZrp9EQUXPCmS8iIgu0Wi0CAgLM3ry8vAAYlwTT0tKQmJgInU6HsLAwbNq0yezjc3NzMXToUOh0Ovj4+GD69OkoKSkxu+df//oXunbtCq1Wi8DAQMyaNcvs8Zs3b+KZZ56Bq6srwsPDsX37dvmxW7duYeLEiWjTpg10Oh3Cw8NrJItE5JiYfBER1cM777yDpKQk/Pjjj5g0aRLGjx+PU6dOAQBKS0sxfPhweHl54ejRo9i0aROysrLMkqu0tDTMnDkT06dPR25uLrZv346OHTuafY53330Xf/nLX3DixAmMGDECEydOxB9//CF//ry8PHzzzTc4deoU0tLS4Ovrq1wAiKj+Gnw0NxFRM5OcnCzUarVwc3Mze1uyZIkQQggAIiUlxexj+vXrJ2bMmCGEEGLVqlXCy8tLlJSUyI9//fXXQqVSifz8fCGEEHq9XixcuLDWMQAQb7/9tvx+SUmJkCRJfPPNN0IIIUaNGiWmTZtmmy+YiBTFmi8iIgvi4uKQlpZmds3b21v+d0xMjNljMTExyMnJAQCcOnUKPXv2hJubm/z4gAEDYDAYcPr0aUiShKtXryI+Pr7OMfTo0UP+t5ubG9zd3VFQUAAAmDFjBpKSknDs2DEkJCRgzJgx6N+/f72+ViJSFpMvIiIL3NzcaiwD/hlJkgAAQgj535bu0el0Vj2fk5NTjY81GAwAgMTERFy4cAFff/01srKyEB8fj5kzZ+KDDz54pDETkfJY80VEVA///ve/a7wfGRkJAOjSpQtycnJw584d+fGDBw9CpVKhU6dOcHd3R7t27fDdd981aAxt2rTB1KlTsX79eqxYsQKrVq1q0PMRkTI480VEZEF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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot_losses(train_losses, val_losses, \"Cox\")" + ] + }, + { + "cell_type": "markdown", + "id": "bd881d14-9646-48e0-bcc3-f29be358161f", + "metadata": {}, + "source": [ + "### Section 1.3: Cox proportional hazards model evaluation\n", + "\n", + "We evaluate the predictive performance of the model using \n", + "\n", + "* the [concordance index](../_autosummary/torchsurv.metrics.cindex.html) (C-index), which measures the the probability that a model correctly predicts which of two comparable samples will experience an event first based on their estimated risk scores,\n", + "* the [Area Under the Receiver Operating Characteristic Curve](../_autosummary/torchsurv.metrics.auc.html) (AUC), which measures the probability that a model correctly predicts which of two comparable samples will experience an event by time t based on their estimated risk scores.\n", + "\n", + "We cannot use the Brier score because this model is not able to estimate the survival function." + ] + }, + { + "cell_type": "markdown", + "id": "0d2e7996", + "metadata": {}, + "source": [ + "We start by evaluating the subject-specific relative hazards on the test set " + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "272a997d-a978-4e9b-bb0b-d90e4f03a530", + "metadata": {}, + "outputs": [], + "source": [ + "with torch.no_grad():\n", + " # test event and test time of length n\n", + " x, (event, time) = next(iter(dataloader_test))\n", + " log_hz = cox_model(x) # log hazard of length n" + ] + }, + { + "cell_type": "markdown", + "id": "77bd0fe9", + "metadata": {}, + "source": [ + "We obtain the concordance index, and its confidence interval" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "3c9ad489-9e53-40ac-8931-8941597760a8", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Cox model performance:\n", + "Concordance-index = 0.6743345260620117\n", + "Confidence interval = tensor([0.5629, 0.7858])\n" + ] + } + ], + "source": [ + "# Concordance index\n", + "cox_cindex = ConcordanceIndex()\n", + "print(\"Cox model performance:\")\n", + "print(f\"Concordance-index = {cox_cindex(log_hz, event, time)}\")\n", + "print(f\"Confidence interval = {cox_cindex.confidence_interval()}\")" + ] + }, + { + "cell_type": "markdown", + "id": "507b410a", + "metadata": {}, + "source": [ + "We can also test whether the observed concordance index is greater than 0.5. The statistical test is specified with H0: c-index = 0.5 and Ha: c-index > 0.5. The p-value of the statistical test is" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "7d34ba82", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "p-value = 0.0010876655578613281\n" + ] + } + ], + "source": [ + "# H0: cindex = 0.5, Ha: cindex > 0.5\n", + "print(\"p-value = {}\".format(cox_cindex.p_value(alternative=\"greater\")))" + ] + }, + { + "cell_type": "markdown", + "id": "a60919a9", + "metadata": {}, + "source": [ + "For time-dependent prediction (e.g., 5-year mortality), the C-index is not a proper measure. Instead, it is recommended to use the AUC. The probability to correctly predicts which of two comparable patients will experience an event by 5-year based on their estimated risk scores is the AUC evaluated at 5-year (1825 days) obtained with" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "907312f9", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "AUC 5-yr = tensor([0.7173])\n", + "AUC 5-yr (conf int.) = tensor([0.6556, 0.7790])\n" + ] + } + ], + "source": [ + "cox_auc = Auc()\n", + "\n", + "new_time = torch.tensor(1825.0)\n", + "\n", + "# auc evaluated at new time = 1825, 5 year\n", + "print(f\"AUC 5-yr = {cox_auc(log_hz, event, time, new_time=new_time)}\")\n", + "print(f\"AUC 5-yr (conf int.) = {cox_auc.confidence_interval()}\")" + ] + }, + { + "cell_type": "markdown", + "id": "41e7e69f", + "metadata": {}, + "source": [ + "As before, we can test whether the observed Auc at 5-year is greater than 0.5. The statistical test is specified with H0: auc = 0.5 and Ha: auc > 0.5. The p-value of the statistical test is" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "id": "702e5a74", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "AUC (p_value) = tensor([0.])\n" + ] + } + ], + "source": [ + "print(f\"AUC (p_value) = {cox_auc.p_value()}\")" + ] + }, + { + "cell_type": "markdown", + "id": "b8f517e6-b0a4-4fbc-aac5-b500b4aca169", + "metadata": {}, + "source": [ + "## Section 2: Weibull accelerated failure time (AFT) model" + ] + }, + { + "cell_type": "markdown", + "id": "769ddcf5", + "metadata": {}, + "source": [ + "In this section, we use the [Weibull accelerated failure (AFT) model](../_autosummary/torchsurv.loss.weibull.html). Given covariate $x_{i}$, the hazard of patient $i$ at time $t$ has the form\n", + "$$\n", + "\\lambda (t|x_{i}) = \\frac{\\rho(x_{i}) } {\\lambda(x_{i}) } + \\left(\\frac{t}{\\lambda(x_{i})}\\right)^{\\rho(x_{i}) - 1}\n", + "$$\n", + "\n", + "Given the hazard form, it can be shown that the event density follows a Weibull distribution parametrized by scale $\\lambda(x_{i})$ and shape $\\rho(x_{i})$. The subject-specific risk of event occurence at time $t$ is captured through the hazards $\\{\\lambda (t|x_{i})\\}_{i = 1, \\dots, N}$. We train a multi-layer perceptron (MLP) to model the subject-specific log scale, $\\log \\lambda(x_{i})$, and the log shape, $\\log\\rho(x_{i})$. " + ] + }, + { + "cell_type": "markdown", + "id": "a580702e", + "metadata": {}, + "source": [ + "### Section 2.1: MLP model for log scale and log shape" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "id": "35b92c10-e5fb-491d-9e27-743bcffdced2", + "metadata": {}, + "outputs": [], + "source": [ + "# Same architecture than Cox model, beside outputs dimension\n", + "weibull_model = torch.nn.Sequential(\n", + " torch.nn.BatchNorm1d(num_features), # Batch normalization\n", + " torch.nn.Linear(num_features, 32),\n", + " torch.nn.ReLU(),\n", + " torch.nn.Dropout(),\n", + " torch.nn.Linear(32, 64),\n", + " torch.nn.ReLU(),\n", + " torch.nn.Dropout(),\n", + " torch.nn.Linear(64, 2), # Estimating log parameters for Weibull model\n", + ")" + ] + }, + { + "cell_type": "markdown", + "id": "e96c6985", + "metadata": {}, + "source": [ + "### Section 2.2: MLP model training" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "id": "3d5c6f77-6245-42b0-ae48-33b57789b651", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch: 000, Training loss: 76835.60\n", + "Epoch: 010, Training loss: 116.18\n", + "Epoch: 020, Training loss: 107.70\n", + "Epoch: 030, Training loss: 96.55\n", + "Epoch: 040, Training loss: 93.25\n", + "Epoch: 050, Training loss: 94.60\n", + "Epoch: 060, Training loss: 93.17\n", + "Epoch: 070, Training loss: 94.66\n", + "Epoch: 080, Training loss: 92.07\n", + "Epoch: 090, Training loss: 90.39\n" + ] + } + ], + "source": [ + "torch.manual_seed(42)\n", + "\n", + "# Init optimizer for Weibull\n", + "optimizer = torch.optim.Adam(weibull_model.parameters(), lr=LEARNING_RATE)\n", + "\n", + "# Initialize empty list to store loss on train and validation sets\n", + "train_losses = []\n", + "val_losses = []\n", + "\n", + "# training loop\n", + "for epoch in range(EPOCHS):\n", + " epoch_loss = torch.tensor(0.0)\n", + " for i, batch in enumerate(dataloader_train):\n", + " x, (event, time) = batch\n", + " optimizer.zero_grad()\n", + " log_params = weibull_model(x) # shape = (16, 2)\n", + " loss = neg_log_likelihood(log_params, event, time, reduction=\"mean\")\n", + " loss.backward()\n", + " optimizer.step()\n", + " epoch_loss += loss.detach()\n", + "\n", + " if epoch % (EPOCHS // 10) == 0:\n", + " print(f\"Epoch: {epoch:03}, Training loss: {epoch_loss:0.2f}\")\n", + "\n", + " # Reccord losses for the following figure\n", + " train_losses.append(epoch_loss)\n", + " with torch.no_grad():\n", + " x, (event, time) = next(iter(dataloader_val))\n", + " val_losses.append(\n", + " neg_log_likelihood(weibull_model(x), event, time, reduction=\"mean\")\n", + " )" + ] + }, + { + "cell_type": "markdown", + "id": "4aba21b6", + "metadata": {}, + "source": [ + "We can visualize the training and validation losses." + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "id": "243a4fa9-f751-46e7-83f3-e623bfd3518e", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot_losses(train_losses, val_losses, \"Weibull\")" + ] + }, + { + "cell_type": "markdown", + "id": "86139132-d337-47b7-a8ad-eac1e255f91d", + "metadata": {}, + "source": [ + "### Section 2.3: Weibull AFT model evaluation\n", + "\n", + "We evaluate the predictive performance of the model using \n", + "\n", + "* the [C-index](../_autosummary/torchsurv.metrics.cindex.html), which measures the the probability that a model correctly predicts which of two comparable samples will experience an event first based on their estimated risk scores,\n", + "* the [AUC](../_autosummary/torchsurv.metrics.auc.html), which measures the probability that a model correctly predicts which of two comparable samples will experience an event by time t based on their estimated risk scores, and\n", + "* the [Brier score](../_autosummary/torchsurv.metrics.brier_score.html), which measures the model's calibration by calculating the mean square error between the estimated survival function and the empirical (i.e., in-sample) event status." + ] + }, + { + "cell_type": "markdown", + "id": "1cb226f5", + "metadata": {}, + "source": [ + "We start by obtaining the subject-specific log hazard and survival probability at every time $t$ observed on the test set" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "id": "11599a1f-597b-4ebf-8a15-d3f9db1ebcca", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "torch.Size([206, 206])\n" + ] + } + ], + "source": [ + "with torch.no_grad():\n", + " # event and time of length n\n", + " x, (event, time) = next(iter(dataloader_test))\n", + " log_params = weibull_model(x) # shape = (n,2)\n", + "\n", + "# Compute the log hazards from weibull log parameters\n", + "log_hz = log_hazard(log_params, time) # shape = (n,n)\n", + "\n", + "# Compute the survival probability from weibull log parameters\n", + "surv = survival_function(log_params, time) # shape = (n,n)" + ] + }, + { + "cell_type": "markdown", + "id": "7e309515", + "metadata": {}, + "source": [ + "We can evaluate the concordance index, its confidence interval and the p-value of the statistical test testing whether the c-index is greater than 0.5:" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "id": "afd7e7a5-c909-41eb-a48f-a9c9832eb33b", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Weibull model performance:\n", + "Concordance-index = 0.5990798473358154\n", + "Confidence interval = tensor([0.4707, 0.7275])\n", + "p-value = 0.06523442268371582\n" + ] + } + ], + "source": [ + "# Concordance index\n", + "weibull_cindex = ConcordanceIndex()\n", + "print(\"Weibull model performance:\")\n", + "print(f\"Concordance-index = {weibull_cindex(log_hz, event, time)}\")\n", + "print(f\"Confidence interval = {weibull_cindex.confidence_interval()}\")\n", + "\n", + "# H0: cindex = 0.5, Ha: cindex >0.5\n", + "print(f\"p-value = {weibull_cindex.p_value(alternative = 'greater')}\")" + ] + }, + { + "cell_type": "markdown", + "id": "d985e48c", + "metadata": {}, + "source": [ + "For time-dependent prediction (e.g., 5-year mortality), the C-index is not a proper measure. Instead, it is recommended to use the AUC. The probability to correctly predicts which of two comparable patients will experience an event by 5-year based on their estimated risk scores is the AUC evaluated at 5-year (1825 days) obtained with" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "id": "ca4e6c56", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "AUC 5-yr = tensor([0.5298])\n", + "AUC 5-yr (conf int.) = tensor([0.4742, 0.5854])\n", + "AUC 5-yr (p value) = tensor([0.1467])\n", + "torch.Size([206])\n" + ] + } + ], + "source": [ + "new_time = torch.tensor(1825.0)\n", + "\n", + "# subject-specific log hazard at \\5-yr\n", + "log_hz_t = log_hazard(log_params, time=new_time) # shape = (n)\n", + "weibull_auc = Auc()\n", + "\n", + "# auc evaluated at new time = 1825, 5 year\n", + "print(f\"AUC 5-yr = {weibull_auc(log_hz_t, event, time, new_time=new_time)}\")\n", + "print(f\"AUC 5-yr (conf int.) = {weibull_auc.confidence_interval()}\")\n", + "print(f\"AUC 5-yr (p value) = {weibull_auc.p_value(alternative='greater')}\")" + ] + }, + { + "cell_type": "markdown", + "id": "66b00e9f", + "metadata": {}, + "source": [ + "Lastly, we can evaluate the time-dependent Brier score and the integrated Brier score" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "id": "b1d99480-b643-4836-acd3-7614fa903543", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Brier score = tensor([0.0849, 0.0897, 0.0969, 0.1017, 0.1075])\n", + "Brier score (conf int.) = tensor([[0.0661, 0.0696, 0.0757, 0.0798, 0.0845],\n", + " [0.1037, 0.1099, 0.1181, 0.1237, 0.1304]])\n", + "Integrated Brier score = 0.18183745443820953\n" + ] + } + ], + "source": [ + "brier_score = BrierScore()\n", + "\n", + "# brier score at first 5 times\n", + "print(f\"Brier score = {brier_score(surv, event, time)[:5]}\")\n", + "print(f\"Brier score (conf int.) = {brier_score.confidence_interval()[:,:5]}\")\n", + "\n", + "# integrated brier score\n", + "print(f\"Integrated Brier score = {brier_score.integral()}\")" + ] + }, + { + "cell_type": "markdown", + "id": "0ca1d08c", + "metadata": {}, + "source": [ + "We can test whether the time-dependent Brier score is smaller than what would be expected if the survival model was not providing accurate predictions beyond random chance. We use a bootstrap permutation test and obtain the p-value with:" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "id": "9754fdcd", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Brier score (p-val) = tensor([0.0090, 0.0420, 0.0490, 0.0700, 0.1420])\n" + ] + } + ], + "source": [ + "# H0: bs = bs0, Ha: bs < bs0; where bs0 is the expected brier score if the survival model was not providing accurate predictions beyond random chance.\n", + "\n", + "# p-value for brier score at first 5 times\n", + "print(f\"Brier score (p-val) = {brier_score.p_value(alternative = 'less')[:5]}\")" + ] + }, + { + "cell_type": "markdown", + "id": "31f7e7f6-8f07-4f82-8653-8d0d2d1ed84f", + "metadata": {}, + "source": [ + "## Section 3: Models comparison\n", + "\n", + "We can compare the predictive performance of the Cox proportional hazards model against the Weibull AFT model." + ] + }, + { + "cell_type": "markdown", + "id": "ed057468-ce75-4d3e-a825-71b55effcec8", + "metadata": {}, + "source": [ + "### Section 3.1: Concordance index\n", + "The statistical test is formulated as follows, H0: cindex cox = cindex weibull, Ha: cindex cox > cindex weibull" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "id": "ea66963f-2537-4390-bb65-c773275b292b", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Cox cindex = 0.6743345260620117\n", + "Weibull cindex = 0.5990798473358154\n", + "p-value = 0.16538496315479279\n" + ] + } + ], + "source": [ + "print(f\"Cox cindex = {cox_cindex.cindex}\")\n", + "print(f\"Weibull cindex = {weibull_cindex.cindex}\")\n", + "print(\"p-value = {}\".format(cox_cindex.compare(weibull_cindex)))" + ] + }, + { + "cell_type": "markdown", + "id": "f478e8df", + "metadata": {}, + "source": [ + "### Section 3.2: AUC at 5-year\n", + "\n", + "The statistical test is formulated as follows, H0: 5-yr auc cox = 5-yr auc weibull, Ha: 5-yr auc cox > 5-yr auc weibull" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "id": "0c4e1651", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Cox 5-yr AUC = tensor([0.7173])\n", + "Weibull 5-yr AUC = tensor([0.6096])\n", + "p-value = tensor([0.0025])\n" + ] + } + ], + "source": [ + "print(f\"Cox 5-yr AUC = {cox_auc.auc}\")\n", + "print(f\"Weibull 5-yr AUC = {weibull_auc.auc}\")\n", + "print(\"p-value = {}\".format(cox_auc.compare(weibull_auc)))" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.10.13" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/docs/notebooks/momentum.ipynb b/docs/notebooks/momentum.ipynb new file mode 100644 index 0000000..2d558f8 --- /dev/null +++ b/docs/notebooks/momentum.ipynb @@ -0,0 +1,494 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "9c99b800-422a-4631-9b0f-192eefab4c6d", + "metadata": {}, + "source": [ + "# Momentum survival: MNIST use case\n", + "\n", + "In this example, we will use the pytorch lightning framework to further show how easy is it to use `torchsurv`" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "eac2861e-9c15-4ab6-85b0-f8120a07119f", + "metadata": {}, + "outputs": [], + "source": [ + "import torch\n", + "import pytorch_lightning as L\n", + "from torchvision.models import resnet18\n", + "from torchvision.transforms import v2\n", + "\n", + "from torchsurv.loss.cox import neg_partial_log_likelihood\n", + "from torchsurv.loss.momentum import Momentum" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "85c14ecf-33f2-4b48-bc94-db582e02bc8f", + "metadata": {}, + "outputs": [], + "source": [ + "# For simplicity (or laziness), we already implemented the datamodule for MNIST. See code for details\n", + "from helpers_momentum import MNISTDataModule, LitMomentum, LitMNIST" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "307fea5f-9a28-4258-90ea-05c3793d5a59", + "metadata": {}, + "outputs": [], + "source": [ + "import warnings\n", + "warnings.filterwarnings('ignore')" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "794004c5-588c-4590-ae96-c6d9e52109ff", + "metadata": {}, + "outputs": [], + "source": [ + "BATCH_SIZE = 256" + ] + }, + { + "cell_type": "markdown", + "id": "75d28cbc-89df-428f-bb6a-a313696ebddf", + "metadata": {}, + "source": [ + "## Model backbone\n", + "\n", + "First we need to define out model backbone. We will use here the resnet18." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "c216fa33-de09-4be2-82cc-83cb73db3a42", + "metadata": {}, + "outputs": [], + "source": [ + "resnet = resnet18(weights=None)\n", + "# Fit grayscale images\n", + "resnet.conv1 = torch.nn.Conv2d(1, 64, kernel_size=(7, 7), stride=(2, 2), padding=(3, 3), bias=False)\n", + "# Output log hazards\n", + "resnet.fc = torch.nn.Linear(in_features=resnet.fc.in_features, out_features=1)" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "8056a675-fbce-4f4b-86c0-ab7dd924e4b1", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "torch.Size([6, 1, 224, 224])\n", + "torch.Size([6, 1])\n" + ] + } + ], + "source": [ + "# Transforms our images\n", + "transforms =v2.Compose([v2.ToImage(), v2.ToDtype(torch.float32, scale=True), v2.Resize(224, antialias=True), v2.Normalize(mean=(0,), std=(1,))])\n", + "\n", + "# Sanity check\n", + "x = torch.randn((6, 1, 28, 28))\n", + "print(f'{transforms(x).shape}')\n", + "print(f'{resnet(transforms(x)).shape}')" + ] + }, + { + "cell_type": "markdown", + "id": "0948492c-3e2a-405e-b239-cbb4483b50b8", + "metadata": {}, + "source": [ + "## Regular training" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "1e7a2c7e-a1ef-42fa-ba74-1d33a1dcf2f3", + "metadata": {}, + "outputs": [], + "source": [ + "model_regular = LitMNIST(resnet)\n" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "5c579509-3b71-4229-a916-6191eb572af7", + "metadata": {}, + "outputs": [], + "source": [ + "# Define experiment\n", + "datamodule = MNISTDataModule(batch_size=BATCH_SIZE, transforms=transforms)" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "3f577acf-a821-41a4-8544-318617755d1e", + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "GPU available: True (mps), used: True\n", + "TPU available: False, using: 0 TPU cores\n", + "IPU available: False, using: 0 IPUs\n", + "HPU available: False, using: 0 HPUs\n", + "Running in `fast_dev_run` mode: will run the requested loop using 5 batch(es). Logging and checkpointing is suppressed.\n" + ] + } + ], + "source": [ + "# Define trainer\n", + "trainer = L.Trainer(\n", + " accelerator=\"auto\",\n", + " logger=False,\n", + " enable_checkpointing=False,\n", + " fast_dev_run=5, # Quick dev, \n", + ")" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "430079cc-4fad-4da2-8ea5-aa904c41ec0e", + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "\n", + " | Name | Type | Params\n", + "---------------------------------\n", + "0 | model | ResNet | 11.2 M\n", + "---------------------------------\n", + "11.2 M Trainable params\n", + "0 Non-trainable params\n", + "11.2 M Total params\n", + "44.683 Total estimated model params size (MB)\n" + ] + }, + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "c50d667ea0d341409feb4e4f0e98157a", + "version_major": 2, + "version_minor": 0 + }, + "text/plain": [ + "Training: | | 0/? 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z#9esZ{9$@#tejQ^an3xHxWTpFW?wnU(0uB(K`S2gT)Y_rm&iZQDA`mgO$w1mkD#h; zKw#y&JB-6KAiYSmUBaY4K9;rEwEpGPmg_X;o3YP6k+}ah4P$&JEL@}?wy5cQ6E0k` zyz3>*qI}ctX18y1N{d)^JOPoI7>ylU-MwUQry|x4=NCbQv)v6iD44M_1OMlsB9QE& z(yCmyxLZY%-g%LCFL~fz!{W9yiYco+AzpKFVW6Z2@sKN?e((r6n zvfjtLehWlFZ1D7G;qq?6V4K+%+HMVxN%_U{$mH@chaLL+VP*Q?|NLi-|ByRc1 z|9QcGUhtn6{O1M#dBJ~P@Shj_=LP?H!T;Y2l(wk%gN`cHaF5a#jvfL3G*onyb8lHb F`#&$9k>>ya literal 0 HcmV?d00001 diff --git a/docs/source/references.bib b/docs/source/references.bib new file mode 100644 index 0000000..1339f0c --- /dev/null +++ b/docs/source/references.bib @@ -0,0 +1,203 @@ +@article{Cox1972, + title = {Regression Models and Life‐Tables}, + volume = {34}, + ISSN = {2517-6161}, + number = {2}, + journal = {Journal of the Royal Statistical Society: Series B (Methodological)}, + publisher = {Wiley}, + author = {Cox, D. R.}, + year = {1972}, + month = jan, + pages = {187–202} +} + +@article{Breslow1975, + title = {Analysis of Survival Data under the Proportional Hazards Model}, + volume = {43}, + ISSN = {0306-7734}, + number = {1}, + journal = {International Statistical Review / Revue Internationale de Statistique}, + publisher = {JSTOR}, + author = {Breslow, N. E.}, + year = {1975}, + month = apr, + pages = {45} +} + +@article{Efron1977, + title = {The Efficiency of Cox’s Likelihood Function for Censored Data}, + volume = {72}, + ISSN = {1537-274X}, + number = {359}, + journal = {Journal of the American Statistical Association}, + publisher = {Informa UK Limited}, + author = {Efron, Bradley}, + year = {1977}, + month = sep, + pages = {557–565} +} + +@article{Kzlers2018, + title = {The Weibull Distribution}, + volume = {15}, + ISSN = {1740-9713}, + number = {2}, + journal = {Significance}, + publisher = {Oxford University Press (OUP)}, + author = {Kızılers\"{u}, Ayşe and Kreer, Markus and Thomas, Anthony W.}, + year = {2018}, + month = apr, + pages = {10–11} +} + +@misc{he2019, + author = {He, Kaiming and Fan, Haoqi and Wu, Yuxin and Xie, Saining and Girshick, Ross}, + description = {Momentum Contrast for Unsupervised Visual Representation Learning}, + keywords = {cs.CV}, + title = {Momentum Contrast for Unsupervised Visual Representation Learning}, + url = {http://arxiv.org/abs/1911.05722}, + year = 2019 +} + +@article{Harrell1996, + title = {Multivariable Prognostic Models: Issues In Developing Models, Evaluating Assumptions And Adequacy, And Measuring And Reducing ErrorsS}, + volume = {15}, + ISSN = {1097-0258}, + number = {4}, + journal = {Statistics in Medicine}, + publisher = {Wiley}, + author = {Harrell, Frank E. and Lee, Kerry L. and Mark, Daniel B.}, + year = {1996}, + month = feb, + pages = {361–387} +} + +@article{Uno2011, + title = {On the C‐statistics for evaluating overall adequacy of risk prediction procedures with censored survival data}, + volume = {30}, + ISSN = {1097-0258}, + number = {10}, + journal = {Statistics in Medicine}, + publisher = {Wiley}, + author = {Uno, Hajime and Cai, Tianxi and Pencina, Michael J. and D’Agostino, Ralph B. and Wei, L. J.}, + year = {2011}, + month = jan, + pages = {1105–1117} +} + +@article{Blanche2018, + title = {The c-index is not proper for the evaluation of $t$-year predicted risks}, + volume = {20}, + ISSN = {1468-4357}, + number = {2}, + journal = {Biostatistics}, + publisher = {Oxford University Press (OUP)}, + author = {Blanche, Paul and Kattan, Michael W and Gerds, Thomas A}, + year = {2018}, + month = feb, + pages = {347–357} +} + +@article{Heagerty2005, + title = {Survival Model Predictive Accuracy and ROC Curves}, + volume = {61}, + ISSN = {1541-0420}, + number = {1}, + journal = {Biometrics}, + publisher = {Oxford University Press (OUP)}, + author = {Heagerty, Patrick J. and Zheng, Yingye}, + year = {2005}, + month = feb, + pages = {92–105} +} + +@article{Blanche2013, + title = {Review and comparison of ROC curve estimators for a time‐dependent outcome with marker‐dependent censoring}, + volume = {55}, + ISSN = {1521-4036}, + number = {5}, + journal = {Biometrical Journal}, + publisher = {Wiley}, + author = {Blanche, Paul and Dartigues, Jean‐Fran\c{c}ois and Jacqmin‐Gadda, Hélène}, + year = {2013}, + month = jun, + pages = {687–704} +} + +@article{Uno2007, + title = {Evaluating Prediction Rules fort-Year Survivors With Censored Regression Models}, + volume = {102}, + ISSN = {1537-274X}, + number = {478}, + journal = {Journal of the American Statistical Association}, + publisher = {Informa UK Limited}, + author = {Uno, Hajime and Cai, Tianxi and Tian, Lu and Wei, L. J}, + year = {2007}, + month = jun, + pages = {527–537} +} + +@article{Blanche2013b, + title = {Estimating and comparing time‐dependent areas under receiver operating characteristic curves for censored event times with competing risks}, + volume = {32}, + ISSN = {1097-0258}, + number = {30}, + journal = {Statistics in Medicine}, + publisher = {Wiley}, + author = {Blanche, Paul and Dartigues, Jean‐Fran\c{c}ois and Jacqmin‐Gadda, Hélène}, + year = {2013}, + month = sep, + pages = {5381–5397} +} + +@article{Pencina2004, + title = {Overall C as a measure of discrimination in survival analysis: model specific population value and confidence interval estimation}, + volume = {23}, + ISSN = {1097-0258}, + number = {13}, + journal = {Statistics in Medicine}, + publisher = {Wiley}, + author = {Pencina, Michael J. and D’Agostino, Ralph B.}, + year = {2004}, + month = jun, + pages = {2109–2123} +} + +@article{Graf1999, + title = {Assessment and comparison of prognostic classification schemes for survival data}, + volume = {18}, + ISSN = {1097-0258}, + number = {17–18}, + journal = {Statistics in Medicine}, + publisher = {Wiley}, + author = {Graf, Erika and Schmoor, Claudia and Sauerbrei, Willi and Schumacher, Martin}, + year = {1999}, + month = sep, + pages = {2529–2545} +} + +@article{Carroll2003, + title = {On the use and utility of the Weibull model in the analysis of survival data}, + volume = {24}, + ISSN = {0197-2456}, + number = {6}, + journal = {Controlled Clinical Trials}, + publisher = {Elsevier BV}, + author = {Carroll, Kevin J.}, + year = {2003}, + month = dec, + pages = {682–701} +} + +@article{Kaplan1958, + title = {Nonparametric Estimation from Incomplete Observations}, + volume = {53}, + ISSN = {1537-274X}, + number = {282}, + journal = {Journal of the American Statistical Association}, + publisher = {Informa UK Limited}, + author = {Kaplan, E. L. and Meier, Paul}, + year = {1958}, + month = jun, + pages = {457–481} +} \ No newline at end of file diff --git a/docs/stats.rst b/docs/stats.rst new file mode 100644 index 0000000..bfff45a --- /dev/null +++ b/docs/stats.rst @@ -0,0 +1,8 @@ +Stats +======= + +.. autosummary:: + :toctree: _autosummary + + torchsurv.stats.kaplan_meier + torchsurv.stats.ipcw diff --git a/pyproject.toml b/pyproject.toml new file mode 100644 index 0000000..fa7ee7f --- /dev/null +++ b/pyproject.toml @@ -0,0 +1,18 @@ +[build-system] +requires = ["setuptools", "wheel"] +build-backend = "setuptools.build_meta" + +[project] +name = "torchsurv" +version = "0.1.0" +description = "Survival analysis made easy with pytorch" +authors = [ + {name = "Thibaud Coroller", email = "thibaud.coroller@novartis.com"}, + {name = "Melodie Monod", email = "melodie.monod@novartis.com"}, + {name = "Peter Krusche", email = "peter.krusche@novartis.com"} +] +license = {file = "LICENSE.txt"} + +[tool.pylint] +max-line-length = 120 +disable = ["C0114", "C0116", "R0801"] diff --git a/src/__init__.py b/src/__init__.py new file mode 100644 index 0000000..e69de29 diff --git a/src/torchsurv/__init__.py b/src/torchsurv/__init__.py new file mode 100644 index 0000000..fd58288 --- /dev/null +++ b/src/torchsurv/__init__.py @@ -0,0 +1,3 @@ +""" This is the main module of the `torchsurv` package. + It contains the main classes and functions to perform + survival analysis using PyTorch.""" diff --git a/src/torchsurv/loss/__init__.py b/src/torchsurv/loss/__init__.py new file mode 100644 index 0000000..d4397ed --- /dev/null +++ b/src/torchsurv/loss/__init__.py @@ -0,0 +1,2 @@ +""" This module defines various loss functions for survival analysis. +""" diff --git a/src/torchsurv/loss/cox.py b/src/torchsurv/loss/cox.py new file mode 100644 index 0000000..4e8cbb1 --- /dev/null +++ b/src/torchsurv/loss/cox.py @@ -0,0 +1,264 @@ +import sys +import warnings + +import torch + + +def neg_partial_log_likelihood( + log_hz: torch.Tensor, + event: torch.Tensor, + time: torch.Tensor, + ties_method: str = "efron", + reduction: str = "mean", + checks: bool = True, +) -> torch.Tensor: + r"""Compute the negative of the partial log likelihood for the Cox proportional hazards model. + + Args: + log_hz (torch.Tensor, float): + Log relative hazard of length n_samples. + event (torch.Tensor, bool): + Event indicator of length n_samples (= True if event occured). + time (torch.Tensor): + Time-to-event or censoring of length n_samples. + ties_method (str): + Method to handle ties in event time. Defaults to "efron". + Must be one of the following: "efron", "breslow". + reduction (str): + Method to reduce losses. Defaults to "mean". + Must be one of the following: "sum", "mean". + checks (bool): + Whether to perform input format checks. + Enabling checks can help catch potential issues in the input data. + Defaults to True. + + Returns: + (torch.tensor, float): + Negative of the partial log likelihood. + + Note: + For each subject :math:`i \in \{1, \cdots, N\}`, denote :math:`X_i` as the survival time and :math:`D_i` as the + censoring time. Survival data consist of the event indicator, :math:`\delta_i=1(X_i\leq D_i)` + (argument ``event``) and the time-to-event or censoring, :math:`T_i = \min(\{ X_i,D_i \})` + (argument ``time``). + + The log hazard function for the Cox proportional hazards model has the form: + + .. math:: + + \log \lambda_i (t) = \log \lambda_{0}(t) + \log \theta_i + + where :math:`\log \theta_i` is the log relative hazard (argument ``log_hz``). + + **No ties in event time.** + If the set :math:`\{T_i: \delta_i = 1\}_{i = 1, \cdots, N}` represent unique event times (i.e., no ties), + the standard Cox partial likelihood can be used :cite:p:`Cox1972`. Let :math:`\tau_1 < \tau_2 < \cdots < \tau_N` + be the ordered times and let :math:`R(\tau_i) = \{ j: \tau_j \geq \tau_i\}` + be the risk set at :math:`\tau_i`. The partial log likelihood is defined as: + + .. math:: + + pll = \sum_{i: \: \delta_i = 1} \left(\log \theta_i - \log\left(\sum_{j \in R(\tau_i)} \theta_j \right) \right) + + **Ties in event time handled with Breslow's method.** + Breslow's method :cite:p:`Breslow1975` describes the approach in which the procedure described above is used unmodified, + even when ties are present. If two subjects A and B have the same event time, subject A will be at risk for the + event that happened to B, and B will be at risk for the event that happened to A. + Let :math:`\xi_1 < \xi_2 < \cdots` denote the unique ordered times (i.e., unique :math:`\tau_i`). Let :math:`H_k` be the set of + subjects that have an event at time :math:`\xi_k` such that :math:`H_k = \{i: \tau_i = \xi_k, \delta_i = 1\}`, and let :math:`m_k` + be the number of subjects that have an event at time :math:`\xi_k` such that :math:`m_k = |H_k|`. + + .. math:: + + pll = \sum_{k} \left( {\sum_{i\in H_{k}}\log \theta_i} - m_k \: \log\left(\sum_{j \in R(\tau_k)} \theta_j \right) \right) + + + **Ties in event time handled with Efron's method.** + An alternative approach that is considered to give better results is the Efron's method :cite:p:`Efron1977`. + As a compromise between the Cox's and Breslow's method, Efron suggested to use the average + risk among the subjects that have an event at time :math:`\xi_k`: + + .. math:: + + \bar{\theta}_{k} = {\frac {1}{m_{k}}}\sum_{i\in H_{k}}\theta_i + + Efron approximation of the partial log likelihood is defined by + + .. math:: + + pll = \sum_{k} \left( {\sum_{i\in H_{k}}\log \theta_i} - \sum_{r =0}^{m_{k}-1} \log\left(\sum_{j \in R(\xi_k)}\theta_j-r\:\bar{\theta}_{j}\right)\right) + + + Examples: + >>> log_hz = torch.tensor([0.1, 0.2, 0.3, 0.4, 0.5]) + >>> event = torch.tensor([1, 0, 1, 0, 1], dtype=torch.bool) + >>> time = torch.tensor([1., 2., 3., 4., 5.]) + >>> neg_partial_log_likelihood(log_hz, event, time) # default, mean of log likelihoods across patients + tensor(1.0071) + >>> neg_partial_log_likelihood(log_hz, event, time, reduction = 'sum') # sun of log likelihoods across patients + tensor(3.0214) + >>> time = torch.tensor([1., 2., 2., 4., 5.]) # Dealing with ties (default: Efron) + >>> neg_partial_log_likelihood(log_hz, event, time, ties_method = "efron") + tensor(1.0873) + >>> neg_partial_log_likelihood(log_hz, event, time, ties_method = "breslow") # Dealing with ties (Bfron) + tensor(1.0873) + + References: + + .. bibliography:: + :filter: False + + Cox1972 + Breslow1975 + Efron1977 + + """ + + if checks: + _check_inputs(log_hz, event, time) + + if any([event.sum() == 0, len(log_hz.size()) == 0]): + warnings.warn("No events OR single sample. Returning zero loss for the batch") + return torch.tensor(0.0, requires_grad=True) + + # sort data by time-to-event or censoring + time_sorted, idx = torch.sort(time) + log_hz_sorted = log_hz[idx] + event_sorted = event[idx] + time_unique = torch.unique(time_sorted) # time-to-event or censoring without ties + + if len(time_unique) == len(time_sorted): + # if not ties, use traditional cox partial likelihood + pll = _partial_likelihood_cox(log_hz_sorted, event_sorted) + else: + # if ties, use either efron or breslow approximation of partial likelihood + if ties_method == "efron": + pll = _partial_likelihood_efron( + log_hz_sorted, + event_sorted, + time_sorted, + time_unique, + ) + elif ties_method == "breslow": + pll = _partial_likelihood_breslow(log_hz_sorted, event_sorted, time_sorted) + else: + raise ValueError( + f'Ties method {ties_method} should be one of ["efron", "breslow"]' + ) + + # Negative partial log likelihood + pll = torch.neg(pll) + if reduction.lower() == "mean": + return pll.nanmean() + elif reduction.lower() == "sum": + return pll.sum() + else: + raise ( + ValueError( + f"Reduction {reduction} is not implemented yet, should be one of ['mean', 'sum']." + ) + ) + + +def _partial_likelihood_cox( + log_hz_sorted: torch.Tensor, + event_sorted: torch.Tensor, +) -> torch.Tensor: + """Calculate the partial log likelihood for the Cox proportional hazards model + in the absence of ties in event time. + """ + log_denominator = torch.logcumsumexp(log_hz_sorted.flip(0), dim=0).flip(0) + return (log_hz_sorted - log_denominator)[event_sorted == True] + + +def _partial_likelihood_efron( + log_hz_sorted: torch.Tensor, + event_sorted: torch.Tensor, + time_sorted: torch.Tensor, + time_unique: torch.Tensor, +) -> torch.Tensor: + """Calculate the partial log likelihood for the Cox proportional hazards model + using Efron's method to handle ties in event time. + """ + J = len(time_unique) + + H = [ + torch.where((time_sorted == time_unique[j]) & (event_sorted == 1))[0] + for j in range(J) + ] + R = [torch.where(time_sorted >= time_unique[j])[0] for j in range(J)] + + m = torch.tensor([len(h) for h in H]) + include = torch.tensor([len(h) > 0 for h in H]) + + log_nominator = torch.stack([torch.sum(log_hz_sorted[h]) for h in H]) + + denominator_naive = torch.stack([torch.sum(torch.exp(log_hz_sorted[r])) for r in R]) + denominator_ties = torch.stack([torch.sum(torch.exp(log_hz_sorted[h])) for h in H]) + + log_denominator_efron = torch.zeros(J).to(log_hz_sorted.device) + for j in range(J): + for l in range(1, m[j] + 1): + log_denominator_efron[j] += torch.log( + denominator_naive[j] - (l - 1) / m[j] * denominator_ties[j] + ) + return (log_nominator - log_denominator_efron)[include == True] + + +def _partial_likelihood_breslow( + log_hz_sorted: torch.Tensor, + event_sorted: torch.Tensor, + time_sorted: torch.Tensor, +): + """Calculate the partial log likelihood for the Cox proportional hazards model + using Breslow's method to handle ties in event time. + """ + N = len(time_sorted) + + R = [torch.where(time_sorted >= time_sorted[i])[0] for i in range(N)] + log_denominator = torch.tensor( + [torch.logsumexp(log_hz_sorted[R[i]], dim=0) for i in range(N)] + ) + + return (log_hz_sorted - log_denominator)[event_sorted == True] + + +def _check_inputs(log_hz: torch.Tensor, event: torch.Tensor, time: torch.Tensor): + if isinstance(log_hz, torch.Tensor) == False: + raise TypeError("Input 'log_hz' must be a tensor.") + + if isinstance(event, torch.Tensor) == False: + raise TypeError("Input 'event' must be a tensor.") + + if isinstance(time, torch.Tensor) == False: + raise TypeError("Input 'time' must be a tensor.") + + if len(log_hz) != len(event): + raise ValueError( + "Length mismatch: 'log_hz' and 'event' must have the same length." + ) + + if len(time) != len(event): + raise ValueError( + "Length mismatch: 'time' must have the same length as 'event'." + ) + + if any(val < 0 for val in time): + raise ValueError("Invalid values: All elements in 'time' must be non-negative.") + + if any(val not in [True, False, 0, 1] for val in event): + raise ValueError( + "Invalid values: 'event' must contain only boolean values (True/False or 1/0)" + ) + + +if __name__ == "__main__": + import doctest + + # Run doctest + results = doctest.testmod() + if results.failed == 0: + print("All tests passed.") + else: + print("Some doctests failed.") + sys.exit(1) diff --git a/src/torchsurv/loss/momentum.py b/src/torchsurv/loss/momentum.py new file mode 100644 index 0000000..3b9f908 --- /dev/null +++ b/src/torchsurv/loss/momentum.py @@ -0,0 +1,198 @@ +import collections +import copy +import sys +from typing import Callable + +import torch +from torch import nn + + +class Momentum(nn.Module): + r""" + Survival framework to momentum update learning to decouple batch size during model training. + Two networks are concurently trained, an online network and a target network. The online network outputs batches + are concanetaed and used by the target network, so it virtually increase its batchsize. + + The target network is updated using an exponential moving average: + + .. math:: + + ( \theta_k \leftarrow m \theta_k + (1 - m) \theta_q) + + Note: + This code is inspired from MoCo :cite:p:`he2019` and its ability to decouple batch size from training size. + + References: + .. bibliography:: + :filter: False + + he2019 + + """ + + def __init__( + self, + backbone: nn.Module, + loss: Callable, + batchsize: int = 16, + n: int = 4, + m: float = 0.999, + ): + """ + Initialise the momentum class. Use must provide their model as backbone. + + Args: + backbone (nn.Module): + Torch model to be use as backbone. The model must return either one (Cox) or two ouputs (Weibull) + loss (Callable): Torchsurv loss function (Cox, Weibull) + batchsize (int, optional): + Number of samples per batch. Defaults to 16. + n (int, optional): + Number of queued batches to be stored for training. Defaults to 4. + m (float, optional): + Exponential moving average rate. Defaults to 0.999. + + Examples: + >>> from torchsurv.loss import cox, weibull + >>> _ = torch.manual_seed(42) + >>> n = 4 + >>> params = torch.randn((n, 16)) + >>> events = torch.randint(low=0, high=2, size=(n,), dtype=torch.bool) + >>> times = torch.randint(low=1, high=100, size=(n,)) + >>> backbone = torch.nn.Sequential(torch.nn.Linear(16, 1)) # Cox expect one ouput + >>> model = Momentum(backbone=backbone, loss=cox.neg_partial_log_likelihood) + >>> model(params, events, times) + tensor(0.0978, grad_fn=) + >>> model.online(params) # online network (q) - w/ gradient + tensor([[-0.7867], + [ 0.3161], + [-1.2158], + [-0.8195]], grad_fn=) + >>> model.target(params) # target network (k) - w/o gradient + tensor([[-0.7867], + [ 0.3161], + [-1.2158], + [-0.8195]]) + + Note: + `self.encoder_k` is the recommended to be used for inference. It refers to the target network (momentum). + """ + super().__init__() + self.m = m + self.online = copy.deepcopy(backbone) # q >> online network + self.target = copy.deepcopy(backbone) # k >> target network (momentum) + self._init_encoder_k() + self.loss = loss + + # survival data structure + self.survtuple = collections.namedtuple( + "survival", field_names=["estimate", "event", "time"] + ) + + # Hazards: current batch & memory + self.memory_q = collections.deque(maxlen=batchsize) # q >> online network + self.memory_k = collections.deque(maxlen=batchsize * n) # k >> target network + + def forward( + self, x: torch.Tensor, event: torch.Tensor, time: torch.Tensor + ) -> torch.Tensor: + """Forward tensor pass over the model + + Args: + x (torch.Tensor): Input tensors to the backbone model + event (torch.Tensor): A boolean tensor indicating whether a patient experienced an event. + time (torch.Tensor): A positive float tensor representing time to event (or censoring time) + + Returns: + torch.Tensor: A loss tensor for the current batch. + + Examples: + >>> from torchsurv.loss import cox, weibull + >>> _ = torch.manual_seed(42) + >>> n = 128 # samples + >>> x = torch.randn((n, 16)) + >>> y = torch.randint(low=0, high=2, size=(n,)).bool() + >>> t = torch.randint(low=1, high=100, size=(n,)) + >>> backbone = torch.nn.Sequential(torch.nn.Linear(16, 1)) # (log hazards) + >>> model_cox = Momentum(backbone, loss=cox.neg_partial_log_likelihood) # Cox loss + >>> with torch.no_grad(): model_cox.forward(x, y, t) + tensor(2.1366) + >>> backbone = torch.nn.Sequential(torch.nn.Linear(16, 2)) # (lambda, rho) + >>> model_weibull = Momentum(backbone, loss=weibull.neg_log_likelihood) # Weibull loss + >>> with torch.no_grad(): torch.round(model_weibull.forward(x, y, t), decimals=2) + tensor(68.0400) + + """ + + estimate_q = self.online(x) + for e in zip(estimate_q, event, time): + self.memory_q.append(self.survtuple(*[e for e in e])) + loss = self._bank_loss() + with torch.no_grad(): + self._update_momentum_encoder() + estimate_k = self.target(x) + for e in zip(estimate_k, event, time): + self.memory_k.append(self.survtuple(*[e for e in e])) + return loss + + def eval(self, x: torch.Tensor) -> torch.Tensor: + """Evaluate data with target network + + Args: + x (torch.Tensor): Input tensors to the backbone model + + Returns: + torch.Tensor: Predictions from target (momentum) network without augmentation (.eval()) nor gradient. + + Examples: + >>> from torchsurv.loss import weibull + >>> _ = torch.manual_seed(42) + >>> backbone = torch.nn.Sequential(torch.nn.Linear(8, 2)) # Cox expect one ouput + >>> model = Momentum(backbone=backbone, loss=weibull.neg_log_likelihood) + >>> model.eval(torch.randn((3, 8))) + tensor([[ 0.5342, 0.0062], + [ 0.6439, 0.7863], + [ 0.9771, -0.8513]]) + + """ + + with torch.no_grad(): + return self.online.eval()(x) + + def _bank_loss(self) -> torch.Tensor: + """computer the negative loss likelyhood from memory bank""" + + # Combine current batch and momentum + bank = self.memory_k + self.memory_q + assert all( + x in bank[0]._fields for x in ["estimate", "event", "time"] + ), "All fields must be present" + return self.loss( + torch.stack([mem.estimate.cpu() for mem in bank]).squeeze(), + torch.stack([mem.event.cpu() for mem in bank]).squeeze(), + torch.stack([mem.time.cpu() for mem in bank]).squeeze(), + ) + + @torch.no_grad() + def _update_momentum_encoder(self): + """Exponantial moving average""" + for param_b, param_m in zip(self.online.parameters(), self.target.parameters()): + param_m.data = param_m.data * self.m + param_b.data * (1.0 - self.m) + + @torch.no_grad() + def _init_encoder_k(self): + for param_q, param_k in zip(self.online.parameters(), self.target.parameters()): + param_k.data.copy_(param_q.data) + param_k.requires_grad = False + + +if __name__ == "__main__": + import doctest + + # Run doctest + results = doctest.testmod() + if results.failed == 0: + print("All tests passed.") + else: + print("Some doctests failed.") + sys.exit(1) diff --git a/src/torchsurv/loss/weibull.py b/src/torchsurv/loss/weibull.py new file mode 100644 index 0000000..e43db66 --- /dev/null +++ b/src/torchsurv/loss/weibull.py @@ -0,0 +1,369 @@ +import sys + +import torch + +TORCH_CLAMP_VALUE = 1e10 + + +def neg_log_likelihood( + log_params: torch.Tensor, + event: torch.Tensor, + time: torch.Tensor, + reduction: str = "mean", + checks: bool = True, +) -> torch.Tensor: + r""" + Negative of the log likelihood for the Weibull Accelerated Time Failure (AFT) survival model. + + Args: + log_params (torch.Tensor, float): + Parameters of the Weibull distribution of shape = (n_samples, 1) or (n_samples, 2). + The first column corresponds to the log scale parameter. The second column + corresponds to the log shape parameter. If the log shape parameter is missing, it is + imputed with 0. + event (torch.Tensor, bool): + Event indicator of length n_samples (= True if event occured). + time (torch.Tensor, float): + Time-to-event or censoring of length n_samples. + reduction (str): + Method to reduce losses. Defaults to "mean". + Must be one of the following: "sum", "mean". + checks (bool): + Whether to perform input format checks. + Enabling checks can help catch potential issues in the input data. + Defaults to True. + + Returns: + (torch.Tensor, float): Negative of the log likelihood. + + Note: + + For each subject :math:`i \in \{1, \cdots, N\}`, denote :math:`X_i` as the survival time and :math:`D_i` as the + censoring time. Survival data consist of the event indicator, :math:`\delta_i=1(X_i\leq D_i)` + (argument ``event``) and the time-to-event or censoring, :math:`T_i = \min(\{ X_i,D_i \})` + (argument ``time``). + + The log hazard function for the Weibull AFT survival model :cite:p:`Carroll2003` of subject :math:`i` at time :math:`t` has the form: + + .. math:: + + \log h_i(t) = \log{\rho_i} - \log{\lambda_i} + (\rho_i -1) \left( \log{t} - \log{\lambda_i}\right) + + where :math:`\log{\lambda_i}` is the log scale parameter (first column of argument ``log_params``) + and :math:`\log{\rho_i}` is the log shape parameter (second column of argument ``log_params``). + The cumulative hazard for the Weibull survival model of subject :math:`i` at time :math:`t` has the form: + + .. math:: + + H_i(t) = \left(\frac{t}{\lambda_i}\right)^{\rho_i} + + The survival function for the Weibull survival model of subject :math:`i` at time :math:`t` has the form: + + .. math:: + + S_i(t) = 1 - F(t | \lambda_i, \rho_i) + + where :math:`F(t | \lambda, \rho)` is the cumulative distribution function (CDF) of the Weibull distribution given + scale parameter :math:`\lambda` and shape parameter :math:`\rho`. + + The log likelihood of the Weibull survival model is + + .. math:: + + ll = \sum_{i: \delta_i = 1} \log h_i(T_i) - \sum_{i = 1}^N H_i(T_i) + + Examples: + >>> _ = torch.manual_seed(42) + >>> n = 4 + >>> log_params = torch.randn((n, 2)) + >>> event = torch.randint(low=0, high=2, size=(n,), dtype=torch.bool) + >>> time = torch.randint(low=1, high=100, size=(n,)) + >>> neg_log_likelihood(log_params, event, time) # Default: mean of log likelihoods across subject + tensor(47.5035) + >>> neg_log_likelihood(log_params, event, time, reduction = 'sum') # Sum of log likelihoods across subject + tensor(190.0141) + >>> neg_log_likelihood(torch.randn((n, 1)), event, time) # Missing shape: exponential decrease + tensor(66.7203) + + References: + + .. bibliography:: + :filter: False + + Carroll2003 + + """ + + if checks: + _check_inputs(log_params, event, time) + + # Negative log likelihood + ll = torch.neg( + event * log_hazard(log_params, time, all_times=False) + - cumulative_hazard(log_params, time, all_times=False) # Huge values here + ) + + if any(torch.isinf(ll)): + # Remove any torch.inf values + ll = ll[~torch.isinf(ll)] + + if reduction.lower() == "mean": + return ll.nanmean() + elif reduction.lower() == "sum": + return ll.sum() + else: + raise ( + ValueError( + f"Reduction {reduction} is not implemented yet, should be one of ['mean', 'sum']." + ) + ) + + +def survival_function( + log_params: torch.Tensor, time: torch.Tensor, all_times: bool = True +) -> torch.Tensor: + """Survival function for the Weibull Accelerated Time Failure (AFT) survival model. + + Args: + log_params (torch.Tensor, float): + Parameters of the Weibull distribution of shape = (n_samples, 1) or (n_samples, 2). + The first column corresponds to the log scale parameter. The second column + corresponds to the log shape parameter. If the log shape parameter is missing, it is + imputed with 0. + time (torch.Tensor, float): + Time at which to evaluate the survival function. + Should be of length n_samples to evaluate the survival function at observed time-to-event or censoring, + or of length one to evaluate the survival function at a new time. + all_times (bool): + If True, subject-specific survival function is evaluated at all ``time`` (used for evaluation metrics). + If False, subject-specific survival function is evaluated at respective ``time``. + Defaults is True. + Ignored if ``time`` is of length one. + + Returns: + (torch.Tensor, float): Subject-specific survival function evaluated at ``time``. + + Examples: + >>> _ = torch.manual_seed(42) + >>> time = torch.randint(low=1, high=100, size=(4,)) + >>> log_params = torch.randn((4, 2)) + >>> survival_function(log_params, time, all_times = False) # Survival at respective time + tensor([0.0002, 0.0000, 0.0299, 0.0000]) + >>> survival_function(log_params, time, all_times = True) # Default. Survival at all observed time + tensor([[1.7941e-04, 0.0000e+00, 0.0000e+00, 0.0000e+00], + [2.8610e-06, 0.0000e+00, 0.0000e+00, 0.0000e+00], + [4.1870e-01, 3.1040e-02, 2.9881e-02, 6.8224e-02], + [9.5576e-04, 0.0000e+00, 0.0000e+00, 0.0000e+00]]) + >>> survival_function(log_params, time=torch.tensor(10.0)) # Survival at one new time (e.g., 10 years) + tensor([1.3709e-06, 5.9605e-08, 3.4954e-01, 1.5438e-05]) + >>> for t in torch.tensor([100.0, 150.0]): survival_function(log_params, time=t) # Subject-specific survival at multiple new times + tensor([0.0000, 0.0000, 0.0288, 0.0000]) + tensor([0.0000, 0.0000, 0.0123, 0.0000]) + + + """ + log_scale, log_shape = _check_log_shape(log_params).unbind(1) + + if time.dim() == 0: + # Use one time for each sample + time = time.repeat(len(log_params)) + elif all([time.size(0) == log_params.size(0), all_times]): + # Use all times for each sample + time = time.unsqueeze(0).expand(len(time), len(time)) # expand across rows + log_scale = log_scale.unsqueeze(1).expand( + len(time), len(time) + ) # expand across columns + log_shape = log_shape.unsqueeze(1).expand( + len(time), len(time) + ) # expand across columns + if time.size(0) != log_params.size(0): + raise ValueError( + f"Dimension mismatch: 'time' ({len(time)}) does not match the length of 'log_params' ({len(log_params)})." + ) + return 1 - torch.distributions.weibull.Weibull( + torch.exp(log_scale), torch.exp(log_shape) + ).cdf(time) + + +def log_hazard( + log_params: torch.Tensor, time: torch.Tensor, all_times: bool = True +) -> torch.Tensor: + """Log hazard of the Weibull Accelerated Time Failure (AFT) survival model. + + Args: + log_params (torch.Tensor, float): + Parameters of the Weibull distribution of shape = (n_samples, 1) or (n_samples, 2). + The first column corresponds to the log scale parameter. The second column + corresponds to the log shape parameter. If the log shape parameter is missing, it is + imputed with 0. + time (torch.Tensor, float): + Time at which to evaluate the log hazard. + Should be of length n_samples to evaluate the log hazard at observed time-to-event or censoring, + or of length one to evaluate the log hazard at a new time. + all_times (bool): + If True, subject-specific log hazard is evaluated at all ``time`` (used for evaluation metrics). + If False, subject-specific log hazard is evaluated at respective ``time``. + Defaults is True. + Ignored if ``time`` is of length one. + + Returns: + (torch.Tensor, float): Subject-specific log hazard evaluated at ``time``. + + Examples: + >>> _ = torch.manual_seed(42) + >>> time = torch.randint(low=1, high=100, size=(4,)) + >>> log_params = torch.randn((4, 2)) + >>> log_hazard(log_params, time, all_times = False) # Log hazard at respective time + tensor([ 0.4392, -0.0303, -3.9672, 0.9140]) + >>> log_hazard(log_params, time, all_times = True) # Default. Log hazard at all time + tensor([[ 0.4392, 1.1174, 1.1227, 0.9913], + [ 0.4148, -0.0303, -0.0338, 0.0525], + [-2.7225, -3.9575, -3.9672, -3.7279], + [ 0.2606, 1.0632, 1.0695, 0.9140]]) + >>> log_hazard(log_params, time=torch.tensor(10.0)) # Log hazard at one new time (e.g., 10 years) + tensor([ 0.5316, 0.3542, -2.8907, 0.3699]) + >>> for t in torch.tensor([100.0, 150.0]): log_hazard(log_params, time=t) # Subject-specific log hazard at multiple new times + tensor([ 1.1280, -0.0372, -3.9767, 1.0757]) + tensor([ 1.2330, -0.1062, -4.1680, 1.1999]) + """ + + log_scale, log_shape = _check_log_shape(log_params).unbind(1) + + if time.dim() == 0: + # Use fixed time for each sample + time = time.repeat(len(log_params)) + elif all([time.size(0) == log_params.size(0), all_times]): + # Use all times for each sample + time = time.unsqueeze(0).expand(len(time), len(time)) # expand across rows + log_scale = log_scale.unsqueeze(1).expand( + len(time), len(time) + ) # expand across columns + log_shape = log_shape.unsqueeze(1).expand( + len(time), len(time) + ) # expand across columns + if time.size(0) != log_params.size(0): + raise ValueError( + f"Dimension mismatch: 'time' ({len(time)}) does not match the length of 'log_params' ({len(log_params)})." + ) + + return ( + log_shape + - log_scale + + torch.expm1(log_shape) + * (torch.log(torch.clip(time, 1e-100, torch.inf)) - log_scale) + ) + + +def cumulative_hazard( + log_params: torch.Tensor, time: torch.Tensor, all_times: bool = True +) -> torch.Tensor: + """Cumulative hazard for the Weibull Accelerated Time Failure (AFT) survival model. + + Args: + log_params (torch.Tensor, float): + Parameters of the Weibull distribution of shape = (n_samples, 1) or (n_samples, 2). + The first column corresponds to the log scale parameter. The second column + corresponds to the log shape parameter. If the log shape parameter is missing, it is + imputed with 0. + time (torch.Tensor, float): + Time-to-event or censoring of length n_samples. + all_times (bool) + If True, subject-specific cumulative hazard is evaluated at all ``time`` (used for evaluation metrics). + If False, subject-specific cumulative hazard is evaluated at respective ``time``. + Defaults is True. + + Returns: + (torch.Tensor, float): Subject-specific cumulative hazard evaluated at ``time``. + + Examples: + >>> _ = torch.manual_seed(42) + >>> time = torch.randint(low=1, high=100, size=(4,)) + >>> log_params = torch.randn((4, 2)) + >>> cumulative_hazard(log_params, time, all_times=False) # Cumulative hazard at respective time + tensor([ 8.6257, 112.2115, 3.5105, 112.6339]) + >>> cumulative_hazard(log_params, time, all_times=True) # Default. Cumulative hazard at all time + tensor([[ 8.6257, 233.0865, 239.2167, 126.2805], + [ 12.7698, 112.2115, 114.1484, 74.9134], + [ 0.8706, 3.4725, 3.5105, 2.6850], + [ 6.9530, 212.7592, 218.5687, 112.6339]]) + """ + log_scale, log_shape = _check_log_shape(log_params).unbind(1) + + if all_times: + # Use all times for each sample + time = time.unsqueeze(0).expand(len(time), len(time)) # expand across rows + log_scale = log_scale.unsqueeze(1).expand( + len(time), len(time) + ) # expand across columns + log_shape = log_shape.unsqueeze(1).expand( + len(time), len(time) + ) # expand across columns + + return torch.clamp( + torch.exp( + torch.exp(log_shape) + * (torch.log(torch.clip(time, 1e-100, torch.inf)) - log_scale) + ), + min=0, + max=TORCH_CLAMP_VALUE, + ) + + +def _check_log_shape(log_params: torch.Tensor) -> torch.Tensor: + """Private function, check if the log shape is missing and impute it with 0 + if needed.""" + if any( + [ + log_params.dim() == 0, + log_params.dim() == 1, # if shape = [n_samples] + log_params.dim() > 1 + and log_params.size(1) == 1, # if shape = [n_samples, 1] + ] + ): + if log_params.dim() == 1: + log_params = log_params.unsqueeze(1) + + # Missing log shape parameter. Creating zeros placeholder instead. + log_params = torch.hstack((log_params, torch.zeros_like(log_params))) + + return log_params + + +def _check_inputs(log_params: torch.Tensor, event: torch.Tensor, time: torch.Tensor): + """Private function, perform input format checks.""" + if isinstance(log_params, torch.Tensor) == False: + raise TypeError("Input 'log_params' must be a tensor.") + + if isinstance(event, torch.Tensor) == False: + raise TypeError("Input 'event' must be a tensor.") + + if isinstance(time, torch.Tensor) == False: + raise TypeError("``Input 'time' must be a tensor.") + + if log_params.shape[0] != len(event): + raise ValueError( + "Length mismatch: The length of 'log_params' must match the length of 'event'." + ) + + if len(time) != len(event): + raise ValueError( + "Length mismatch: The length of 'time' must match the length of 'event'.`" + ) + + if any(val < 0 for val in time): + raise ValueError("All elements in 'time' must be non-negative.") + + if any(val not in [True, False, 0, 1] for val in event): + raise ValueError("All elements in 'event' must be boolean (True/False or 0/1).") + + +if __name__ == "__main__": + import doctest + + # Run doctest + results = doctest.testmod() + if results.failed == 0: + print("All tests passed.") + else: + print("Some doctests failed.") + sys.exit(1) diff --git a/src/torchsurv/metrics/__init__.py b/src/torchsurv/metrics/__init__.py new file mode 100644 index 0000000..05262e1 --- /dev/null +++ b/src/torchsurv/metrics/__init__.py @@ -0,0 +1 @@ +""" Module with metrics for model evaluation. """ diff --git a/src/torchsurv/metrics/auc.py b/src/torchsurv/metrics/auc.py new file mode 100644 index 0000000..5400d68 --- /dev/null +++ b/src/torchsurv/metrics/auc.py @@ -0,0 +1,1297 @@ +""" AUC metrics module """ + +import sys +from typing import Optional + +import torch +from scipy import stats +from torchmetrics import regression + +from ..stats.kaplan_meier import KaplanMeierEstimator +from ..tools.validate_inputs import ( + validate_estimate, + validate_evaluation_time, + validate_survival_data, +) + + +class Auc: + def __init__(self, checks: bool = True, tied_tol: float = 1e-8): + """Initialize an Auc for survival class model evaluation. + + Args: + tied_tol (float): + Tolerance for tied risk scores. + Defaults to 1e-8. + checks (bool): + Whether to perform input format checks. + Enabling checks can help catch potential issues in the input data. + Defaults to True. + + Examples: + >>> _ = torch.manual_seed(42) + >>> n = 10 + >>> time = torch.randint(low=5, high=250, size=(n,)).float() + >>> event = torch.randint(low=0, high=2, size=(n,)).bool() + >>> estimate = torch.randn((n,)) + >>> auc = Auc() + >>> auc(estimate, event, time) # default: auc cumulative/dynamic + tensor([0.7500, 0.4286, 0.3333]) + >>> auc.integral() + tensor(0.5040) + >>> auc.confidence_interval() # default: Blanche, two_sided + tensor([[0.4213, 0.0000, 0.0000], + [1.0000, 0.9358, 0.7289]]) + >>> auc.p_value() + tensor([0.1360, 0.7826, 0.4089]) + """ + self.tied_tol = tied_tol + self.checks = checks + + def __call__( + self, + estimate: torch.Tensor, + event: torch.Tensor, + time: torch.Tensor, + auc_type: str = "cumulative", + weight: Optional[torch.Tensor] = None, + new_time: Optional[torch.Tensor] = None, + weight_new_time: Optional[torch.Tensor] = None, + instate: bool = True, + ) -> torch.Tensor: + r"""Compute the time-dependent Area Under the Receiver Operating Characteristic Curve (AUC). + + The AUC at time :math:`t` is the probability that a model correctly predicts + which of two comparable samples will experience an event by time :math:`t` based on their + estimated risk scores. + The AUC is particularly useful for evaluating time-dependent predictions (e.g., 10-year mortality). + It is recommended to use AUC instead of the concordance index for such time-dependent predictions, as + AUC is proper in this context, while the concordance index is not :cite:p:`Blanche2018`. + + Args: + estimate (torch.Tensor): + Estimated risk of event occurrence (i.e., risk score). + Can be of shape = (n_samples,) if subject-specific risk score is time-independent, + of shape = (n_samples, n_samples) if subject-specific risk score is evaluated at ``time``, + or of shape = (n_samples, n_times) if subject-specific risk score is evaluated at ``new_time``. + event (torch.Tensor, boolean): + Event indicator of size n_samples (= True if event occured). + time (torch.Tensor, float): + Time-to-event or censoring of size n_samples. + auc_type (str, optional): + AUC type. Defaults to "cumulative". + Must be one of the following: "cumulative" for cumulative/dynamic, "incident" for incident/dynamic. + weight (torch.Tensor, optional): + Optional sample weight evaluated at ``time`` of size n_samples. + Defaults to 1. + new_time (torch.Tensor, optional): + Time points at which to evaluate the AUC of size n_times. Values must be within the range of follow-up in ``time``. + Defaults to the event times excluding maximum (because number of controls for t > max(time) is 0). + weight_new_time (torch.tensor): + Optional sample weight evaluated at ``new_time`` of size n_times. + Defaults to 1. + + Returns: + torch.Tensor: AUC evaluated at ``new_time``. + + Note: + The function evaluates either the cumulative/dynamic (C/D) or the incident/dynamic (I/D) AUC (argument ``auc_type``) + at time :math:`t \in \{t_1, \cdots, t_K\}` (argument ``new_time``). + + For each subject :math:`i \in \{1, \cdots, N\}`, denote :math:`X_i` as the survival time and :math:`D_i` as the + censoring time. Survival data consist of the event indicator, :math:`\delta_i=(X_i\leq D_i)` + (argument ``event``) and the time-to-event or censoring, :math:`T_i = \min(\{ X_i,D_i \})` + (argument ``time``). + + The risk score measures the risk (or a proxy thereof) that a subject has an event. + The function accepts time-dependent risk score or time-independent risk score. The time-dependent risk score + of subject :math:`i` is specified through a function :math:`q_i: [0, \infty) \rightarrow \mathbb{R}`. + The time-independent risk score of subject :math:`i` is specified by a constant :math:`q_i`. + The argument ``estimate`` is the estimated risk score. + For time-dependent risk score: if ``new_time`` is specified, the argument ``estimate`` should be of shape = (N,K) + (:math:`(i,k)` th element is :math:`\hat{q}_i(t_k)`); + if ``new_time`` is not specified, the argument ``estimate`` should be of shape = (N,N) + (:math:`(i,j)` th element is :math:`\hat{q}_i(T_j)`) . + For time-independent risk score, the argument ``estimate`` should be of length + N (:math:`i` th element is :math:`\hat{q}_i`). + + The AUC C/D and AUC I/D evaluated at time :math:`t` are defined by + + .. math:: + \text{AUC}^{C/D}(t) = p(q_i(t) > q_j(t) \: | \: X_i \leq t, X_j > t) \\ + \text{AUC}^{I/D}(t) = p(q_i(t) > q_j(t) \: | \: X_i = t, X_j > t). + + + The default estimators of the AUC C/D and AUC I/D at time :math:`t` :cite:p:`Blanche2013` returned by the function are + + .. math:: + + \hat{\text{AUC}}^{C/D}(t) = \frac{\sum_i \sum_j \delta_i \: I(T_i \leq t, T_j > t) I(\hat{q}_i(t) > \hat{q}_j(t))}{\sum_i \delta_i \: I(T_i \leq t) \sum_j I(T_j > t)} \\ + \hat{\text{AUC}}^{I/D}(t) = \frac{\sum_i \sum_j \delta_i \: I(T_i = t, T_j > t) I(\hat{q}_i(t) > \hat{q}_j(t))}{\sum_i \delta_i \: I(T_i = t) \sum_j I(T_j > t)}. + + These estimators are considered naive because, when the event times are censored, all subjects censored + before time point :math:`t` are ignored. Additionally, the naive estimators + converge to an association measure that involves the censoring distribution. + To address this shortcoming, :cite:t:`Uno2007` proposed to employ the + inverse probability weighting technique. In this context, each subject included at time + :math:`t` is weighted by the inverse probability of censoring :math:`\omega(t) = 1 / \hat{D}(t)`, where + :math:`\hat{D}(t)` is the Kaplan-Meier estimate of the censoring distribution, :math:`P(D>t)`. + The censoring-adjusted AUC C/D estimate at time :math:`t` is + + .. math:: + + \hat{\text{AUC}}^{C/D}(t) = \frac{\sum_i \sum_j \delta_i \: \omega(T_i) \: I(T_i \leq t, T_j > t) I(\hat{q}_i(t) > \hat{q}_j(t))}{\sum_i \delta_i \: \omega(T_i) \: I(T_i \leq t) \sum_j I(T_j > t)} \\ + + Note that the censoring-adjusted AUC I/D estimate is the same as the "naive" estimate because the weights are all equal to :math:`\omega(t)`. + + The censoring-adjusted AUC C/D estimate can be obtained by specifying the argument + ``weight``, the weights evaluated at each ``time`` (:math:`\omega(T_1), \cdots, \omega(T_N)`). + If ``new_time`` is specified, the argument ``weight_new_time`` + should also be specified accordingly, the weights evaluated at each ``new_time`` + (:math:`\omega(t_1), \cdots, \omega(t_K)`). The latter is required to compute the standard error of the AUC. + In the context of train/test split, the weights should be derived from the censoring distribution estimated in the training data. + Specifically, the censoring distribution is estimated using the training set and then evaluated at the subject time within the test set. + + Examples: + >>> from torchsurv.stats.ipcw import get_ipcw + >>> _ = torch.manual_seed(42) + >>> n = 20 + >>> time = torch.randint(low=5, high=250, size=(n,)).float() + >>> event = torch.randint(low=0, high=2, size=(n,)).bool() + >>> estimate = torch.randn((n,)) + >>> auc = Auc() + >>> auc(estimate, event, time) # default: naive auc c/d + tensor([0.9474, 0.5556, 0.5294, 0.6429, 0.5846, 0.6389, 0.5844, 0.5139, 0.4028, + 0.5400, 0.4545, 0.7500]) + >>> auc(estimate, event, time, auc_type = "incident") # naive auc i/d + tensor([0.9474, 0.1667, 0.4706, 0.9286, 0.3846, 0.8333, 0.3636, 0.2222, 0.0000, + 0.8000, 0.5000, 1.0000]) + >>> ipcw = get_ipcw(event, time) # ipcw weight at time + >>> auc(estimate, event, time, weight = ipcw) # Uno's auc c/d + tensor([0.9474, 0.5556, 0.5294, 0.6521, 0.5881, 0.6441, 0.5865, 0.5099, 0.3929, + 0.5422, 0.4534, 0.7996]) + >>> new_time = torch.unique(torch.randint(low=100, high=150, size=(n,)).float()) # new time at which to evaluate auc + >>> ipcw_new_time = get_ipcw(event, time, new_time) # ipcw at new_time + >>> auc(estimate, event, time, new_time = new_time, weight = ipcw, weight_new_time = ipcw_new_time) # Uno's auc c/d at new_time + tensor([0.5333, 0.5333, 0.5333, 0.5333, 0.6521, 0.6521, 0.5881, 0.5881, 0.5865, + 0.5865, 0.5865, 0.5865, 0.5865, 0.6018, 0.6018, 0.5099]) + + References: + + .. bibliography:: + :filter: False + + Blanche2018 + Blanche2013 + Uno2007 + """ + + # mandatory input format checks + Auc._validate_auc_inputs( + estimate, time, auc_type, new_time, weight, weight_new_time + ) + + # update inputs as required + estimate, new_time, weight, weight_new_time = Auc._update_auc_new_time( + estimate, event, time, new_time, weight, weight_new_time + ) + estimate = Auc._update_auc_estimate(estimate, new_time) + weight, weight_new_time = Auc._update_auc_weight( + time, new_time, weight, weight_new_time + ) + + # further input format checks + if self.checks: + validate_survival_data(event, time) + validate_evaluation_time(new_time, time) + validate_estimate(estimate, time, new_time) + + # sample size and length of time + n_samples, n_times = estimate.shape[0], new_time.shape[0] + + # Expand arrays to (n_samples, n_times) shape + time_long = time.unsqueeze(1).expand((n_samples, n_times)) + event_long = event.unsqueeze(1).expand((n_samples, n_times)) + weight_long = weight.unsqueeze(1).expand((n_samples, n_times)) + new_time_long = new_time.unsqueeze(0).expand( + n_samples, n_times + ) # Size n_times, unsqueeze(0) instead + + # sort each time point (columns) by risk score (descending) + index = torch.argsort(-estimate, dim=0) + time_long, event_long, estimate, weight_long = map( + lambda x: torch.gather(x, 0, index), + [time_long, event_long, estimate, weight_long], + ) + + # find case and control + if auc_type == "incident": + is_case = (time_long == new_time_long) & event_long + elif auc_type == "cumulative": + is_case = (time_long <= new_time_long) & event_long + is_control = time_long > new_time_long + n_controls = is_control.sum(axis=0) + + # estimate censoring adjusted true positive rate and false positive rate + cumsum_tp = torch.cumsum(is_case * weight_long, axis=0) + cumsum_fp = torch.cumsum(is_control, axis=0) + true_pos = cumsum_tp / cumsum_tp[-1] + false_pos = cumsum_fp / n_controls + + # prepend row of infinity values + estimate_diff = torch.cat( + (torch.full((1, n_times), float("inf")), estimate), dim=0 + ) + is_tied = torch.abs(torch.diff(estimate_diff, dim=0)) <= self.tied_tol + + # initialize empty tensor to store auc + auc = torch.zeros_like(new_time) + + # iterate over time + for i in range(n_times): + # Extract relevant columns for the current time point + tp, fp, mask = true_pos[:, i], false_pos[:, i], is_tied[:, i] + + # Create a boolean mask with False at the indices where ties occur + mask_no_ties = torch.ones(tp.numel(), dtype=torch.bool) + mask_no_ties[torch.nonzero(mask) - 1] = False + + # Extract values without ties using the boolean mask + tp_no_ties = tp[mask_no_ties] + fp_no_ties = fp[mask_no_ties] + + # Add an extra threshold position + # to make sure that the curve starts at (0, 0) + tp_no_ties = torch.cat([torch.tensor([0]), tp_no_ties]) + fp_no_ties = torch.cat([torch.tensor([0]), fp_no_ties]) + + # Calculate AUC using trapezoidal rule for numerical integration + auc[i] = torch.trapz(tp_no_ties, fp_no_ties) + + # Create/overwrite internal attributes states + if instate: + index_rev = torch.argsort(index, dim=0) + estimate, is_case, is_control = map( + lambda x: torch.gather(x, 0, index_rev), + [estimate, is_case, is_control], + ) + + # sort all objects by time + self.order_time = torch.argsort(time, dim=0) + self.time = time[self.order_time] + self.event = event[self.order_time] + self.weight = weight[self.order_time] + self.new_time = new_time + self.weight_new_time = weight_new_time + self.estimate = torch.index_select(estimate, 0, self.order_time) + self.is_case = torch.index_select(is_case, 0, self.order_time) + self.is_control = torch.index_select(is_control, 0, self.order_time) + self.auc_type = auc_type + self.auc = auc + + return auc + + def integral(self, tmax: Optional[torch.Tensor] = None): + """Compute the integral of the time-dependent AUC. + + Args: + tmax (torch.Tensor, optional): + A number specifying the upper limit of the time range to compute the AUC integral. + Defaults to ``new_time[-1]`` for cumulative/dynamic AUC and ``new_time[-1]-1`` for incident/dynamic AUC. + + Returns: + torch.Tensor: Integral of AUC over [0-``tmax``]. + + Examples: + >>> _ = torch.manual_seed(42) + >>> n = 10 + >>> time = torch.randint(low=5, high=250, size=(n,)).float() + >>> event = torch.randint(low=0, high=2, size=(n,)).bool() + >>> estimate = torch.randn((n,)) + >>> auc = Auc() + >>> auc(estimate, event, time, auc_type = "incident") + tensor([0.7500, 0.1429, 0.1667]) + >>> auc.integral() # integral of the auc incident/dynamic + tensor(0.4667) + + Notes: + In case ``auc_type`` = "cumulative" (cumulative/dynamic AUC), the values of AUC are weighted by + the estimated event density. In case ``auc_type`` = "incident" + (incident/dynamic AUC), the values of AUC are weighted by 2 times the product of the estimated + event density and the estimated survival function :cite:p:`Heagerty2005`. + The estimated survival + function is the Kaplan-Meier estimate. The estimated event density + is obtained from the discrete incremental changes of the estimated survival function. + + References: + + .. bibliography:: + :filter: False + + Heagerty2005 + """ + # Only one time step available + if len(self.new_time) == 1: + return self.auc[0] + else: + # handle cases where tmax is not specified + if tmax is None: + tmax = ( + self.new_time[-1] + if self.auc_type == "cumulative" + else self.new_time[-1] - 1 + ) + + # estimate of survival distribution + km = KaplanMeierEstimator() + km(self.event, self.time) + S = km.predict(self.new_time) + + # integral of auc + if self.auc_type == "cumulative": + return self._integrate_AUC_cumulative(S, tmax) + else: + return self._integrate_AUC_incident(S, tmax) + + def confidence_interval( + self, + method: str = "blanche", + alpha: float = 0.05, + alternative: str = "two_sided", + n_bootstraps: int = 999, + ) -> torch.Tensor: + """Compute the confidence interval of the AUC. + + This function calculates either the pointwise confidence interval or the bootstrap + confidence interval for the AUC. The pointwise confidence interval is computed + assuming that the AUC is normally distributed and using the standard error estimated with + :cite:t:`Blanche2013b` method. The bootstrap confidence interval is constructed based on the + distribution of bootstrap samples. + + Args: + method (str): + Method for computing confidence interval. Defaults to "blanche". + Must be one of the following: "blanche", "bootstrap". + alpha (float): + Significance level. Defaults to 0.05. + alternative (str): + Alternative hypothesis. Defaults to "two_sided". + Must be one of the following: "two_sided", "greater", "less". + n_bootstraps (int): + Number of bootstrap samples. Defaults to 999. + Ignored if ``method`` is not "bootstrap". + + Returns: + torch.Tensor([lower,upper]): + Lower and upper bounds of the confidence interval. + + Examples: + >>> _ = torch.manual_seed(42) + >>> n = 10 + >>> time = torch.randint(low=5, high=250, size=(n,)).float() + >>> event = torch.randint(low=0, high=2, size=(n,)).bool() + >>> estimate = torch.randn((n,)) + >>> auc = Auc() + >>> auc(estimate, event, time) + tensor([0.7500, 0.4286, 0.3333]) + >>> auc.confidence_interval() # Default: Blanche, two_sided + tensor([[0.4213, 0.0000, 0.0000], + [1.0000, 0.9358, 0.7289]]) + >>> auc.confidence_interval(method = "bootstrap", alternative = "greater") + tensor([[0.3750, 0.1667, 0.0833], + [1.0000, 1.0000, 1.0000]]) + + References: + + .. bibliography:: + :filter: False + + Blanche2013b + """ + + assert ( + hasattr(self, "auc") and self.auc is not None + ), "Error: Please calculate AUC using `Auc()` before calling `confidence_interval()`." + + if alternative not in ["less", "greater", "two_sided"]: + raise ValueError( + "'alternative' parameter must be one of ['less', 'greater', 'two_sided']." + ) + + if method == "blanche": + return self._confidence_interval_blanche(alpha, alternative) + elif method == "bootstrap": + return self._confidence_interval_bootstrap( + alpha, alternative, n_bootstraps + ).squeeze() + else: + raise ValueError( + "Method not implemented. Please choose either 'blanche' or 'bootstrap'." + ) + + def p_value( + self, + method: str = "blanche", + alternative: str = "two_sided", + n_bootstraps: int = 999, + ) -> torch.Tensor: + """Perform a one-sample hypothesis test on the AUC. + + This function calculates either the pointwise p-value or the bootstrap p-value + for testing the null hypothesis that the AUC is equal to 0.5. + The pointwise p-value is computed assuming that the AUC is normally distributed + and using the standard error estimated using :cite:t:`Blanche2013b` method. + The bootstrap p-value is derived by permuting risk predictions to estimate + the sampling distribution under the null hypothesis. + + Args: + method (str): + Method for computing p-value. Defaults to "blanche". + Must be one of the following: "blanche", "bootstrap". + alternative (str): + Alternative hypothesis. Defaults to "two_sided". + Must be one of the following: "two_sided" (AUC is not equal to 0.5), + "greater" (AUC is greater than 0.5), "less" (AUC is less than 0.5). + n_bootstraps (int): + Number of bootstrap samples. Defaults to 999. + Ignored if ``method`` is not "bootstrap". + + Returns: + torch.Tensor: p-value of the statistical test. + + Examples: + >>> _ = torch.manual_seed(42) + >>> n = 10 + >>> time = torch.randint(low=5, high=250, size=(n,)).float() + >>> event = torch.randint(low=0, high=2, size=(n,)).bool() + >>> estimate = torch.randn((n,)) + >>> auc = Auc() + >>> auc(estimate, event, time) + tensor([0.7500, 0.4286, 0.3333]) + >>> auc.p_value() # Default: Blanche, two_sided + tensor([0.1360, 0.7826, 0.4089]) + >>> auc.p_value(method = "bootstrap", alternative = "greater") + tensor([0.2400, 0.5800, 0.7380]) + + """ + + assert ( + hasattr(self, "auc") and self.auc is not None + ), "Error: Please calculate AUC using `Auc()` before calling `p_value()`." + + if alternative not in ["less", "greater", "two_sided"]: + raise ValueError( + "'alternative' parameter must be one of ['less', 'greater', 'two_sided']." + ) + + if method == "blanche": + return self._p_value_blanche(alternative) + elif method == "bootstrap": + return self._p_value_bootstrap(alternative, n_bootstraps) + else: + raise ValueError( + "Method not implemented. Please choose either 'blanche' or 'bootstrap'." + ) + + def compare( + self, other, method: str = "blanche", n_bootstraps: int = 999 + ) -> torch.tensor: + """Compare two AUCs. + + This function compares two AUCs computed on the same data with different + risk predictions. The statistical hypotheses are + formulated as follows, null hypothesis: auc1 = auc2 and alternative + hypothesis: auc1 > auc2. + The statistical test is either a Student t-test for dependent samples or + a two-sample bootstrap test. The Student t-test assumes that the AUC is normally distributed + and uses the standard errors estimated with :cite:t:`Blanche2013b` method. + + Args: + other (Auc): + Another instance of the Auc class representing auc2. + method (str): + Statistical test used to perform the hypothesis test. Defaults to "blanche". + Must be one of the following: "blanche", "bootstrap". + n_bootstraps (int): + Number of bootstrap samples. Defaults to 999. + Ignored if ``method`` is not "bootstrap". + + Returns: + torch.tensor: p-value of the statistical test. + + Examples: + >>> _ = torch.manual_seed(42) + >>> n = 10 + >>> time = torch.randint(low=5, high=250, size=(n,)).float() + >>> event = torch.randint(low=0, high=2, size=(n,)).bool() + >>> auc1 = Auc() + >>> auc1(torch.randn((n,)), event, time) + tensor([0.7500, 0.4286, 0.3333]) + >>> auc2 = Auc() + >>> auc2(torch.randn((n,)), event, time) + tensor([0.0000, 0.1429, 0.0556]) + >>> auc1.compare(auc2) # default: Blanche + tensor([0.0008, 0.2007, 0.1358]) + >>> auc1.compare(auc2, method = "bootstrap") + tensor([0.0220, 0.1970, 0.1650]) + + """ + + assert ( + hasattr(self, "auc") and self.auc is not None + ), "Error: Please calculate AUC using `Auc()` before calling `compare()`." + + # assert that the same data were used to compute the two auc + if torch.any(self.event != other.event) or torch.any(self.time != other.time): + raise ValueError( + "Mismatched survival data: 'time' and 'event' should be the same for both AUC computations." + ) + if torch.any(self.new_time != other.new_time): + raise ValueError( + "Mismatched evaluation times: 'new_time' should be the same for both AUC computations." + ) + if self.auc_type != other.auc_type: + raise ValueError( + "Mismatched AUC types: 'auc_type' should be the same for both AUC computations." + ) + + if method == "blanche": + return self._compare_blanche(other) + if method == "bootstrap": + return self._compare_bootstrap(other, n_bootstraps) + else: + raise ValueError( + "Method not implemented. Please choose either 'blanche' or 'bootstrap'." + ) + + def _integrate_AUC_incident( + self, S: torch.tensor, tmax: torch.tensor + ) -> torch.Tensor: + """Integrates the incident/dynamic AUC, int_t AUC(t) x w(t) dt + where w(t) = 2*f(t)*S(t) and f(t) is the lifeline distribution, + S(t) is the survival distribution estimated with the Kaplan + Meier estimator. + """ + + # Get the number of unique event times + n_S = len(S) + + # Find the index corresponding to tmax in times + maxI = torch.sum(self.new_time <= tmax) + + # Initialize an array to store the density function f(t) + f = torch.zeros_like(S) + + # Compute the density function f(t) + f[0] = 1.0 - S[0] + for i in range(1, n_S): + f[i] = S[i - 1] - S[i] + + # Initialize a variable to accumulate the weighted sum of f(t)*S(t) + wT = 0.0 + + # Accumulate the weighted sum up to maxI + for i in range(maxI): + wT += 2.0 * f[i] * S[i] + + # Initialize the integrated AUC + i_auc = 0 + + # Calculate the integrated AUC using the weight + for i in range(maxI): + if wT != 0.0: + if f[i] > torch.finfo(torch.double).eps: + i_auc += self.auc[i] * (2.0 * f[i] * S[i]) / wT + + return i_auc + + def _integrate_AUC_cumulative( + self, S: torch.tensor, tmax: torch.tensor + ) -> torch.Tensor: + """Integrates the cumulative/dynamic AUC, int_t AUC(t) · f(t) dt + where f(t) is the lifeline distribution estimated from the discrete + incremental changes of the Kalpan-Meier estimate of the survival function. + """ + + # Get the number of unique event times + n_S = len(S) + + # Find the index corresponding to tmax in times + maxI = torch.sum(self.new_time <= tmax) + + # Initialize an array to store the density function f(t) + f = torch.zeros_like(S) + + # Compute the density function f(t) + f[0] = 1.0 - S[0] + for i in range(1, n_S): + f[i] = S[i - 1] - S[i] + + # Initialize a variable to accumulate the weighted sum of f(t) + wT = 0.0 + + # Accumulate the weighted sum up to maxI + for i in range(maxI): + if f[i] > torch.finfo(torch.double).eps: + wT += f[i] + + # Initialize the integrated AUC + i_auc = 0 + + # Calculate the integrated AUC using the weight + for i in range(maxI): + if wT != 0.0: + if f[i] > torch.finfo(torch.double).eps: + i_auc += self.auc[i] * (f[i]) / wT + + return i_auc + + def _confidence_interval_blanche( + self, alpha: float, alternative: str + ) -> torch.Tensor: + """Confidence interval of AUC assuming that the AUC + is normally distributed and using + standard error estimated with Blanche et al.'s method.""" + + alpha = alpha / 2 if alternative == "two_sided" else alpha + + auc_se = self._auc_se() + + if torch.all(auc_se) >= 0: + ci = ( + -torch.distributions.normal.Normal(0, 1).icdf(torch.tensor(alpha)) + * auc_se + ) + lower = torch.max(torch.tensor(0.0), self.auc - ci) + upper = torch.min(torch.tensor(1.0), self.auc + ci) + + if alternative == "less": + lower = torch.zeros_like(lower) + elif alternative == "greater": + upper = torch.ones_like(upper) + else: + raise ValueError("The standard error of AUC must be a positive value.") + + return torch.stack([lower, upper], dim=0).squeeze() + + def _confidence_interval_bootstrap( + self, alpha: float, alternative: str, n_bootstraps: int + ) -> torch.tensor: + """Bootstrap confidence interval of the AUC using Efron percentile method. + + References: + Efron, Bradley; Tibshirani, Robert J. (1993). + An introduction to the bootstrap, New York: Chapman & Hall, software. + """ + + # auc bootstraps given bootstrap distribution + auc_bootstrap = self._bootstrap_auc( + metric="confidence_interval", n_bootstraps=n_bootstraps + ) + + # intialize tensor to store confidence intervals + lower = torch.zeros_like(self.auc) + upper = torch.zeros_like(self.auc) + + # iterate over time + for index_t in range(len(self.auc)): + # obtain confidence interval + if alternative == "two_sided": + lower[index_t], upper[index_t] = torch.quantile( + auc_bootstrap[:, index_t], + torch.tensor([alpha / 2, 1 - alpha / 2], device=self.auc.device), + ) + elif alternative == "less": + upper[index_t] = torch.quantile( + auc_bootstrap[:, index_t], + torch.tensor(1 - alpha, device=self.auc.device), + ) + lower[index_t] = torch.tensor(0.0, device=self.auc.device) + elif alternative == "greater": + lower[index_t] = torch.quantile( + auc_bootstrap[:, index_t], + torch.tensor(alpha, device=self.auc.device), + ) + upper[index_t] = torch.tensor(1.0, device=self.auc.device) + + return torch.stack([lower, upper], dim=0).squeeze() + + def _p_value_blanche( + self, alternative: str, null_value: float = 0.5 + ) -> torch.tensor: + """p-value for a one-sample hypothesis test of the AUC + assuming that the AUC is normally distributed and using standard error estimated + with Blanche et al's method. + """ + + auc_se = self._auc_se() + + # get p-value + if torch.all(auc_se) >= torch.tensor(0.0): + p = torch.distributions.normal.Normal(0, 1).cdf( + (self.auc - null_value) / auc_se + ) + if alternative == "two_sided": + mask = self.auc >= torch.tensor(0.5) + p[mask] = torch.tensor(1.0) - p[mask] + p *= torch.tensor(2.0) + elif alternative == "greater": + p = torch.tensor(1.0) - p + else: + raise ValueError("The standard error of AUC must be a positive value.") + + return p + + def _p_value_bootstrap(self, alternative, n_bootstraps) -> torch.tensor: + """p-value for a one-sample hypothesis test of the AUC using + permutation of risk prediction to estimate sampling distribution under the null + hypothesis. + """ + + # auc boostraps given null distribution auc = 0.5 + auc0 = self._bootstrap_auc(metric="p_value", n_bootstraps=n_bootstraps) + + # intialize empty tensor to store p-values + p_values = torch.zeros_like(self.auc) + + # iterate over time + for index_t in range(len(self.auc)): + # Derive p-value + p = ( + torch.tensor(1.0) + torch.sum(auc0[:, index_t] <= self.auc[index_t]) + ) / torch.tensor(n_bootstraps + 1.0) + if alternative == "two_sided": + if self.auc[index_t] >= torch.tensor(0.5): + p = torch.tensor(1.0) - p + p *= torch.tensor(2.0) + p = torch.min( + torch.tensor(1.0, device=self.auc.device), p + ) # in case very small bootstrap sample size is used + elif alternative == "greater": + p = torch.tensor(1.0) - p + + p_values[index_t] = p + + return p_values + + def _compare_blanche(self, other): + """Student t-test for dependent samples given Blanche's standard error to + compare two AUCs. + """ + + # sample size + N = self.estimate.shape[0] + + # compute noether standard error + auc1_se = self._auc_se() + auc2_se = other._auc_se() + + # intialize empty vector to store p_values + p_values = torch.zeros_like(self.auc) + + # iterate over time + for index_t in range(len(self.auc)): + # compute spearman correlation between risk prediction + corr = regression.SpearmanCorrCoef()( + self.estimate[:, index_t], other.estimate[:, index_t] + ) + + # check for perfect positive monotonic relationship between two variables + if 1 - torch.abs(corr) < 1e-15: + p_values[index_t] = 1.0 + else: + # compute t-stat + t_stat = (self.auc[index_t] - other.auc[index_t]) / torch.sqrt( + auc1_se[index_t] ** 2 + + auc2_se[index_t] ** 2 + - 2 * corr * auc1_se[index_t] * auc2_se[index_t] + ) + + # p-value + p_values[index_t] = torch.tensor( + 1 + - stats.t.cdf( + t_stat, df=N - 1 + ), # student-t cdf not available on torch + dtype=self.auc.dtype, + device=self.auc.device, + ) + + return p_values + + def _compare_bootstrap(self, other, n_bootstraps): + """Boostrap two-sample test to compare two AUCs.""" + + # auc bootstraps given null hypothesis that auc1 and + # auc2 come from the same distribution + auc1_null = self._bootstrap_auc( + metric="compare", other=other, n_bootstraps=n_bootstraps + ) + auc2_null = self._bootstrap_auc( + metric="compare", other=other, n_bootstraps=n_bootstraps + ) + + # Bootsrapped test statistics + t_boot = auc1_null - auc2_null + + # observed test statistics + t_obs = self.auc - other.auc + + # intialize empty tensor to store p-values + p_values = torch.zeros_like(self.auc) + + # iterate over time + for index_t in range(len(self.auc)): + p_values[index_t] = 1 - ( + 1 + torch.sum(t_boot[:, index_t] <= t_obs[index_t]) + ) / (n_bootstraps + 1) + + return p_values + + def _auc_se(self): + """AUC's standard error estimated using Blanche et al's method.""" + + # sample size and length of time + n_samples, n_times = self.estimate.shape[0], self.new_time.shape[0] + + # number of effective subjects + N = torch.sum(self.weight) + + # survival distribution estimated with KM + km = KaplanMeierEstimator() + km(self.event, self.time) + S = km.predict(self.new_time) + + # Expand arrays to (n_samples, n_times) shape + time_long = torch.unsqueeze(self.time, dim=1).expand((n_samples, n_times)) + new_time_long = self.new_time.unsqueeze(0).expand(n_samples, n_times) + survival_long = S.unsqueeze(0).expand(n_samples, n_times) + + # element (i, t) = I(T_i > t) / S(t) + ipsw = (time_long >= new_time_long) / survival_long + + # element (i,k) = int_0^{T_i} M_Ck(t) / S dt, where M_Ck(t) = I(delta_k = 0, T_k <= t) - int_0^t dLambda_c(u) + integral_M_div_S = self._integral_censoring_martingale_divided_survival() + + # element (i, t) = f_i1t = I(T_i <= t, delta_i = 1) * W(T_i) (if incident, condition for case is T_i = t) + f = self.is_case * self.weight.unsqueeze(1).expand(-1, n_times) + + # element (t) = F_1t = 1/n * sum_i f_i1t + F = 1 / n_samples * torch.sum(f, dim=0) + + # initialize empty tensor to store standard error of auc + auc_se = torch.zeros_like(self.new_time) + + # iterate over time + for index_t in range(n_times): + # element(i,j) given t = h*_tij = I(T_i <= t, delta_i = 1) * I(U_j > t) * (I(M_i > M_j) + 0.5 * I(M_i > M_j)) * W(T_i) * W(t) + h_t = ( + self.is_case[:, index_t].unsqueeze(1) * self.is_control[:, index_t] + ).float() + h_t *= ( + self.estimate[:, index_t].unsqueeze(1) + > self.estimate[:, index_t].unsqueeze(0) + ).float() + 0.5 * ( + self.estimate[:, index_t].unsqueeze(1) + == self.estimate[:, index_t].unsqueeze(0) + ).float() + h_t *= self.weight.unsqueeze(1) + h_t *= self.weight_new_time[index_t] + + # h*_t = 1 / n^2 * sum_i sum_j h_tij + H_t = (1 / (n_samples**2)) * torch.sum(h_t) + + # phi*(t), eq.bottom page 3 of Supplementary Material of Blanche et al. (2013) + phi = Auc._phi_blanche( + h_t, + H_t, + f[:, index_t], + F[index_t], + S[index_t], + integral_M_div_S, + ipsw[:, index_t], + n_samples, + ) + + # sum of phi + sum_phi = ( + torch.sum( + phi, axis=(1, 2) + ) # sum_j sum_k phi_ijk = Les_sum_jk_a_i_fixe * n_samples in Blanche's code + + torch.sum( + phi, axis=(0, 2) + ) # sum_i sum_k phi_ijk = Les_sum_ik_a_j_fixe * n_samples in Blanche's code + + torch.sum( + phi, axis=(0, 1) + ) # sum_i sum_j phi_ijk = Les_sum_ij_a_k_fixe * n_samples in Blanche's code + ) + + # estimate of influence function + hat_IF = 1 / (n_samples**2) * sum_phi + + # estimate of auc standard error + auc_se[index_t] = torch.std(hat_IF) / (n_samples ** (1 / 2)) + + return auc_se + + def _integral_censoring_martingale_divided_survival(self) -> torch.tensor: + """Compute the integral of the censoring martingale divided by the survival distribution.""" + + # Number of samples + n_samples = len(self.time) + + # check that time is ordered + if torch.any(self.time != self.time[torch.argsort(self.time, dim=0)]): + raise ValueError( + "The 'time' values in `self.time` should be ordered in ascending order." + ) + + # find censoring events + censoring = self.event == 0.0 + + # Compute censoring hazard, denoted lambda_C in in Blanche et al's paper + censoring_hazard = censoring / torch.arange(n_samples, 0, -1) + + # cumulative censoring hazard, denoted Lambda_C in Blanche et al's paper + cumsum_censoring_hazard = torch.cumsum(censoring_hazard, dim=0) + + # censoring martingale, denoted M_C in in Blanche et al's paper + censoring_martingale = torch.zeros((n_samples, n_samples), dtype=torch.float32) + for i in range(n_samples): + censoring_martingale[:, i] = censoring[i].float() * ( + self.time[i] <= self.time + ).float() - torch.cat( + ( + cumsum_censoring_hazard[0:i], + torch.full((n_samples - i,), cumsum_censoring_hazard[i]), + ) + ) + + # derivative of censoring martingal, denoted d M_C in Blanche et al's paper + d_censoring_martingale = torch.cat( + ( + censoring_martingale[0, :].view(1, -1), + censoring_martingale[1:, :] - censoring_martingale[:-1, :], + ) + ) + + # divide by empirical survival function + d_censoring_martingale_div_S = torch.stack( + [ + ( + lambda v: v + / torch.cat( + (torch.tensor([1.0]), 1 - torch.arange(1, len(v)) / len(v)) + ) + )(d_censoring_martingale[:, i]) + for i in range(n_samples) + ], + dim=1, + ) + + return torch.cumsum(d_censoring_martingale_div_S, dim=0) + + @staticmethod + def _phi_blanche( + h_t: torch.Tensor, + H_t: torch.Tensor, + f_t: torch.Tensor, + F_t: torch.Tensor, + S_t: torch.Tensor, + integral_M_div_S: torch.Tensor, + ipsw_t: torch.Tensor, + n_samples: int, + ) -> torch.Tensor: + """Compute the three components of the influence function.""" + + phi = torch.zeros( + (n_samples, n_samples, n_samples), + dtype=h_t.dtype, + device=h_t.device, + ) + for i in range(n_samples): + _phi = 1 + integral_M_div_S[:, i] + _phi *= f_t + _phi -= F_t + _phi /= F_t + _phi += ipsw_t + _phi *= -H_t + _phi = _phi.unsqueeze(1).expand(-1, n_samples) + _phi = _phi + ( + h_t * ((1 + integral_M_div_S[:, i]).unsqueeze(1).expand(-1, n_samples)) + ) + _phi /= S_t * F_t + + phi[:, :, i] = _phi + + return phi + + def _bootstrap_auc( + self, metric: str, n_bootstraps: int, other=None + ) -> torch.tensor: + """Compute bootstrap samples of the AUC. + + Args: + metric (str): Must be one of the following: "p_value", "confidence_interval", "compare". + If "p_value", computes bootstrap samples of the AUC given the sampling distribution + under the null hypothesis (AUC = 0.5). If "confidence_interval", computes bootstrap + samples of the AUC given the data distribution. If "compare", computes + bootstrap samples of the AUC given the sampling distribution under the comparison test + null hypothesis (auc1 = auc2). + n_bootstraps (int): Number of boostrap samples. + other (optional, Auc): + Another instance of the Auc class representing auc2. + Only required for ``metric`` is equal to "compare". + + + Returns: + torch.tensor: Bootstrap samples of AUC. + """ + import copy + + # Initiate empty list to store auc + aucs = [] + + # Get the boostrap samples of auc + for _ in range(n_bootstraps): + if ( + metric == "p_value" + ): # bootstrap samples given null distribution (auc = 0.5) + estimate = copy.deepcopy(self.estimate) + estimate = estimate[ + torch.randperm(estimate.shape[0]), : + ] # Shuffle estimate + aucs.append( + self( + estimate, + self.event, + self.time, + self.auc_type, + self.weight, + self.new_time, + self.weight_new_time, + instate=False, + ) + ) # Run without saving internal state + elif ( + metric == "confidence_interval" + ): # bootstrap samples given data distribution + index = torch.randint( + low=0, + high=self.estimate.shape[0], + size=(self.estimate.shape[0] - 2,), + ) + # auc is evaluated at new_time: + # so need to keep the min and max time to ensure that new_time is within follow-up time + index_max_time = torch.argmax(self.time).unsqueeze(0) + index_min_time = torch.nonzero( + self.time == self.time[self.event].min() + ).squeeze(1) + index = torch.cat( + ( + index, + index_max_time, + index_min_time, + ), + dim=0, + ) + + aucs.append( + self( + self.estimate[index, :], + self.event[index], + self.time[index], + self.auc_type, + self.weight[index], + self.new_time, + self.weight_new_time, + instate=False, + ) + ) # Run without saving internal state + + elif ( + metric == "compare" + ): # bootstrap samples given null distribution (auc1 = auc2) + # index included in bootstrap samples + index = torch.randint( + low=0, + high=self.estimate.shape[0] * 2, + size=(self.estimate.shape[0] - 2,), + ) + + # auc is evaluated at new_time: need to keep the indices corresponding to min and max time + # to ensure that new_time is within follow-up time + # with prob 0.5, take the index corresponding to max time from self and with prob 0.5 from other + # same for min time + index_max_time = torch.argmax(self.time).unsqueeze(0) + index_max_time += (torch.rand(1) < 0.5) * self.estimate.shape[0] + index_min_time = torch.nonzero( + self.time == self.time[self.event].min() + ).squeeze(1) + index_min_time += (torch.rand(1) < 0.5) * self.estimate.shape[0] + index = torch.cat( + (index, index_min_time, index_max_time), + dim=0, + ) + + # with prob 0.5, take the weight_new_time from self and with prob 0.5 from other + weight_new_time = ( + self.weight_new_time + if torch.rand(1) < 0.5 + else other.weight_new_time + ) + + aucs.append( + self( # sample with replacement from pooled sample + torch.cat((self.estimate, other.estimate))[index, :], + torch.cat((self.event, other.event))[index], + torch.cat((self.time, other.time))[index], + self.auc_type, + torch.cat((self.weight, other.weight))[index], + self.new_time, + weight_new_time, + instate=False, + ) + ) + + aucs = torch.stack(aucs) + + if torch.any(torch.isnan(aucs)): + raise ValueError("The AUC computed using bootstrap should not be NaN.") + + return aucs + + @staticmethod + def _find_torch_unique_indices( + inverse_indices: torch.tensor, counts: torch.tensor + ) -> torch.tensor: + """return unique_sorted_indices such that + sorted_unique_tensor[inverse_indices] = original_tensor + original_tensor[unique_sorted_indices] = sorted_unique_tensor + + Usage: + _, inverse_indices, counts = torch.unique( + x, sorted=True, return_inverse=True, return_counts=True + ) + sorted_unique_indices = Auc._find_torch_unique_indices( + inverse_indices, counts + ) + """ + + _, ind_sorted = torch.sort(inverse_indices, stable=True) + cum_sum = counts.cumsum(0) + cum_sum = torch.cat((torch.tensor([0]), cum_sum[:-1])) + return ind_sorted[cum_sum] + + @staticmethod + def _validate_auc_inputs( + estimate, time, auc_type, new_time, weight, weight_new_time + ): + + # check new_time and weight are provided, weight_new_time should be provided + if all([new_time is not None, weight is not None, weight_new_time is None]): + raise ValueError( + "Please provide 'weight_new_time', the weight evaluated at 'new_time'." + ) + + # check if auc type is correct + if auc_type not in ["cumulative", "incident"]: + raise ValueError( + "The 'auc_type' parameter must be either 'cumulative' or 'incident'." + ) + + # check if new_time are not specified and time-dependent estimate are not evaluated at time + if new_time is None and estimate.ndim == 2 and estimate.shape[1] != 1: + if len(time) != estimate.shape[1]: + raise ValueError( + "Mismatched dimensions: The number of columns in 'estimate' does not match the length of 'time'. " + "Please provide the times at which 'estimate' is evaluated using the 'new_time' input." + ) + + @staticmethod + def _update_auc_new_time( + estimate: torch.tensor, + event: torch.tensor, + time: torch.tensor, + new_time: torch.tensor, + weight: torch.tensor, + weight_new_time: torch.tensor, + ) -> torch.tensor: + + # update new time + if ( + new_time is not None + ): # if new_time are specified: ensure it has the correct format + + # ensure that new_time are float + if isinstance(new_time, int): + new_time = torch.tensor([new_time]).float() + + # example if new_time is tensor(12), unsqueeze to tensor([12]) + if new_time.ndim == 0: + new_time = new_time.unsqueeze(0) + + else: # else: find new_time + + # if new_time are not specified, use unique event time + mask = event & (time < torch.max(time)) + new_time, inverse_indices, counts = torch.unique( + time[mask], sorted=True, return_inverse=True, return_counts=True + ) + sorted_unique_indices = Auc._find_torch_unique_indices( + inverse_indices, counts + ) + + # select weight corresponding at new time + if weight is not None: + weight_new_time = (weight[mask])[sorted_unique_indices] + + # for time-dependent estimate, select those corresponding to new time + if estimate.ndim == 2 and estimate.shape[1] > 1: + estimate = estimate[:, sorted_unique_indices] + + return estimate, new_time, weight, weight_new_time + + @staticmethod + def _update_auc_estimate( + estimate: torch.tensor, new_time: torch.tensor + ) -> torch.tensor: + + # squeeze estimate if shape = (n_samples, 1) + if estimate.ndim == 2 and estimate.shape[1] == 1: + estimate = estimate.squeeze(1) + + # Ensure estimate is (n_samples, n_times) shape + if estimate.ndim == 1: + estimate = estimate.unsqueeze(1).expand( + (estimate.shape[0], new_time.shape[0]) + ) + + return estimate + + @staticmethod + def _update_auc_weight( + time: torch.tensor, + new_time: torch.tensor, + weight: torch.tensor, + weight_new_time: torch.tensor, + ) -> torch.tensor: + + # if weight was not specified, weight of 1 + if weight is None: + weight = torch.ones_like(time) + weight_new_time = torch.ones_like(new_time) + + return weight, weight_new_time + + +if __name__ == "__main__": + import doctest + + # Run doctest + results = doctest.testmod() + if results.failed == 0: + print("All tests passed.") + else: + print("Some doctests failed.") + sys.exit(1) diff --git a/src/torchsurv/metrics/brier_score.py b/src/torchsurv/metrics/brier_score.py new file mode 100644 index 0000000..9553223 --- /dev/null +++ b/src/torchsurv/metrics/brier_score.py @@ -0,0 +1,902 @@ +import sys +from typing import Optional + +import torch +from scipy import stats + +from ..tools.validate_inputs import ( + validate_estimate, + validate_evaluation_time, + validate_survival_data, +) + + +class BrierScore: + def __init__(self, checks: bool = True): + """Initialize a BrierScore for survival class model evaluation. + + Args: + checks (bool): + Whether to perform input format checks. + Enabling checks can help catch potential issues in the input data. + Defaults to True. + + Examples: + >>> _ = torch.manual_seed(52) + >>> n = 10 + >>> time = torch.randint(low=5, high=250, size=(n,)).float() + >>> event = torch.randint(low=0, high=2, size=(n,)).bool() + >>> estimate = torch.rand((n,len(time))) + >>> brier_score = BrierScore() + >>> brier_score(estimate, event, time) + tensor([0.2463, 0.2740, 0.3899, 0.1964, 0.3608, 0.2821, 0.1932, 0.2978, 0.1950, + 0.1668]) + >>> brier_score.integral() # integrated brier score + tensor(0.2862) + >>> brier_score.confidence_interval() # default: parametric, two-sided + tensor([[0.1061, 0.0604, 0.2360, 0.0533, 0.1252, 0.0795, 0.0000, 0.1512, 0.0381, + 0.0051], + [0.3866, 0.4876, 0.5437, 0.3394, 0.5965, 0.4847, 0.4137, 0.4443, 0.3520, + 0.3285]]) + >>> brier_score.p_value() # default: bootstrap permutation test, two-sided + tensor([1.0000, 0.7860, 1.0000, 0.3840, 1.0000, 1.0000, 0.3840, 1.0000, 0.7000, + 0.2380]) + """ + self.checks = checks + + def __call__( + self, + estimate: torch.Tensor, + event: torch.Tensor, + time: torch.Tensor, + new_time: Optional[torch.Tensor] = None, + weight: Optional[torch.Tensor] = None, + weight_new_time: Optional[torch.Tensor] = None, + instate: bool = True, + ) -> torch.Tensor: + r"""Compute the Brier Score. + + Args: + estimate (torch.Tensor): + Estimated probability of remaining event-free (i.e., survival function). + Can be of shape = (n_samples, n_samples) if subject-specific survival is evaluated at ``time``, + or of shape = (n_samples, n_times) if subject-specific survival is evaluated at ``new_time``. + event (torch.Tensor, boolean): + Event indicator of size n_samples (= True if event occured) + time (torch.Tensor, float): + Time-to-event or censoring of size n_samples. + new_time (torch.Tensor, float, optional): + Time points at which to evaluate the Brier score of size n_times. + Defaults to unique ``time``. + weight (torch.Tensor, optional): + Optional sample weight evaluated at ``time`` of size n_samples. + Defaults to 1. + weight_new_time (torch.tensor, optional): + Optional sample weight evaluated at ``new_time`` of size n_times. + Defaults to 1. + + Returns: + torch.Tensor: Brier score evaluated at ``new_time``. + + Note: + The function evaluates the time-dependent Brier score at time :math:`t \in \{t_1, \cdots, t_T\}` (argument ``new_time``). + + For each subject :math:`i \in \{1, \cdots, N\}`, denote :math:`X_i` as the survival time and :math:`D_i` as the + censoring time. Survival data consist of the event indicator, :math:`\delta_i=(X_i\leq D_i)` + (argument ``event``) and the time-to-event or censoring, :math:`T_i = \min(\{ X_i,D_i \})` + (argument ``time``). + + The survival function, of subject :math:`i` + is specified through :math:`S_i: [0, \infty) \rightarrow [0,1]`. + The argument ``estimate`` is the estimated survival function. If ``new_time`` is specified, it should be of + shape = (N,T) (:math:`(i,k)` th element is :math:`\hat{S}_i(t_k)`); if ``new_time`` is not specified, + it should be of shape = (N,N) (:math:`(i,j)` th element is :math:`\hat{S}_i(T_j)`). + + The time-dependent Brier score :cite:p:`Graf1999` at time :math:`t` is the mean squared error of the event status + + .. math:: + + BS(t) = \mathbb{E}\left[\left(1\left(X > t\right) - \hat{S}(t)\right)^2\right] + + The default Brier score estimate is + + .. math:: + + \hat{BS}(t) = \frac{1}{n}\sum_i 1(T_i \leq t, \delta_i = 1) (0 - \hat{S}_i(t))^2 + 1(T_1 > t) (1- \hat{S}_i(t))^2 + + To account for the fact that the event time are censored, the + inverse probability weighting technique can be used. In this context, + each subject associated with time + :math:`t` is weighted by the inverse probability of censoring :math:`\omega(t) = 1 / \hat{D}(t)`, where + :math:`\hat{D}(t)` is the Kaplan-Meier estimate of the censoring distribution, :math:`P(D>t)`. + The censoring-adjusted Brier score is + + .. math:: + + \hat{BS}(t) = \frac{1}{n}\sum_i \omega(T_i) 1(T_i \leq t, \delta_i = 1) (0 - \hat{S}_i(t))^2 + \omega(t) 1(T_1 > t) (1- \hat{S}_i(t))^2 + + The censoring-adjusted Brier score can be obtained by specifying the argument + ``weight``, the weights evaluated at each ``time`` (:math:`\omega(T_1), \cdots, \omega(T_N)`). + If ``new_time`` is specified, the argument ``weight_new_time`` + should also be specified accordingly, the weights evaluated at each ``new_time`` + (:math:`\omega(t_1), \cdots, \omega(t_K)`). + In the context of train/test split, the weights should be derived from the censoring distribution estimated in the training data. + + + Examples: + >>> from torchsurv.stats.ipcw import get_ipcw + >>> _ = torch.manual_seed(52) + >>> n = 10 + >>> time = torch.randint(low=5, high=250, size=(n,)).float() + >>> event = torch.randint(low=0, high=2, size=(n,)).bool() + >>> estimate = torch.rand((n,len(time))) + >>> brier_score = BrierScore() + >>> brier_score(estimate, event, time) + tensor([0.2463, 0.2740, 0.3899, 0.1964, 0.3608, 0.2821, 0.1932, 0.2978, 0.1950, + 0.1668]) + >>> ipcw = get_ipcw(event, time) # ipcw at time + >>> brier_score(estimate, event, time, weight=ipcw) # censoring-adjusted brier-score + tensor([0.2463, 0.2740, 0.4282, 0.2163, 0.4465, 0.3826, 0.2630, 0.3888, 0.2219, + 0.1882]) + >>> new_time = torch.unique(torch.randint(low=5, high=time.max().int(), size=(n*2,)).float()) + >>> ipcw_new_time = get_ipcw(event, time, new_time) # ipcw at new_time + >>> estimate = torch.rand((n,len(new_time))) + >>> brier_score(estimate, event, time, new_time, ipcw, ipcw_new_time) # censoring-adjusted brier-score at new time + tensor([0.4036, 0.3014, 0.2517, 0.3947, 0.4200, 0.3908, 0.3766, 0.3737, 0.3596, + 0.2088, 0.4922, 0.3237, 0.2255, 0.1841, 0.3029, 0.6919, 0.2357, 0.3507, + 0.4364, 0.3312]) + + References: + + .. bibliography:: + :filter: False + + Graf1999 + + """ + + # mandatory input format checks + BrierScore._validate_brier_score_inputs( + estimate, time, new_time, weight, weight_new_time + ) + + # update inputs as required + estimate, new_time, weight, weight_new_time = ( + BrierScore._update_brier_score_new_time( + estimate, time, new_time, weight, weight_new_time + ) + ) + weight, weight_new_time = BrierScore._update_brier_score_weight( + time, new_time, weight, weight_new_time + ) + + # further input format checks + if self.checks: + validate_survival_data(event, time) + validate_evaluation_time(new_time, time, within_follow_up=False) + validate_estimate(estimate, time, new_time) + + # Calculating the residuals for each subject and time point + residuals = torch.zeros_like(estimate) + for i, t in enumerate(new_time): + est = estimate[:, i] + is_case = ((time <= t) & (event == True)).int() + is_control = (time > t).int() + + residuals[:, i] = ( + torch.square(est) * is_case * weight + + torch.square(1.0 - est) * is_control * weight_new_time[i] + ) + + # Calculating the brier scores at each time point + brier_score = torch.mean(residuals, axis=0) + + # Create/overwrite internal attributes states + if instate: + # sort all objects by time + self.order_time = torch.argsort(time, dim=0) + self.time = time[self.order_time] + self.event = event[self.order_time] + self.weight = weight[self.order_time] + self.new_time = new_time + self.weight_new_time = weight_new_time + self.estimate = torch.index_select(estimate, 0, self.order_time) + self.brier_score = brier_score + self.residuals = residuals + + return brier_score + + def integral(self): + r"""Compute the integrated Brier Score. + + Returns: + torch.Tensor: Integrated Brier Score. + + Examples: + >>> _ = torch.manual_seed(52) + >>> n = 10 + >>> time = torch.randint(low=5, high=250, size=(n,)).float() + >>> event = torch.randint(low=0, high=2, size=(n,)).bool() + >>> estimate = torch.rand((n,len(time))) + >>> brier_score = BrierScore() + >>> brier_score(estimate, event, time) + tensor([0.2463, 0.2740, 0.3899, 0.1964, 0.3608, 0.2821, 0.1932, 0.2978, 0.1950, + 0.1668]) + >>> brier_score.integral() # integrated brier score + tensor(0.2862) + + Note: + + The integrated Brier score is the integral of the time-dependent Brier score over the interval + :math:`[t_1, t_2]`, where :math:`t_1 = \min\left(\{T_i\}_{i = 1, \cdots, N}\right)` and :math:`t_2 = \max\left(\{T_i\}_{i = 1, \cdots, N}\right)`. + It is defined by :cite:p:`Graf1999` + + .. math:: + + \hat{IBS} = \int_{t_1}^{t_2} \hat{BS}(t) dW(t) + + where :math:`W(t) = t / t_2`. + + The integral is estimated with the trapzoidal rule. + + """ + + if len(self.new_time) == 1: + return self.brier_score[0] + else: + return torch.trapezoid(self.brier_score, self.new_time) / ( + self.new_time[-1] - self.new_time[0] + ) + + def confidence_interval( + self, + method: str = "parametric", + alpha: float = 0.05, + alternative: str = "two_sided", + n_bootstraps: int = 999, + ) -> torch.Tensor: + """Compute the confidence interval of the Brier Score. + + This function calculates either the pointwise confidence interval or the bootstrap + confidence interval for the Brier Score. The pointwise confidence interval is computed + assuming that the Brier score is normally distributed and using empirical standard errors. + The bootstrap confidence interval is constructed based on the distribution of bootstrap samples. + + Args: + method (str): + Method for computing confidence interval. Defaults to "parametric". + Must be one of the following: "parametric", "bootstrap". + alpha (float): + Significance level. Defaults to 0.05. + alternative (str): + Alternative hypothesis. Defaults to "two_sided". + Must be one of the following: "two_sided", "greater", "less". + n_bootstraps (int): + Number of bootstrap samples. Defaults to 999. + Ignored if ``method`` is not "bootstrap". + + Returns: + torch.Tensor([lower,upper]): + Lower and upper bounds of the confidence interval. + + Examples: + >>> _ = torch.manual_seed(52) + >>> n = 10 + >>> time = torch.randint(low=5, high=250, size=(n,)).float() + >>> event = torch.randint(low=0, high=2, size=(n,)).bool() + >>> estimate = torch.rand((n,len(time))) + >>> brier_score = BrierScore() + >>> brier_score(estimate, event, time) + tensor([0.2463, 0.2740, 0.3899, 0.1964, 0.3608, 0.2821, 0.1932, 0.2978, 0.1950, + 0.1668]) + >>> brier_score.confidence_interval() # default: parametric, two-sided + tensor([[0.1061, 0.0604, 0.2360, 0.0533, 0.1252, 0.0795, 0.0000, 0.1512, 0.0381, + 0.0051], + [0.3866, 0.4876, 0.5437, 0.3394, 0.5965, 0.4847, 0.4137, 0.4443, 0.3520, + 0.3285]]) + >>> brier_score.confidence_interval(method = "bootstrap", alternative = "greater") + tensor([[0.1455, 0.1155, 0.2741, 0.0903, 0.1985, 0.1323, 0.0245, 0.1938, 0.0788, + 0.0440], + [1.0000, 1.0000, 1.0000, 1.0000, 1.0000, 1.0000, 1.0000, 1.0000, 1.0000, + 1.0000]]) + + + """ + + assert ( + hasattr(self, "brier_score") and self.brier_score is not None + ), "Error: Please calculate brier score using `BrierScore()` before calling `confidence_interval()`." + + if alternative not in ["less", "greater", "two_sided"]: + raise ValueError( + "'alternative' parameter must be one of ['less', 'greater', 'two_sided']." + ) + + if method == "bootstrap": + return self._confidence_interval_bootstrap(alpha, alternative, n_bootstraps) + elif method == "parametric": + return self._confidence_interval_parametric(alpha, alternative) + else: + raise ValueError( + "Method not implemented. Please choose either 'parametric' or 'bootstrap'." + ) + + def p_value( + self, + method: str = "bootstrap", + alternative: str = "two_sided", + n_bootstraps: int = 999, + null_value: float = None, + ) -> torch.Tensor: + """Perform a one-sample hypothesis test on the Brier score. + + This function calculates either the pointwise p-value or the bootstrap p-value + for testing the null hypothesis that the estimated brier score is equal to + bs0, where bs0 is the brier score that would be expected if the survival model + was not providing accurate predictions beyond + random chance. The pointwise p-value is computed assuming that the + Brier score is normally distributed and using the empirical standard errors. + To obtain the pointwise p-value, the Brier score under the null, bs0, must + be provided. + The bootstrap p-value is derived by permuting survival function's predictions + to estimate the the sampling distribution under the null hypothesis. + + Args: + method (str): + Method for computing p-value. Defaults to "bootstrap". + Must be one of the following: "parametric", "bootstrap". + alternative (str): + Alternative hypothesis. Defaults to "two_sided". + Must be one of the following: "two_sided" (Brier score is not equal to bs0), + "greater" (Brier score is greater than bs0), "less" (Brier score is less than bs0). + n_bootstraps (int): + Number of bootstrap samples. Defaults to 999. + Ignored if ```method``` is not "bootstrap". + null_value (float): + The Brier score expected if the survival model was not + providing accurate predictions beyond what would be beyond + by random chance alone, i.e., bs0. + + + Returns: + torch.Tensor: p-value of the statistical test. + + Examples: + >>> _ = torch.manual_seed(52) + >>> n = 10 + >>> time = torch.randint(low=5, high=250, size=(n,)).float() + >>> event = torch.randint(low=0, high=2, size=(n,)).bool() + >>> new_time = torch.unique(time) + >>> estimate = torch.rand((n,len(new_time))) + >>> brier_score = BrierScore() + >>> brier_score(estimate, event, time, new_time) + tensor([0.3465, 0.5310, 0.4222, 0.4582, 0.3601, 0.3395, 0.2285, 0.1975, 0.3120, + 0.3883]) + >>> brier_score.p_value() # Default: bootstrap, two_sided + tensor([1.0000, 0.0560, 1.0000, 1.0000, 1.0000, 1.0000, 0.8320, 0.8620, 1.0000, + 1.0000]) + >>> brier_score.p_value(method = "parametric", alternative = "less", null_value = 0.3) # H0: bs = 0.3, Ha: bs < 0.3 + tensor([0.7130, 0.9964, 0.8658, 0.8935, 0.6900, 0.6630, 0.1277, 0.1128, 0.5383, + 0.8041]) + + """ + + assert ( + hasattr(self, "brier_score") and self.brier_score is not None + ), "Error: Please calculate the brier score using `BrierScore()` before calling `p_value()`." + + if alternative not in ["less", "greater", "two_sided"]: + raise ValueError( + "'alternative' parameter must be one of ['less', 'greater', 'two_sided']." + ) + + if method == "parametric" and null_value is None: + raise ValueError( + "Error: If the method is 'parametric', you must provide the 'null_value'." + ) + + if method == "parametric": + return self._p_value_parametric(alternative, null_value) + elif method == "bootstrap": + return self._p_value_bootstrap(alternative, n_bootstraps) + else: + raise ValueError( + "Method not implemented. Please choose either 'parametric' or 'bootstrap'." + ) + + def compare( + self, other, method: str = "parametric", n_bootstraps: int = 999 + ) -> torch.tensor: + """Compare two Brier scores. + + This function compares two Brier scores computed on the + same data with different risk scores. The statistical hypotheses are + formulated as follows, null hypothesis: brierscore1 = brierscore2 and alternative + hypothesis: brierscore1 < brierscore2. + The statistical test is either a Student t-test for paired samples or a two-sample bootstrap test. + The Student t-test for paired samples assumes that the Brier Scores are normally distributed + and uses the Brier scores' empirical standard errors. + + Args: + other (BrierScore): + Another instance of the BrierScore class representing brierscore2. + method (str): + Statistical test used to perform the hypothesis test. Defaults to "parametric". + Must be one of the following: "parametric", "bootstrap". + n_bootstraps (int): + Number of bootstrap samples. Defaults to 999. + Ignored if ``method`` is not "bootstrap". + + Returns: + torch.tensor: p-value of the statistical test. + + Examples: + >>> _ = torch.manual_seed(52) + >>> n = 10 + >>> time = torch.randint(low=5, high=250, size=(n,)).float() + >>> event = torch.randint(low=0, high=2, size=(n,)).bool() + >>> brier_score = BrierScore() + >>> brier_score(torch.rand((n,len(time))), event, time) + tensor([0.2463, 0.2740, 0.3899, 0.1964, 0.3608, 0.2821, 0.1932, 0.2978, 0.1950, + 0.1668]) + >>> brier_score2 = BrierScore() + >>> brier_score2(torch.rand((n,len(time))), event, time) + tensor([0.4136, 0.2750, 0.3002, 0.2826, 0.2030, 0.2643, 0.2525, 0.2964, 0.1804, + 0.3109]) + >>> brier_score.compare(brier_score2) # default: parametric + tensor([0.1793, 0.4972, 0.7105, 0.1985, 0.9254, 0.5591, 0.3455, 0.5060, 0.5437, + 0.0674]) + >>> brier_score.compare(brier_score2, method = "bootstrap") + tensor([0.1360, 0.5030, 0.7310, 0.2090, 0.8630, 0.5490, 0.3120, 0.5110, 0.5460, + 0.1030]) + + """ + + assert ( + hasattr(self, "brier_score") and self.brier_score is not None + ), "Error: Please calculate the brier score using `BrierScore()` before calling `compare()`." + + # assert that the same data were used to compute the two brier score + if torch.any(self.event != other.event) or torch.any(self.time != other.time): + raise ValueError( + "Mismatched survival data: 'time' and 'event' should be the same for both brier score computations." + ) + if torch.any(self.new_time != other.new_time): + raise ValueError( + "Mismatched evaluation times: 'new_time' should be the same for both brier score computations." + ) + + if method == "parametric": + return self._compare_parametric(other) + if method == "bootstrap": + return self._compare_bootstrap(other, n_bootstraps) + else: + raise ValueError( + "Method not implemented. Please choose either 'parametric' or 'bootstrap'." + ) + + def _brier_score_se(self): + """Brier Score's empirical standard errors.""" + + return torch.std(self.residuals, axis=0) / (self.time.shape[0] ** (1 / 2)) + + def _confidence_interval_parametric( + self, alpha: float, alternative: str + ) -> torch.Tensor: + """Confidence interval of Brier score assuming that the Brier score + is normally distributed and using empirical standard errors. + """ + + alpha = alpha / 2 if alternative == "two_sided" else alpha + + brier_score_se = self._brier_score_se() + + if torch.all(brier_score_se) > 0: + ci = ( + -torch.distributions.normal.Normal(0, 1).icdf(torch.tensor(alpha)) + * brier_score_se + ) + lower = torch.max(torch.tensor(0.0), self.brier_score - ci) + upper = torch.min(torch.tensor(1.0), self.brier_score + ci) + + if alternative == "less": + lower = torch.zeros_like(lower) + elif alternative == "greater": + upper = torch.ones_like(upper) + else: + raise ValueError( + "The standard error of the brier score must be a positive value." + ) + + return torch.stack([lower, upper], dim=0) + + def _confidence_interval_bootstrap( + self, alpha: float, alternative: str, n_bootstraps: int + ) -> torch.tensor: + """Bootstrap confidence interval of the Brier Score using Efron percentile method. + + References: + Efron, Bradley; Tibshirani, Robert J. (1993). + An introduction to the bootstrap, New York: Chapman & Hall, software. + """ + + # brier score given bootstrap distribution + brier_score_bootstrap = self._bootstrap_brier_score( + metric="confidence_interval", n_bootstraps=n_bootstraps + ) + + # intialize tensor to store confidence intervals + lower = torch.zeros_like(self.brier_score) + upper = torch.zeros_like(self.brier_score) + + # iterate over time + for index_t in range(len(self.brier_score)): + # obtain confidence interval + if alternative == "two_sided": + lower[index_t], upper[index_t] = torch.quantile( + brier_score_bootstrap[:, index_t], + torch.tensor( + [alpha / 2, 1 - alpha / 2], device=self.brier_score.device + ), + ) + elif alternative == "less": + upper[index_t] = torch.quantile( + brier_score_bootstrap[:, index_t], + torch.tensor(1 - alpha, device=self.brier_score.device), + ) + lower[index_t] = torch.tensor(0.0, device=self.brier_score.device) + elif alternative == "greater": + lower[index_t] = torch.quantile( + brier_score_bootstrap[:, index_t], + torch.tensor(alpha, device=self.brier_score.device), + ) + upper[index_t] = torch.tensor(1.0, device=self.brier_score.device) + + return torch.stack([lower, upper], dim=0) + + def _p_value_parametric( + self, alternative: str, null_value: float = 0.5 + ) -> torch.tensor: + """p-value for a one-sample hypothesis test of the Brier score + assuming that the Brier score is normally distributed and using empirical standard error. + """ + + brier_score_se = self._brier_score_se() + + # get p-value + if torch.all(brier_score_se) > 0: + p = torch.distributions.normal.Normal(0, 1).cdf( + (self.brier_score - null_value) / brier_score_se + ) + if alternative == "two_sided": + mask = self.brier_score >= 0.5 + p[mask] = 1 - p[mask] + p *= 2 + p = torch.min( + torch.tensor(1.0, device=self.brier_score.device), p + ) # in case critical value is below 0.5 + elif alternative == "greater": + p = 1 - p + else: + raise ValueError( + "The standard error of the brier score must be a positive value." + ) + + return p + + def _p_value_bootstrap(self, alternative, n_bootstraps) -> torch.tensor: + """p-value for a one-sample hypothesis test of the Brier score using + permutation of survival distribution prediction to estimate sampling distribution under the null + hypothesis. + """ + + # brier score bootstraps given null distribution + brierscore0 = self._bootstrap_brier_score( + metric="p_value", n_bootstraps=n_bootstraps + ) + + # intialize empty tensor to store p-values + p_values = torch.zeros_like(self.brier_score) + + # iterate over time + for index_t in range(len(self.brier_score)): + # Derive p-value + p = ( + 1 + torch.sum(brierscore0[:, index_t] <= self.brier_score[index_t]) + ) / (n_bootstraps + 1) + if alternative == "two_sided": + if self.brier_score[index_t] >= 0.5: + p = 1 - p + p *= 2 + p = torch.min( + torch.tensor(1.0, device=self.brier_score.device), p + ) # in case very small bootstrap sample size is used + elif alternative == "greater": + p = 1 - p + + p_values[index_t] = p + + return p_values + + def _compare_parametric(self, other): + """Student t-test for paired samples assuming that + the Brier scores are normally distributed and using + empirical standard errors.""" + + # sample size + n_samples = self.time.shape[0] + + # intialize empty vector to store p_values + p_values = torch.zeros_like(self.brier_score) + + # iterate over time + for index_t in range(len(self.brier_score)): + # compute standard error of the difference + paired_se = torch.std( + self.residuals[:, index_t] - other.residuals[:, index_t] + ) / (n_samples ** (1 / 2)) + + # compute t-stat + t_stat = ( + self.brier_score[index_t] - other.brier_score[index_t] + ) / paired_se + + # p-value + p_values[index_t] = torch.tensor( + stats.t.cdf( + t_stat, df=n_samples - 1 + ), # student-t cdf not available on torch + dtype=self.brier_score.dtype, + device=self.brier_score.device, + ) + + return p_values + + def _compare_bootstrap(self, other, n_bootstraps): + """Boostrap two-sample test to compare two Brier scores.""" + + # bootstrap brier scores given null hypothesis that brierscore1 and + # brierscore2 come from the same distribution + brier_score1_null = self._bootstrap_brier_score( + metric="compare", other=other, n_bootstraps=n_bootstraps + ) + brier_score2_null = self._bootstrap_brier_score( + metric="compare", other=other, n_bootstraps=n_bootstraps + ) + + # bootsrapped test statistics + t_boot = brier_score1_null - brier_score2_null + + # observed test statistics + t_obs = self.brier_score - other.brier_score + + # intialize empty tensor to store p-values + p_values = torch.zeros_like(self.brier_score) + + # iterate over time + for index_t in range(len(self.brier_score)): + p_values[index_t] = ( + 1 + torch.sum(t_boot[:, index_t] <= t_obs[index_t]) + ) / (n_bootstraps + 1) + + return p_values + + def _bootstrap_brier_score( + self, metric: str, n_bootstraps: int, other=None + ) -> torch.tensor: + """Compute bootstrap samples of the Brier Score. + + Args: + metric (str): Must be one of the following: "confidence_interval", "compare". + If "confidence_interval", computes bootstrap + samples of the Brier score given the data distribution. If "compare", computes + bootstrap samples of the Brier score given the sampling distribution under the comparison test + null hypothesis (brierscore1 = brierscore2). + n_bootstraps (int): Number of boostrap samples. + other (optional, BrierScore): + Another instance of the BrierScore class representing brierscore2. + Only required if ``metric`` is "compare". + + + Returns: + torch.tensor: Bootstrap samples of Brier score. + """ + import copy + + # Initiate empty list to store brier score + brier_scores = [] + + # Get the bootstrap samples of brier score + for _ in range(n_bootstraps): + if ( + metric == "confidence_interval" + ): # bootstrap samples given data distribution + index = torch.randint( + low=0, + high=self.estimate.shape[0], + size=(self.estimate.shape[0],), + ) + brier_scores.append( + self( + self.estimate[index, :], + self.event[index], + self.time[index], + self.new_time, + self.weight[index], + self.weight_new_time, + instate=False, + ) + ) # Run without saving internal state + elif ( + metric == "compare" + ): # bootstrap samples given null distribution (brierscore1 = brierscore2) + index = torch.randint( + low=0, + high=self.estimate.shape[0] * 2, + size=(self.estimate.shape[0],), + ) + + # with prob 0.5, take the weight_new_time from self and with prob 0.5 from other + weight_new_time = ( + self.weight_new_time + if torch.rand(1) < 0.5 + else other.weight_new_time + ) + + brier_scores.append( + self( # sample with replacement from pooled sample + torch.cat((self.estimate, other.estimate))[index, :], + torch.cat((self.event, other.event))[index], + torch.cat((self.time, other.time))[index], + self.new_time, + torch.cat((self.weight, other.weight))[index], + weight_new_time, + instate=False, + ) + ) + elif ( + metric == "p_value" + ): # bootstrap samples given null distribution (estimate are not informative) + estimate = copy.deepcopy(self.estimate) + estimate = estimate[ + torch.randperm(estimate.shape[0]), : + ] # Shuffle estimate + brier_scores.append( + self( + estimate, + self.event, + self.time, + self.new_time, + self.weight, + self.weight_new_time, + instate=False, + ) + ) # Run without saving internal state + + brier_scores = torch.stack(brier_scores, dim=0) + + if torch.any(torch.isnan(brier_scores)): + raise ValueError( + "The brier score computed using bootstrap should not be NaN." + ) + + return brier_scores + + @staticmethod + def _find_torch_unique_indices( + inverse_indices: torch.tensor, counts: torch.tensor + ) -> torch.tensor: + """return unique_sorted_indices such that + sorted_unique_tensor[inverse_indices] = original_tensor + original_tensor[unique_sorted_indices] = sorted_unique_tensor + + Usage: + _, inverse_indices, counts = torch.unique( + x, sorted=True, return_inverse=True, return_counts=True + ) + sorted_unique_indices = Auc._find_torch_unique_indices( + inverse_indices, counts + ) + """ + + _, ind_sorted = torch.sort(inverse_indices, stable=True) + cum_sum = counts.cumsum(0) + cum_sum = torch.cat((torch.tensor([0]), cum_sum[:-1])) + return ind_sorted[cum_sum] + + @staticmethod + def _validate_brier_score_inputs( + estimate: torch.tensor, + time: torch.tensor, + new_time: torch.tensor, + weight: torch.tensor, + weight_new_time: torch.tensor, + ) -> torch.tensor: + + # check new_time and weight are provided, weight_new_time should be provided + if all([new_time is not None, weight is not None, weight_new_time is None]): + raise ValueError( + "Please provide 'weight_new_time', the weight evaluated at 'new_time'." + ) + + # check that estimate has 2 dimensions estimate are probabilities + if torch.any(estimate < 0) or torch.any(estimate > 1): + raise ValueError( + "The 'estimate' input should contain estimated survival probabilities between 0 and 1." + ) + + # check if estimate is of the correct dimension + if estimate.ndim != 2: + raise ValueError("The 'estimate' input should have two dimensions.") + + # check if new_time are not specified and estimate are not evaluated at time + if new_time is None and len(time) != estimate.shape[1]: + raise ValueError( + "Mismatched dimensions: The number of columns in 'estimate' does not match the length of 'time'. " + "Please provide the times at which 'estimate' is evaluated using the 'new_time' input." + ) + + @staticmethod + def _update_brier_score_new_time( + estimate: torch.tensor, + time: torch.tensor, + new_time: torch.tensor, + weight: torch.tensor, + weight_new_time: torch.tensor, + ) -> torch.tensor: + + # check format of new_time + if ( + new_time is not None + ): # if new_time are specified: ensure it has the correct format + if isinstance(new_time, int): + new_time = torch.tensor([new_time]).float() + + if new_time.ndim == 0: + new_time = new_time.unsqueeze(0) + + else: # else: find new_time + + # if new_time are not specified, use unique time + new_time, inverse_indices, counts = torch.unique( + time, sorted=True, return_inverse=True, return_counts=True + ) + sorted_unique_indices = BrierScore._find_torch_unique_indices( + inverse_indices, counts + ) + + # for time-dependent estimate, select those corresponding to new time + estimate = estimate[:, sorted_unique_indices] + + if weight is not None: + # select weight corresponding at new time + weight_new_time = weight[sorted_unique_indices] + + return estimate, new_time, weight, weight_new_time + + @staticmethod + def _update_brier_score_weight( + time: torch.tensor, + new_time: torch.tensor, + weight: torch.tensor, + weight_new_time: torch.tensor, + ) -> torch.tensor: + + # if weight was not specified, weight of 1 + if weight is None: + weight = torch.ones_like(time) + weight_new_time = torch.ones_like(new_time) + + return weight, weight_new_time + + +if __name__ == "__main__": + import doctest + + # Run doctest + results = doctest.testmod() + if results.failed == 0: + print("All tests passed.") + else: + print("Some doctests failed.") + sys.exit(1) diff --git a/src/torchsurv/metrics/cindex.py b/src/torchsurv/metrics/cindex.py new file mode 100644 index 0000000..1c0e6a5 --- /dev/null +++ b/src/torchsurv/metrics/cindex.py @@ -0,0 +1,884 @@ +import copy +import sys +from typing import Optional, Tuple + +import torch +from scipy import stats +from torchmetrics import regression + +from ..tools.validate_inputs import validate_estimate, validate_survival_data + + +class ConcordanceIndex: + def __init__( + self, + tied_tol: float = 1e-8, + checks: bool = True, + ) -> dict: + """Initialize a ConcordanceIndex for survival class model evaluation. + + Args: + tied_tol (float): + Tolerance for tied risk scores. + Defaults to 1e-8. + checks (bool): + Whether to perform input format checks. + Enabling checks can help catch potential issues in the input data. + Defaults to True. + + Examples: + >>> _ = torch.manual_seed(42) + >>> n = 64 + >>> time = torch.randint(low=5, high=250, size=(n,)).float() + >>> event = torch.randint(low=0, high=2, size=(n,)).bool() + >>> estimate = torch.randn((n,)) + >>> cindex = ConcordanceIndex() + >>> cindex(estimate, event, time) + tensor(0.5337) + >>> cindex.confidence_interval() # default: Noether, two_sided + tensor([0.3251, 0.7423]) + >>> cindex.p_value(method='bootstrap', alternative='greater') + tensor(0.2620) + """ + self.tied_tol = tied_tol + self.checks = checks + + def __call__( + self, + estimate: torch.Tensor, + event: torch.Tensor, + time: torch.Tensor, + weight: Optional[torch.Tensor] = None, + tmax: Optional[torch.Tensor] = None, + instate: bool = True, + ) -> torch.Tensor: + r"""Compute the Concordance Index (C-index). + + The concordance index is the probability that a model correctly predicts + which of two comparable samples will experience an event first based on their + estimated risk scores. + + Args: + estimate (torch.Tensor): + Estimated risk of event occurrence (i.e., risk score). + Can be of shape = (n_samples,) if subject-specific risk score is time-independent, + or of shape = (n_samples, n_samples) if subject-specific risk score is evaluated at ``time``. + event (torch.Tensor, boolean): + Event indicator of size n_samples (= True if event occured). + time (torch.Tensor, float): + Time-to-event or censoring of size n_samples. + weight (torch.Tensor, optional): + Optional sample weight of size n_samples. Defaults to 1. + tmax (torch.Tensor, optional): + Truncation time. Defaults to None. + ``tmax`` should be chosen such that the probability of + being censored after time ``tmax`` is non-zero. If ``tmax`` is None, no truncation + is performed. + instate (bool): + Whether to create/overwrite internal attributes states. + Defaults to True. + + Returns: + torch.Tensor: Concordance-index + + Note: + + The concordance index provides a global assessment of a fitted survival model over the entire observational + period rather than focussing on the prediction for a fixed time (e.g., 10-year mortality). + It is recommended to use AUC instead of the concordance index for such time-dependent predictions, as + AUC is proper in this context, while the concordance index is not :cite:p:`Blanche2018`. + + For each subject :math:`i \in \{1, \cdots, N\}`, denote :math:`X_i` as the survival time and :math:`D_i` as the + censoring time. Survival data consist of the event indicator, :math:`\delta_i=(X_i\leq D_i)` + (argument ``event``) and the time-to-event or censoring, :math:`T_i = \min(\{ X_i,D_i \})` + (argument ``time``). + + The risk score measures the risk (or a proxy thereof) that a subject has an event. + The function accepts time-dependent risk score and time-independent risk score. The time-dependent risk score + of subject :math:`i` is specified through a function :math:`q_i: [0, \infty) \rightarrow \mathbb{R}`. + The time-independent risk score of subject :math:`i` is specified by a constant :math:`q_i`. + The argument ``estimate`` is the estimated risk score. + For time-dependent risk score, the argument ``estimate`` should be a tensor of shape = (N,N) + (:math:`(i,j)` th element is :math:`\hat{q}_i(T_j)`). For time-independent risk score, the argument ``estimate`` + should be a tensor of size N (:math:`i` th element is :math:`\hat{q}_i`). + + For a pair :math:`(i,j)`, we say that the pair is comparable if the event of :math:`i` has occured before + the event of :math:`j`, i.e., :math:`X_i < X_j`. Given that the pair is comparable, we say that the pair is + concordant if :math:`q_i(X_i) > q_j(X_i)`. + + The concordance index measures the probability that, for a pair of randomly selected comparable samples, + the one that experiences an event first has a higher risk. The concordance index is defined as + + .. math:: + + C = p(q_i(X_i) > q_j(X_i) \: | \: X_i < X_j) + + The default concordance index estimate is the popular nonparametric estimation proposed by :cite:t:`Harrell1996` + + .. math:: + + \hat{C} = \frac{\sum_i\sum_j \delta_i \: I(T_i < T_j)\left(I \left( \hat{q}_i(T_i) > \hat{q}_j(T_i) \right) + \frac{1}{2} I\left(\hat{q}_i(T_i) = \hat{q}_j(T_i)\right)\right)}{\sum_i\sum_j \delta_i\: I\left(T_i < T_j\right)} + + When the event time are censored, the Harrell's concordance index converges to an association measure that + involves the censoring distribution. + To address this shortcoming, :cite:t:`Uno2011` proposed to employ the + inverse probability weighting technique. In this context, each subject with event time at + :math:`t` is weighted by the inverse probability of censoring :math:`\omega(t) = 1 / \hat{D}(t)`, where + :math:`\hat{D}(t)` is the Kaplan-Meier estimate of the censoring distribution, :math:`P(D>t)`. + Let :math:`\omega(T_i)` be the weight associated with subject time :math:`i` (argument ``weight``). + The concordance index estimate with weight is, + + .. math:: + + \hat{C} = \frac{\sum_i\sum_j \delta_i \: \omega(T_i)^2 \: I(T_i < T_j)\left(I \left( \hat{q}_i(T_i) > \hat{q}_j(T_i) \right) + \frac{1}{2} I\left(\hat{q}_i(T_i) = \hat{q}_j(T_i)\right)\right)}{\sum_i\sum_j \delta_i \: \omega(T_i)^2\: I\left(T_i < T_j\right)} + + In the context of train/test split, the weights should be derived from the censoring distribution estimated in the training data. + Specifically, the censoring distribution is estimated using the training set and then evaluated at the subject time within the test set. + + Examples: + >>> from torchsurv.stats.ipcw import get_ipcw + >>> _ = torch.manual_seed(42) + >>> n = 64 + >>> time = torch.randint(low=5, high=250, size=(n,)).float() + >>> event = torch.randint(low=0, high=2, size=(n,)).bool() + >>> estimate = torch.randn((n,)) + >>> cindex = ConcordanceIndex() + >>> cindex(estimate, event, time) # Harrell's c-index + tensor(0.5337) + >>> ipcw = get_ipcw(event, time) # ipcw at subject time + >>> cindex(estimate, event, time, weight=ipcw) # Uno's c-index + tensor(0.5453) + + References: + + .. bibliography:: + :filter: False + + Blanche2018 + Harrell1996 + Uno2011 + + """ + # update inputs if necessary + estimate = ConcordanceIndex._update_cindex_estimate(estimate) + weight = ConcordanceIndex._update_weight(time, weight, tmax) + + # square the weight + weight_squared = torch.square(weight) + + # Inputs checks + if self.checks: + validate_survival_data(event, time) + validate_estimate(estimate, time) + + # find comparable pairs + comparable = self._get_comparable_and_tied_time(event, time) + + # get order index by time + order = torch.argsort(time) + + # Initialize variables to count concordant, discordant, and tied risk pairs + concordant, discordant, tied_risk = [], [], [] + + # Initialize numerator and denominator for calculating the concordance index + numerator, denominator = 0.0, 0.0 + + # Iterate through the comparable items over time + # (dictionary with indices that have an event occured at time and boolean masks of comparable pair a time) + for ind, mask in comparable.items(): + # Extract risk score, event indicator and weight for the current sample + est_i, event_i, w_i = ( + estimate[order[ind], order[ind]], + event[order[ind]], + weight_squared[order[ind]], + ) + + # Extract risk score of comparable pairs and the number of comparable samples + est_j, N = estimate[order[mask], order[ind]], mask.sum() + + # Check that the current sample is uncensored + assert ( + event_i + ), f"Got censored sample at index {order[ind]}, but expected uncensored" + + # Identify tied pairs based on a tolerance (ties) + ties = ( + torch.absolute(est_j.float() - est_i.float()) <= self.tied_tol + ) # ties + n_ties = ties.sum() + + # Identify concordant pairs + con = est_j < est_i + n_con = con[~ties].sum() + + # Update numerator and denominator for concordance index calculation + numerator += w_i * n_con + 0.5 * w_i * n_ties + denominator += w_i * N + + # Update counts for tied, concordant, and discordant pairs + tied_risk.append(w_i * n_ties) + concordant.append(w_i * n_con) + discordant.append(w_i * N - w_i * n_con - w_i * n_ties) + + # Create/overwrite internal attributes states + if instate: + self.time = time + self.event = event + self.estimate = estimate + self.cindex = numerator / denominator + self.concordant = torch.stack(concordant, dim=0) + self.discordant = torch.stack(discordant, dim=0) + self.tied_risk = torch.stack(tied_risk, dim=0) + self.weight = weight + self.weight_squared = weight_squared + self.tmax = tmax + + return numerator / denominator # cindex + + def confidence_interval( + self, + method: str = "noether", + alpha: float = 0.05, + alternative: str = "two_sided", + n_bootstraps: int = 999, + ) -> torch.Tensor: + """Compute the confidence interval of the Concordance index. + + This function calculates either the pointwise confidence interval or the bootstrap + confidence interval for the concordance index. The pointwise confidence interval is computed + assuming that the concordance index is normally distributed and using the standard error estimated with either the Noether or + the conservative method :cite:p:`Pencina2004`. + The bootstrap confidence interval is constructed based on the distribution of bootstrap samples. + + Args: + method (str): + Method for computing confidence interval. Defaults to "noether". + Must be one of the following: "noether", "conservative", "bootstrap". + alpha (float): + Significance level. Defaults to 0.05. + alternative (str): + Alternative hypothesis. Defaults to "two_sided". + Must be one of the following: "two_sided", "greater", "less". + n_bootstraps (int): + Number of bootstrap samples. Defaults to 999. + Ignored if ``method`` is not "bootstrap". + + Returns: + torch.Tensor([lower,upper]): + Lower and upper bounds of the confidence interval. + + Examples: + >>> _ = torch.manual_seed(42) + >>> n = 64 + >>> time = torch.randint(low=5, high=250, size=(n,)).float() + >>> event = torch.randint(low=0, high=2, size=(n,)).bool() + >>> estimate = torch.randn((n,)) + >>> cindex = ConcordanceIndex() + >>> cindex(estimate, event, time) + tensor(0.5337) + >>> cindex.confidence_interval() # default: Noether, two_sided + tensor([0.3251, 0.7423]) + >>> cindex.confidence_interval(method="bootstrap", alternative="greater") + tensor([0.4459, 1.0000]) + >>> cindex.confidence_interval(method="conservative", alternative="less") + tensor([0.0000, 0.7558]) + + References: + .. bibliography:: + :filter: False + + Pencina2004 + """ + + assert ( + hasattr(self, "cindex") and self.cindex is not None + ), "Error: Please calculate the concordance index using `ConcordanceIndex()` before calling `confidence_interval()`." + + if alternative not in ["less", "greater", "two_sided"]: + raise ValueError( + "'alternative' parameter must be one of ['less', 'greater', 'two_sided']." + ) + + if method == "noether": + return self._confidence_interval_noether(alpha, alternative) + elif method == "bootstrap": + return self._confidence_interval_bootstrap(alpha, alternative, n_bootstraps) + elif method == "conservative": + return self._confidence_interval_conservative(alpha, alternative) + else: + raise ValueError( + "Method not implemented. Please choose either 'noether', 'conservative' or 'bootstrap'." + ) + + def p_value( + self, + method: str = "noether", + alternative: str = "two_sided", + n_bootstraps: int = 999, + ) -> torch.Tensor: + """Perform one-sample hypothesis test on the Concordance index. + + This function calculates either the pointwise p-value or the bootstrap p-value + for testing the null hypothesis that the concordance index is equal to 0.5. + The pointwise p-value is computed assuming that the concordance index is normally distributed and using the + standard error estimated using the Noether's method :cite:p:`Pencina2004`. + The bootstrap p-value is derived by permuting risk predictions to estimate + the sampling distribution under the null hypothesis. + + Args: + method (str): + Method for computing p-value. Defaults to "noether". + Must be one of the following: "noether", "bootstrap". + alternative (str): + Alternative hypothesis. Defaults to "two_sided". + Must be one of the following: "two_sided" (concordance index is not equal to 0.5), + "greater" (concordance index is greater than 0.5), "less" (concordance index is less than 0.5). + n_bootstraps (int): + Number of bootstrap samples. Defaults to 999. + Ignored if ``method`` is not "bootstrap". + + Returns: + torch.Tensor: p-value of statistical test. + + Examples: + >>> _ = torch.manual_seed(42) + >>> n = 64 + >>> time = torch.randint(low=5, high=250, size=(n,)).float() + >>> event = torch.randint(low=0, high=2, size=(n,)).bool() + >>> estimate = torch.randn((n,)) + >>> cindex = ConcordanceIndex() + >>> cindex(estimate, event, time) + tensor(0.5337) + >>> cindex.p_value() # default: Noether, two_sided + tensor(0.7516) + >>> cindex.p_value(method="bootstrap", alternative="greater") + tensor(0.2620) + + """ + + assert ( + hasattr(self, "cindex") and self.cindex is not None + ), "Error: Please calculate the concordance index using `ConcordanceIndex()` before calling `p_value()`." + + if alternative not in ["less", "greater", "two_sided"]: + raise ValueError( + "'alternative' parameter must be one of ['less', 'greater', 'two_sided']." + ) + + if method == "noether": + return self._p_value_noether(alternative) + elif method == "bootstrap": + return self._p_value_bootstrap(alternative, n_bootstraps) + else: + raise ValueError( + "Method not implemented. Please choose either 'noether' or 'bootstrap'." + ) + + def compare( + self, other, method: str = "noether", n_bootstraps: int = 999 + ) -> torch.tensor: + """Compare two Concordance indices. + + This function compares two concordance indices computed on the + same data with different risk scores. The statistical hypotheses are + formulated as follows, null hypothesis: cindex1 = cindex2 and alternative + hypothesis: cindex1 > cindex2. + The statistical test is either a Student t-test for dependent samples or + a two-sample bootstrap test. The Student t-test assumes that the concordance index is normally distributed + and uses standard errors estimated with the Noether's method :cite:p:`Pencina2004`. + + Args: + other (ConcordanceIndex): + Another instance of the ConcordanceIndex class representing cindex2. + method (str): + Statistical test used to perform the hypothesis test. Defaults to "noether". + Must be one of the following: "noether", "bootstrap". + n_bootstraps (int): + Number of bootstrap samples. Defaults to 999. + Ignored if ``method`` is not "bootstrap". + + Returns: + torch.tensor: p-value of the statistical test. + + Examples: + >>> _ = torch.manual_seed(42) + >>> n = 64 + >>> time = torch.randint(low=5, high=250, size=(n,)).float() + >>> event = torch.randint(low=0, high=2, size=(n,)).bool() + >>> cindex1 = ConcordanceIndex() + >>> cindex1(torch.randn((n,)), event, time) + tensor(0.5337) + >>> cindex2 = ConcordanceIndex() + >>> cindex2(torch.randn((n,)), event, time) + tensor(0.5047) + >>> cindex1.compare(cindex2) # default: Noether + tensor(0.4267) + >>> cindex1.compare(cindex2, method = "bootstrap") + tensor(0.3620) + + """ + + assert ( + hasattr(self, "cindex") and self.cindex is not None + ), "Error: Please calculate the concordance index using `ConcordanceIndex()` before calling `compare()`." + + # assert that the same data were used to compute the two c-index + if torch.any(self.event != other.event) or torch.any(self.time != other.time): + raise ValueError( + "Mismatched survival data: 'time' and 'event' should be the same for both concordance index computations." + ) + + if self.tmax != other.tmax: + raise ValueError( + "Mismatched truncation time: 'tmax' should be the same for both concordance index computations." + ) + + if method == "noether": + return self._compare_noether(other) + if method == "bootstrap": + return self._compare_bootstrap(other, n_bootstraps) + else: + raise ValueError( + "Method not implemented. Please choose either 'noether' or 'bootstrap'." + ) + + def _confidence_interval_noether(self, alpha, alternative) -> torch.Tensor: + """Confidence interval of Concordance index assuming that the concordance index + is normally distributed and using standard errors estimated using Noether's method. + """ + + alpha = alpha / 2 if alternative == "two_sided" else alpha + + cindex_se = self._concordance_index_se() + + if cindex_se > 0: + ci = ( + -torch.distributions.normal.Normal(0, 1).icdf( + torch.tensor(alpha, device=self.cindex.device) + ) + * cindex_se + ) + lower = torch.max( + torch.tensor(0.0, device=self.cindex.device), self.cindex - ci + ) + upper = torch.min( + torch.tensor(1.0, device=self.cindex.device), self.cindex + ci + ) + + if alternative == "less": + lower = torch.tensor(0.0, device=self.cindex.device) + elif alternative == "greater": + upper = torch.tensor(1.0, device=self.cindex.device) + else: + raise ValueError( + "The standard error of the concordance index must be a positive value." + ) + + return torch.stack([lower, upper], dim=0) + + def _confidence_interval_conservative(self, alpha, alternative) -> torch.tensor: + """Confidence interval of Concordance index assuming that the concordance index + is normally distributed and using the conservative method. + """ + alpha = alpha / 2 if alternative == "two_sided" else alpha + + N = torch.sum(self.weight) + + pc = (1 / (N * (N - 1))) * torch.sum(self.concordant) + pd = (1 / (N * (N - 1))) * torch.sum(self.discordant) + + w = ( + ( + torch.distributions.normal.Normal(0, 1).icdf( + torch.tensor(alpha, device=self.cindex.device) + ) + ** 2 + ) + * 2 + ) / (N * (pc + pd)) + + ci = torch.sqrt(w**2 + 4 * w * self.cindex * (1 - self.cindex)) / (2 * (1 + w)) + point = (w + 2 * self.cindex) / (2 * (1 + w)) + + lower = point - ci + upper = point + ci + + if alternative == "less": + lower = torch.tensor(0.0, device=self.cindex.device) + elif alternative == "greater": + upper = torch.tensor(1.0, device=self.cindex.device) + + return torch.stack([lower, upper]) + + def _confidence_interval_bootstrap( + self, alpha: float, alternative: str, n_bootstraps: int + ) -> torch.tensor: + """Bootstrap confidence interval of the Concordance index using + Efron's percentile method. + + References: + Efron, Bradley; Tibshirani, Robert J. (1993). + An introduction to the bootstrap, New York: Chapman & Hall, software. + """ + + # c-index bootstraps given bootstrap distribution + cindex_bootstrap = self._bootstrap_cindex( + metric="confidence_interval", n_bootstraps=n_bootstraps + ) + + # obtain confidence interval + if alternative == "two_sided": + lower, upper = torch.quantile( + cindex_bootstrap, + torch.tensor([alpha / 2, 1 - alpha / 2], device=self.cindex.device), + ) + elif alternative == "less": + upper = torch.quantile( + cindex_bootstrap, torch.tensor(1 - alpha, device=self.cindex.device) + ) + lower = torch.tensor(0.0, device=self.cindex.device) + elif alternative == "greater": + lower = torch.quantile( + cindex_bootstrap, torch.tensor(alpha, device=self.cindex.device) + ) + upper = torch.tensor(1.0, device=self.cindex.device) + + return torch.stack([lower, upper]) + + def _p_value_noether(self, alternative, null_value: float = 0.5) -> torch.tensor: + """p-value for a one-sample hypothesis test of the Concordance index + assuming that the concordance index is normally distributed and using standard + errors estimated with Noether's method. + """ + + cindex_se = self._concordance_index_se() + + # get p-value + if cindex_se > 0: + p = torch.distributions.normal.Normal(0, 1).cdf( + (self.cindex - null_value) / cindex_se + ) + if alternative == "two_sided": + if self.cindex >= torch.tensor(0.5): + p = torch.tensor(1.0) - p + p *= torch.tensor(2.0) + elif alternative == "greater": + p = torch.tensor(1.0) - p + else: + raise ValueError( + "The standard error of concordance index must be a positive value." + ) + + return p + + def _p_value_bootstrap(self, alternative, n_bootstraps) -> torch.tensor: + """p-value for a one-sample hypothesis test of the Concordance Index using + permutation of risk prediction to estimate sampling distribution under the null + hypothesis. + """ + + # c-index boostraps given null distribution cindex = 0.5 + cindex0 = self._bootstrap_cindex(metric="p_value", n_bootstraps=n_bootstraps) + + # Derive p-value + p = (torch.tensor(1) + torch.sum(cindex0 <= self.cindex)) / torch.tensor( + n_bootstraps + 1 + ) + if alternative == "two_sided": + if self.cindex >= torch.tensor(0.5): + p = torch.tensor(1.0) - p + p *= torch.tensor(2.0) + p = torch.min( + torch.tensor(1.0, device=self.cindex.device), p + ) # in case very small bootstrap sample size is used + elif alternative == "greater": + p = torch.tensor(1.0) - p + + return p + + def _compare_noether(self, other): + """Student t-test for dependent samples given Noether's standard error to + compare two concordance indices. + """ + + # sample size + N = sum(self.weight) + + # compute noether standard error + cindex1_se = self._concordance_index_se() + cindex2_se = other._concordance_index_se() + + # compute spearman correlation between risk prediction + corr = regression.SpearmanCorrCoef()( + self.estimate.reshape(-1), other.estimate.reshape(-1) + ) + + # check for perfect positive monotonic relationship between two variables + if 1 - torch.abs(corr) < 1e-15: + return 1.0 + + # compute t-stat + t_stat = (self.cindex - other.cindex) / torch.sqrt( + cindex1_se**2 + cindex2_se**2 - 2 * corr * cindex1_se * cindex2_se + ) + + # return p-value + return torch.tensor( + 1 - stats.t.cdf(t_stat, df=N - 1), + dtype=self.cindex.dtype, + device=self.cindex.device, + ) # student-t cdf not available on torch + + def _compare_bootstrap(self, other, n_bootstraps): + """Boostrap two-sample test to compare two concordance indices.""" + + # c-index bootstraps given null hypothesis that cindex1 + # and cindex2 come from the same distribution + cindex1_null = self._bootstrap_cindex( + metric="compare", other=other, n_bootstraps=n_bootstraps + ) + cindex2_null = self._bootstrap_cindex( + metric="compare", other=other, n_bootstraps=n_bootstraps + ) + + # bootsrapped test statistics + t_boot = cindex1_null - cindex2_null + + # observed test statistics + t_obs = self.cindex - other.cindex + + # return p-value + return torch.tensor(1) - ( + torch.tensor(1) + torch.sum(t_boot <= t_obs) + ) / torch.tensor(n_bootstraps + 1) + + def _concordance_index_se(self): + """Standard error of concordance index using Noether's method.""" + + N = sum(self.weight) + + pc = (1 / (N * (N - 1))) * torch.sum(self.concordant) + pd = (1 / (N * (N - 1))) * torch.sum(self.discordant) + pcc = (1 / (N * (N - 1) * (N - 2))) * torch.sum( + self.concordant * (self.concordant - 1) + ) + pdd = (1 / (N * (N - 1) * (N - 2))) * torch.sum( + self.discordant * (self.discordant - 1) + ) + pcd = (1 / (N * (N - 1) * (N - 2))) * torch.sum( + self.concordant * self.discordant + ) + varp = (4 / (pc + pd) ** 4) * (pd**2 * pcc - 2 * pc * pd * pcd + pc**2 * pdd) + + return torch.sqrt(varp / N) + + def _bootstrap_cindex( + self, metric: str, n_bootstraps: int, other=None + ) -> torch.tensor: + """Compute bootstrap samples of the Concordance Index (C-index). + + Args: + metric (str): Must be one of the following: "p_value", "confidence_interval", "compare". + If "p_value", computes bootstrap samples of the concordance index given the sampling distribution + under the null hypothesis (c-index = 0.5). If "confidence_interval", computes bootstrap + samples of the c-index given the data distribution. If "compare", computes + bootstrap samples of the c-index given the sampling distribution under the comparison test + null hypothesis (c-index1 = cindex2). + n_bootstraps (int): Number of boostrap samples. + other (optional, ConcordanceIndex): + Another instance of the ConcordanceIndex class representing cindex2. + Only required for the ``metric`` is "compare". + + + Returns: + torch.tensor: bootstrap samples of Concordance index. + """ + + # Initiate empty list to store concordance index + cindexes = [] + + # Get the boostrap samples of concordance index + for _ in range(n_bootstraps): + if ( + metric == "p_value" + ): # bootstrap samples given null distribution (cindex = 0.5) + estimate = copy.deepcopy(self.estimate) + estimate = estimate[ + torch.randperm(len(estimate)), : + ] # Shuffle estimate + cindexes.append( + self( + estimate, + self.event, + self.time, + self.weight, + self.tmax, + instate=False, + ) + ) # Run Concordance index, without saving internal state + elif ( + metric == "confidence_interval" + ): # bootstrap samples given data distribution + index = torch.randint( + low=0, + high=len(self.event), + size=( + len( + self.event, + ), + ), + ) + cindexes.append( + self( # sample with replacement from sample + self.estimate[index, :][:, index], + self.event[index], + self.time[index], + self.weight, + self.tmax, + instate=False, + ) + ) # Run Concordance index, without saving internal state + elif ( + metric == "compare" + ): # bootstrap samples given null distribution (cindex1 = cindex2) + index = torch.randint( + low=0, + high=len(self.event) * 2, + size=( + len( + self.event, + ), + ), + ) + estimate = torch.cat( + ( + torch.cat((self.estimate, self.estimate), dim=1), + torch.cat((other.estimate, other.estimate), dim=1), + ), + dim=0, + ) # create n_samples*2, n_samples*2 tensor + cindexes.append( + self( # sample with replacement from pooled sample + estimate[index, :][:, index], + torch.cat((self.event, other.event))[index], + torch.cat((self.time, other.time))[index], + torch.cat((self.weight, other.weight))[index], + self.tmax, + instate=False, + ) + ) + + return torch.stack(cindexes) + + @staticmethod + def _get_comparable_and_tied_time( + event, + time, + ) -> Tuple[torch.Tensor, torch.Tensor]: + """Identify comparable pairs and count tied time pairs. + The function iterates through the sorted time points to identify comparable samples + (those with the same time point) and count the number of tied time points. + + Returns: + Tuple[torch.Tensor, torch.Tensor]: + - comparable (torch.Tensor): Dictionary containing indices as keys + and boolean masks as values, indicating which samples are comparable. + - tied_time (torch.Tensor): Number of tied time points. + + Note: + - 'comparable' dictionary maps indices to boolean masks, where True indicates + that the corresponding sample is comparable to others at the same time point. + - 'tied_time' counts the total number of tied time points. + + """ + # Number of samples + n_samples = len(time) + + # Sort indices based on time + order = torch.argsort(time) + + # Initalize dictionary to store comparable samples + comparable = {} + + # Initalize count + tied_time = 0 + + # Initialize index for storing unique values + i = 0 + + # Iterate through the sorted time points + while i < n_samples - 1: + time_i = time[order[i]] + + # Find the range of samples with the same time point + start = i + 1 + end = start + while end < n_samples and time[order[end]] == time_i: + end += 1 + + # check for tied event times + event_at_same_time = event[order[i:end]] + censored_at_same_time = torch.logical_not(event_at_same_time) + + # Iterate through the sample with the same time point + for j in range(i, end): + # If event occured at time + if event[order[j]]: + # Create a boolean mask for comparability + mask = torch.zeros_like(time).bool() + mask[end:] = True + + # Store the comparability mask for the event + mask[i:end] = censored_at_same_time + comparable[j] = mask + tied_time += censored_at_same_time.sum() + i = end + + if len(comparable) == 0: + raise ValueError("No comparable pairs, denominator is 0.") + else: + return comparable + + @staticmethod + def _update_weight( + time: torch.Tensor, + weight: torch.Tensor, + tmax: Optional[torch.Tensor] = None, + ) -> torch.Tensor: + """Obtain subject-specific weight.""" + + # If weight is not provided, use ones instead. + weight_updated = torch.zeros_like(time) + + # If tmax is provided, truncate time after tmax (mask = False) + masks = torch.ones_like(time).bool() if tmax is None else time < tmax + weight_updated[masks] = ( + torch.tensor(1.0, dtype=weight_updated.dtype, device=time.device) + if weight is None + else weight[masks] + ) + + return weight_updated + + @staticmethod + def _update_cindex_estimate(estimate: torch.Tensor) -> torch.Tensor: + # Ensure estimate is (n_samples, n_samples) shape + if estimate.ndim == 1: + estimate = estimate.unsqueeze(1) + + if estimate.shape[1] == 1: + estimate = estimate.expand((estimate.shape[0], estimate.shape[0])) + + return estimate + + +if __name__ == "__main__": + import doctest + + # Run doctest + results = doctest.testmod() + if results.failed == 0: + print("All tests passed.") + else: + print("Some doctests failed.") + sys.exit(1) diff --git a/src/torchsurv/metrics/weight.py b/src/torchsurv/metrics/weight.py new file mode 100644 index 0000000..e69de29 diff --git a/src/torchsurv/stats/ipcw.py b/src/torchsurv/stats/ipcw.py new file mode 100644 index 0000000..66e76c4 --- /dev/null +++ b/src/torchsurv/stats/ipcw.py @@ -0,0 +1,117 @@ +import sys +import warnings +from typing import Optional + +import torch + +from ..tools.validate_inputs import validate_survival_data +from .kaplan_meier import KaplanMeierEstimator + + +def get_ipcw( + event: torch.tensor, + time: torch.tensor, + new_time: Optional[torch.tensor] = None, + checks: bool = True, +) -> torch.Tensor: + """Calculate the inverse probability censoring weights (IPCW). + + Args: + event (torch.Tensor, boolean): + Event indicator of size n_samples (= True if event occured). + time (torch.Tensor, float): + Time-to-event or censoring of size n_samples. + new_time (torch.Tensor, float, optional): + New time at which to evaluate the IPCW. + Defaults to ``time``. + checks (bool): + Whether to perform input format checks. + Enabling checks can help catch potential issues in the input data. + Defaults to True. + Returns: + torch.Tensor: IPCW evaluated at ``new_time``. + + Examples: + >>> _ = torch.manual_seed(42) + >>> n = 5 + >>> event = torch.randint(low=0, high=2, size=(n,)).bool() + >>> time = torch.randint(low=1, high=100, size=(n,)).float() + >>> new_time = torch.randint(low=1, high=100, size=(n*2,)) + >>> get_ipcw(event, time) # ipcw evaluated at time + tensor([1.8750, 1.2500, 3.7500, 0.0000, 1.2500]) + >>> get_ipcw(event, time, new_time) # ipcw evaluated at new_time + tensor([1.8750, 1.8750, 3.7500, 3.7500, 0.0000, 1.2500, 0.0000, 1.2500, 1.2500, + 1.2500]) + + Note: + The inverse probability of censoring weight at time :math:`t` is defined by + + .. math:: + \omega(t) = 1 / \hat{D}(t), + + where :math:`\hat{D}(t)` is the Kaplan-Meier estimate of the censoring distribution, :math:`P(D>t)`. + + + """ + + if checks: + validate_survival_data(event, time) + + # time on which to evaluate IPCW + if new_time is None: # if none, return ipcw of same size as time + new_time = time + + # fit KM censoring estimator + km = KaplanMeierEstimator() + km(event, time, censoring_dist=True) + + # predict censoring distribution at time + ct = km.predict(new_time) + + # caclulate ipcw + mask = ct > 0 + ipcw = torch.zeros_like(new_time, dtype=time.dtype) + ipcw[mask] = _inverse_censoring_dist(ct[mask]) + + return ipcw + + +def _inverse_censoring_dist(ct: torch.Tensor) -> torch.Tensor: + """Compute inverse of the censoring distribution. + + Args: + ct (torch.Tensor): + Estimated censoring distribution. + Must be strictly positive. + + Returns: + torch.Tensor: 1/ct if ct > 0, else 1. + + Examples: + >>> _ = torch.manual_seed(42) + >>> ct = torch.randn((4,)) + >>> _inverse_censoring_dist(ct) + tensor([2.9701, 7.7634, 4.2651, 4.3415]) + + """ + if torch.any(ct.eq(0.0)): + warnings.warn( + "Censoring distribution zero at one or more time points. Returning ones as weight" + ) + return torch.ones_like(ct, dtype=ct.dtype) + else: + weight = torch.ones(1, dtype=ct.dtype) / ct + + return weight + + +if __name__ == "__main__": + import doctest + + # Run doctest + results = doctest.testmod() + if results.failed == 0: + print("All tests passed.") + else: + print("Some doctests failed.") + sys.exit(1) diff --git a/src/torchsurv/stats/kaplan_meier.py b/src/torchsurv/stats/kaplan_meier.py new file mode 100644 index 0000000..d1ff9ed --- /dev/null +++ b/src/torchsurv/stats/kaplan_meier.py @@ -0,0 +1,211 @@ +import itertools +import sys +from typing import Tuple + +import torch + +from ..tools.validate_inputs import validate_survival_data + + +class KaplanMeierEstimator: + def __call__( + self, + event: torch.tensor, + time: torch.tensor, + censoring_dist: bool = False, + check: bool = True, + ): + """Kaplan-Meier estimate of survival or censoring distribution for right-censored data :cite:p:`Kaplan1958`. + + Args: + event (torch.tensor, bool): + Event indicator of size n_samples (= True if event occured). + time (torch.tensor, float): + Time-to-event or censoring of size n_samples. + censoring_dist (bool, optional): + If False, returns the Kaplan-Meier estimate of the survival distribution. + If True, returns the Kaplan-Meier estimate of the censoring distribution. + Defaults to False. + check (bool): + Whether to perform input format checks. + Enabling checks can help catch potential issues in the input data. + Defaults to True. + + Examples: + >>> _ = torch.manual_seed(42) + >>> n = 32 + >>> time = torch.randint(low=0, high=8, size=(n,)).float() + >>> event = torch.randint(low=0, high=2, size=(n,)).bool() + >>> s = KaplanMeierEstimator() # estimate survival distribution + >>> s(event, time) + >>> s.km_est + tensor([1.0000, 1.0000, 0.8214, 0.7143, 0.6391, 0.6391, 0.5113, 0.2556]) + >>> c = KaplanMeierEstimator() # estimate censoring distribution + >>> c(event, time, censoring_dist = True) + >>> c.km_est + tensor([0.9688, 0.8750, 0.8750, 0.8312, 0.6357, 0.4890, 0.3667, 0.0000]) + + References: + + .. bibliography:: + :filter: False + + Kaplan1958 + """ + + # create attribute state + self.event = event + self.time = time + + # Check input validity if required + if check: + validate_survival_data(event, time) + + # Compute the counts of events, censorings, and the number at risk at each unique time + uniq_times, n_events, n_at_risk, n_censored = self._compute_counts() + + # If 'censoring_dist' is True, estimate the censoring distribution instead of the survival distribution + if censoring_dist: + n_at_risk -= n_events + n_events = n_censored + + # Compute the Kaplan-Meier estimator + ratio = torch.where( + n_events != 0, # Check if the number of events is not equal to zero + n_events + / n_at_risk, # Element-wise division when the number of events is not zero + torch.zeros_like( + n_events, dtype=torch.float + ), # Set to zero when the number of events is zero to avoid division by zero + ) + values = ( + 1.0 - ratio + ) # Compute the survival (or censoring) probabilities at each unique time + y = torch.cumprod( + values, dim=0 + ) # Cumulative product to get the Kaplan-Meier estimator + + # Keep track of the unique times and Kaplan-Meier estimator values + self.time = uniq_times + self.km_est = y + + def predict(self, new_time: torch.Tensor) -> torch.Tensor: + """Predicts the Kaplan-Meier estimate on new time points. + If the new time points do not match any times used to fit, the left-limit is used. + + Args: + new_time (torch.tensor): + New time points at which to predict the Kaplan-Meier estimate. + + Returns: + Kaplan-Meier estimate evaluated at ``new_time``. + + Examples: + >>> _ = torch.manual_seed(42) + >>> n = 8 + >>> time = torch.randint(low=1, high=10, size=(n * 4,)).float() + >>> event = torch.randint(low=0, high=2, size=(n * 4,)).bool() + >>> km = KaplanMeierEstimator() + >>> km(event, time) + >>> km.predict(torch.randint(low=0, high=10, size=(n,))) # predict survival distribution + tensor([1.0000, 0.9062, 0.8700, 1.0000, 0.9062, 0.9062, 0.4386, 0.0000]) + + """ + + # add probability of 1 of survival before time 0 + ref_time = torch.cat((-torch.tensor([torch.inf]), self.time), dim=0) + km_est_ = torch.cat((torch.ones(1), self.km_est)) + + # Check if newtime is beyond the last observed time point + extends = new_time > torch.max(ref_time) + if km_est_[torch.argmax(ref_time)] > 0 and extends.any(): + raise ValueError( + "Cannot predict survival/censoring distribution after the largest observed training event time point: {}".format( + ref_time[-1].item() + ) + ) + + # beyond last time point is zero probability + km_pred = torch.zeros_like(new_time, dtype=km_est_.dtype) + km_pred[extends] = 0.0 + + # find new time points that match train time points + idx = torch.searchsorted(ref_time, new_time[~extends], side="left") + + # For non-exact matches, take the left limit (shift the index to the left) + eps = torch.finfo(ref_time.dtype).eps + idx[torch.abs(ref_time[idx] - new_time[~extends]) >= eps] -= 1 + + # predict + km_pred[~extends] = km_est_[idx] + + return km_pred + + def _compute_counts( + self, + ) -> Tuple[torch.tensor, torch.tensor, torch.tensor, torch.tensor]: + """Compute the counts of events, censorings and risk set at ``time``. + + Returns: Tuple[torch.tensor, torch.tensor, torch.tensor, torch.tensor] + unique times + number of events at unique times + number at risk at unique times + number of censored at unique times + """ + # Get the number of samples + n_samples = len(self.event) + + # Sort indices based on time + order = torch.argsort(self.time, dim=0) + + # Initialize arrays to store unique times, event counts, and total counts + uniq_times = torch.empty_like(self.time) + uniq_events = torch.empty_like(self.time, dtype=torch.long) + uniq_counts = torch.empty_like(self.time, dtype=torch.long) + + # Group indices by unique time values + groups = itertools.groupby( + range(len(self.time)), key=lambda i: self.time[order[i]] + ) + + # Initialize index for storing unique values + j = 0 + + # Iterate through unique times + for _, group_indices in groups: + group_indices = list(group_indices) + + # Count events and total occurrences + count_event = sum(self.event[order[i]].item() for i in group_indices) + count = len(group_indices) + + # Store unique time, event count, and total count + uniq_times[j] = self.time[order[group_indices[0]]].item() + uniq_events[j] = count_event + uniq_counts[j] = count + j += 1 + + # Extract valid values based on the index + times = uniq_times[:j] + n_events = uniq_events[:j] + total_count = uniq_counts[:j] + n_censored = total_count - n_events + + # Offset cumulative sum by one to get the number at risk + n_at_risk = n_samples - torch.cumsum( + torch.cat([torch.tensor([0]), total_count]), dim=0 + ) + + return times, n_events, n_at_risk[:-1], n_censored + + +if __name__ == "__main__": + import doctest + + # Run doctest + results = doctest.testmod() + if results.failed == 0: + print("All tests passed.") + else: + print("Some doctests failed.") + sys.exit(1) diff --git a/src/torchsurv/tools/validate_inputs.py b/src/torchsurv/tools/validate_inputs.py new file mode 100644 index 0000000..1d19023 --- /dev/null +++ b/src/torchsurv/tools/validate_inputs.py @@ -0,0 +1,125 @@ +import torch + + +def validate_survival_data(event, time): + """Perform format and validity checks for survival data. + + Args: + event (torch.Tensor, boolean): + Event indicator of size n_samples (= True if event occured). + time (torch.Tensor, float): + Event or censoring time of size n_samples. + + Raises: + TypeError: If ``event`` or ``time`` are not tensors. + ValueError: If ``event`` is not boolean. + ValueError: If ``event`` and ``time`` are not of the same length. + ValueError: If all ``event`` are False. + ValueError: If any ``time`` are negative. + """ + if not torch.is_tensor(event) or not torch.is_tensor(time): + raise TypeError("Inputs 'event' and 'time' should be tensors") + + if not event.dtype == torch.bool: + raise ValueError("Input 'event' should be of boolean type.") + + if not torch.is_floating_point(time): + raise ValueError("Input 'time' should be of float type.") + + if len(event) != len(time): + raise ValueError( + "Dimension mismatch: Incompatible length between inputs 'time' and 'event'." + ) + + if torch.sum(event) <= 0: + raise ValueError("All samples are censored.") + + if torch.any(time < 0.0): + raise ValueError("Input 'time' should be non-negative.") + + +def validate_evaluation_time(new_time, time, within_follow_up=True): + """Perform format and validity checks for evaluation time. + + Args: + new_time (torch.Tensor, optional): + Time points for metric computation of size n_times. + time (torch.Tensor, float): + Event or censoring time of size n_samples. + within_follow_up (bool, optional): + Whether values of ``new_time`` must be within values in ``time``. + Defaults to True. + + Raises: + ValueError: If ``new_time`` contains duplicate values. + ValueError: If ``new_time`` is not sorted. + TypeError: If ``new_time`` is not a tensor. + ValueError: If ``new_time`` is not of floating-point type. + ValueError: + If ``new_time`` is not within the range of follow-up in ``time``. + Assessed only if ``within_follow_up`` is True. + """ + new_time_sorted, indices = torch.unique(new_time, return_inverse=True) + + if len(new_time_sorted) != len(new_time): + raise ValueError("'Value error: Input 'new_time' should contain unique values.") + + if not torch.all(indices == torch.arange(len(new_time))): + raise ValueError( + "Value error: Input 'new_time' should be sorted from the smallest time to the largest." + ) + + if not torch.is_tensor(new_time): + raise TypeError("Type error: Input 'new_time' should be a tensor.") + + if not torch.is_floating_point(new_time): + raise ValueError( + "Value error: Input 'new_time' should be of floating-point type." + ) + + if within_follow_up: + if new_time.max() >= time.max() or new_time.min() < time.min(): + raise ValueError( + "Value error: All new_time must be within follow-up time of test data: [{}; {}[".format( + time.min(), time.max() + ) + ) + + +def validate_estimate(estimate, time, new_time=None) -> None: + """Perform format and validity checks for estimate. + + Args: + estimate (torch.Tensor): + Estimates of shape = (n_samples,) or (n_samples, n_times). + time (torch.Tensor, float): + Time of event or censoring of size n_samples. + new_time (torch.Tensor, optional): + Time points for metric computation of size n_times. + + Raises: + TypeError: If ``estimate`` is not a tensor. + ValueError: If ``estimate`` has more than 2 dimensions. + ValueError: If number of rows of ``estimate`` is not n_samples. + ValueError: + If number of columns of ``estimate`` is not n_times. + Assessed only if ``new_time`` is not None. + """ + if not torch.is_tensor(estimate): + raise TypeError("Type error: Input 'estimate' should be a tensor.") + + if estimate.ndim > 2: + raise ValueError("Value error: Input 'estimate' should have 1 or 2 dimensions.") + + if estimate.shape[0] != time.shape[0]: + raise ValueError( + "Dimension mismatch: Inconsistent number of samples between inputs 'time' and 'estimate'." + ) + + if not new_time is None: + if estimate.ndim == 2 and estimate.shape[1] != new_time.shape[0]: + raise ValueError( + "Dimension mismatch: Expected inputs 'estimate' with {} columns, but got {}".format( + new_time.shape[0], estimate.shape[1] + ) + ) diff --git a/tests/README.md b/tests/README.md new file mode 100644 index 0000000..e6a5549 --- /dev/null +++ b/tests/README.md @@ -0,0 +1,79 @@ +# Unit Tests + +## Structure + +Comprehensive tests on API functionalities help maintain their reliability, accuracy, and robustness. Each functionality of the API is thoroughly tested in separate files named `test_$FUNCTIONALITY.py`. The tests cover various aspects: + +- **Value Comparison:** The values returned by the functions are compared against benchmarks on real data (e.g., North Central Cancer Treatment Group's [lung dataset](https://lifelines.readthedocs.io/en/latest/lifelines.datasets.html#lifelines.datasets.load_lung) and the German Breast Cancer Study Group [gbsg dataset](https://lifelines.readthedocs.io/en/latest/lifelines.datasets.html#lifelines.datasets.load_gbsg2)) as well as simulated data, including edge cases. This ensures that the functions produce accurate results across different scenarios. + +- **Output Format:** The expected format of the function outputs is rigorously tested to ensure consistency and compatibility with other parts of the system or downstream processes. + +- **Error Handling:** Input or edge cases that should raise errors are explicitly tested to verify that the functions behave as expected. + + +## Benchmark Comparison + +The values obtained from the unit tests are compared against benchmarks generated using R and Python packages. Below is a table indicating the packages used for benchmarking each functionality: + +| `torchsurv` functionality | R Package | Python Package | File name | +|---------------------------------|------------------|------------------|---------------------| +| `loss.cox` | `survival` | / | `tests/test_cox.py` | +| `loss.weibull` | `survival` | `lifelines` | `tests/test_weibull.py` | +| `metrics.auc` | `survAUC`, `RiskRegression`, `timeROC` | `sksurv` | `tests/test_auc.py` | +| `metrics.cindex` | `survival`, `survcomp`, `survAUC`, `survC1` | `sksurv` |`tests/test_cindex.py` | +| `metrics.brier_score` | `survAUC`, `survMetrics` | `sksurv` |`tests/test_brier_score.py` | +| `stats.ipcw` | `pec` | `sksurv` |`tests/test_ipcw.py` | +| `stats.kaplan_meier` | `survival` | `sksurv` |`tests/test_kaplan_meier.py` | + + +## Obtaining Benchmarks on R + +Benchmark values from R packages are obtained using R Scripts in `benchmark_script/` and are saved in `benchmark_data/`. Make sure to install the following R libraries before running the scripts: + +- `jsonlite`, v.1.8.7 +- `survival`, v3.5-7 (2023-08-14) +- `riskRegression`, v.2023.12.21 (2023-12-19) +- `timeROC`, v.0.4 (2019-12-18) +- `survAUC`, v.1.2-0 (2023-03-21) +- `SurvMetrics`, v.0.5.0 (2022-09-03) +- `survcomp`, v.1.52.0 (2023-10-24) +- `survC1`, v.1.0-3 (2021-02-10) +- `pec`, v.2023.04.12 (2023-04-11) + +## Benchmark Comparison Figures + +Below are the comparison figures showing the values of the API functionalities against benchmarks generated using different packages: + +### `loss.cox`: Partial log likelihood of Cox proportional hazards model + +The partial log likelihood of Cox proportional hazards models fitted on two real datasets. Models are parameterized with one, two, or all covariates. The standard Cox partial log likelihood was evaluated using only observations with unique time-to-event (without ties), while Efron's and Breslow's corrections were applied using all observations, accounting for ties in event times. + +![](../docs/source/benchmark_cox.png) + +### `loss.weibull`: Log likelihood of Weibull accelerated failure time (AFT) model + +The log likelihood of Weibull Accelerated Failure Time (AFT) models fitted to two real datasets. Models are parameterized with one, two, or all covariates. In the 'scale only' model, only the scale parameter was estimated with a fixed shape, while in the 'shape and scale' model, both the scale and shape parameters were estimated. + + + + +### `metrics.auc`: Area Under the Receiver Operating Characteristic Curve (AUC) + +Time-dependent Uno's AUC evaluated using the log hazard estimated with a Cox proportional hazards model fitted on the 'lung' dataset. In the unit tests, the AUC evaluated on other model specifications (with one, two, or all covariates) and a second dataset were also compared to this benchmark. + + + +### `metrics.cindex`: Concordance index + +Harrell's and Uno's C-index evaluated using the log hazard estimated with a Cox proportional hazards model fitted on the 'lung' dataset. In the unit tests, the C-index evaluated on other model specifications (with one, two, or all covariates) and a second dataset were also compared to this benchmark. + + + + + +### `metrics.brier_score`: Brier score + +Time-dependent Brier score evaluated using the survival function estimated with a Weibull AFT model fitted on the 'lung' dataset. In the unit tests, the Brier score evaluated on other model specifications (with one, two, or all covariates) and a second dataset were also compared to this benchmark. + + + diff --git a/tests/benchmark_data/benchmark_auc.json b/tests/benchmark_data/benchmark_auc.json new file mode 100644 index 0000000..76a5935 --- /dev/null +++ b/tests/benchmark_data/benchmark_auc.json @@ -0,0 +1 @@ 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diff --git a/tests/benchmark_data/benchmark_brier_score.json b/tests/benchmark_data/benchmark_brier_score.json new file mode 100644 index 0000000..7ed2ecc --- /dev/null +++ b/tests/benchmark_data/benchmark_brier_score.json @@ -0,0 +1 @@ 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diff --git a/tests/benchmark_data/benchmark_cindex.json b/tests/benchmark_data/benchmark_cindex.json new file mode 100644 index 0000000..d138e7b --- /dev/null +++ b/tests/benchmark_data/benchmark_cindex.json @@ -0,0 +1 @@ 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diff --git a/tests/benchmark_data/benchmark_ipcw.json b/tests/benchmark_data/benchmark_ipcw.json new file mode 100644 index 0000000..c339ce1 --- /dev/null +++ b/tests/benchmark_data/benchmark_ipcw.json @@ -0,0 +1 @@ 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diff --git a/tests/benchmark_data/benchmark_kaplan_meier.json b/tests/benchmark_data/benchmark_kaplan_meier.json new file mode 100644 index 0000000..6c08fc5 --- /dev/null +++ b/tests/benchmark_data/benchmark_kaplan_meier.json @@ -0,0 +1 @@ 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diff --git a/tests/benchmark_data/benchmark_weibull.json b/tests/benchmark_data/benchmark_weibull.json new file mode 100644 index 0000000..a52fea6 --- /dev/null +++ b/tests/benchmark_data/benchmark_weibull.json @@ -0,0 +1 @@ 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diff --git a/tests/benchmark_script/test_auc.R b/tests/benchmark_script/test_auc.R new file mode 100644 index 0000000..949ee79 --- /dev/null +++ b/tests/benchmark_script/test_auc.R @@ -0,0 +1,208 @@ +library(survival) +library(jsonlite) +library(riskRegression) +library(timeROC) +library(survAUC) + +# function to get metrics +get_auc <- function(TR, TE, train.fit){ + + # survival data object + Surv.rsp <- survival::Surv(TR$time, TR$status) + Surv.rsp.new <- survival::Surv(TE$time, TE$status) + + # times to estimate auc + times <- sort(unique(TE$time[TE$status == 1])) + last_time_event = F + if(max(TE$time) %in% times){ + last_time_event = T + times <- times[times < max(TE$time)] + + } + + # survival probability KM estimate + surv.prob <- unique(survfit(Surv(TE$time,TE$status)~1)$surv) + surv.prob = surv.prob[-length(surv.prob)] + + # predictors train and test data + lp <- predict(train.fit, newdata = TR) + lpnew <- predict(train.fit, newdata = TE) + + + # + # SurvAUC + + # SurvAUC: AUC C/D with ipcw + AUC_Uno <- survAUC::AUC.uno(Surv.rsp, Surv.rsp.new, lpnew, times) + auc_cd_survAUC <- AUC_Uno$auc + + # SurvAUC: integral of C/D with ipcw + iauc_cd_survAUC <- survAUC::IntAUC(AUC_Uno$auc, AUC_Uno$times, surv.prob, max(times), auc.type="cumulative") + + # SurvAUC: Integral of AUC I/D Soug and Zhou (2008) definition + auc_SZ <- survAUC::AUC.sh(Surv.rsp, Surv.rsp.new, lp, lpnew, times, type="incident") + auc_id_sz_survAUC <- auc_SZ$auc + i_auc_id_sz_survAUC <- auc_SZ$iauc + + + # + # TimeROC + # There is a bug when auc is evaluated at event time because case are defined + # as T < t instead of T <= t. So instead we samples new_time in between the + # event times. + times_se <- quantile(times, probs=seq(0.2,0.8,0.1)) + + # TimeROC: Uno's AUC C/D + auc_cd_Uno_timeROC <- timeROC_DEBUG(T=TE$time, + delta=TE$status, + marker=lpnew, + cause=1, + weighting="marginal", + times=times_se, + iid=TRUE)$AUC + + # TimeROC: standard error of Uno's AUC C/D + auc_cd_Uno_se_timeROC <- timeROC_DEBUG(T=TE$time, + delta=TE$status, + marker=lpnew, + cause=1, + weighting="marginal", + times=times_se, + iid=TRUE)$inference$vect_sd_1 + + + # + # riskRegression + + # riskRegression: Uno's AUC C/D + auc_cd_Uno_riskRegression <- riskRegression::Score(list("model"=train.fit), + formula=Surv(time,status)~1, + data=TE, + cens.method = "ipcw", + metrics="auc", + times=times)$AUC$score$AUC + + # riskRegression: standard error of Uno's AUC C/D + auc_cd_Uno_se_riskRegression <- riskRegression::Score(list("model"=train.fit), + formula=Surv(time,status)~1, + data=TE, + cens.method = "ipcw", + metrics="auc", + times=times)$AUC$score$se + + return(list(train_time = TR$time, train_status = TR$status, + test_time = TE$time, test_status = TE$status, + estimate = lpnew, times = times, + surv.prob = surv.prob, + auc_cd_survAUC = auc_cd_survAUC, iauc_cd_survAUC = iauc_cd_survAUC, + auc_id_sz_survAUC = auc_id_sz_survAUC, i_auc_id_sz_survAUC = i_auc_id_sz_survAUC, + auc_cd_Uno_riskRegression = auc_cd_Uno_riskRegression, + auc_cd_Uno_se_riskRegression = auc_cd_Uno_se_riskRegression, + times_se = times_se, + auc_cd_Uno_timeROC = auc_cd_Uno_timeROC, + auc_cd_Uno_se_timeROC = auc_cd_Uno_se_timeROC + + )) + + +} + +# bugfix timeROC function +bugfix_TimeROC_compute_iid_decomposition <- function(){ + timeROC_DEBUG <<-timeROC::timeROC + compute_iid_decomposition_DEBUG <<- timeROC:::compute_iid_decomposition + compute_iid_decomposition_survival_DEBUG <<- timeROC:::compute_iid_decomposition_survival + + print(body(timeROC_DEBUG)[[41]][[3]][[2]][[4]][[15]][[4]][[2]][[3]][[2]][[3]][[1]]) + body(timeROC_DEBUG)[[41]][[3]][[2]][[4]][[15]][[4]][[2]][[3]][[2]][[3]][[1]] <<- substitute(compute_iid_decomposition_DEBUG) + print(body(timeROC_DEBUG)[[41]][[3]][[2]][[4]][[15]][[4]][[2]][[3]][[2]][[3]][[1]]) + + print(body(compute_iid_decomposition_DEBUG)[[5]][[4]][[2]][[1]]) + body(compute_iid_decomposition_DEBUG)[[5]][[4]][[2]][[1]] <<- substitute(compute_iid_decomposition_survival_DEBUG) + print(body(compute_iid_decomposition_DEBUG)[[5]][[4]][[2]][[1]]) + + # wrong division by St to get ipsw + print(body(compute_iid_decomposition_survival_DEBUG)[[28]]) + body(compute_iid_decomposition_survival_DEBUG)[[28]] <<- substitute( + vect_Tisupt <- as.numeric(Mat_data[, c("T")] >= t)/St + ) +} + + +# bugfix timeROC function +bugfix_TimeROC_compute_iid_decomposition() + +# create list to save aucs +aucs <- list() +i = 1 + + +# +# lung dataset +# + + +lung <- survival::lung +lung$sex = lung$sex == 1 +lung$status = lung$status == 2 +lung$age = (lung$age - mean(lung$age)) / sd(lung$age) + +midpoint = floor(nrow(lung) / 2) +mask = 1:nrow(lung) %in% 1:midpoint +TR <- lung[1:midpoint,] +TE <- lung[(midpoint + 1):nrow(lung),] +TR_complete <- TR[complete.cases(TR),] +TE_complete <- TE[complete.cases(TE),] + + +# one and two covariates and all covariates ignore missing values +train.fit_1 <- coxph(Surv(time, status) ~ age, data = TR, method = 'efron', x= T, y = T) +train.fit_2 <- coxph(Surv(time, status) ~ age + sex, data = TR, method = 'efron', x= T, y = T) +train.fit_3 <- coxph(Surv(time, status) ~ age + sex + ph.ecog + ph.karno + + pat.karno + meal.cal + wt.loss, data = TR_complete, method = 'efron', x= T, y = T) + +# save aucs +aucs[[i]] <- get_auc(TR, TE, train.fit_1); i = i + 1 +aucs[[i]] <- get_auc(TR, TE, train.fit_2); i = i + 1 +aucs[[i]] <- get_auc(TR_complete, TE_complete, train.fit_3); i = i + 1 + + +# +# gbsg dataset +# + +gbsg <- survival::gbsg +gbsg$age = (gbsg$age - mean(gbsg$age)) / sd(gbsg$age) +gbsg$size = (gbsg$size - mean(gbsg$size)) / sd(gbsg$size) +gbsg$time = gbsg$rfstime + +midpoint = floor(nrow(gbsg) / 2) +mask = 1:nrow(gbsg) %in% 1:midpoint +TR <- gbsg[1:midpoint,] +TE <- gbsg[(midpoint + 1):nrow(gbsg),] + +# one and two covariates and all covariates +train.fit_1 <- coxph(Surv(rfstime, status) ~ age, data = TR, method = 'efron', x= T, y = T) +train.fit_2 <- coxph(Surv(rfstime, status) ~ age + size, data = TR, method = 'efron', x= T, y = T) +train.fit_3 <- coxph(Surv(rfstime, status) ~ age + size + grade + + nodes + pgr + er + hormon, data = TR, method = 'efron', x= T, y = T) + +aucs[[i]] <- get_auc(TR, TE, train.fit_1); i = i + 1 +aucs[[i]] <- get_auc(TR, TE, train.fit_2); i = i + 1 +aucs[[i]] <- get_auc(TR, TE, train.fit_3); i = i + 1 + + +# +# Save +# + + +write_json(aucs, file.path("../benchmark_data/benchmark_auc.json")) + + +# +# AUC I/D +# Note: risksetROC::risksetAUC uses a smoothing methods to estimate AUC I/D +# --> not compared to torchsurv + + diff --git a/tests/benchmark_script/test_brier_score.R b/tests/benchmark_script/test_brier_score.R new file mode 100644 index 0000000..166d6ea --- /dev/null +++ b/tests/benchmark_script/test_brier_score.R @@ -0,0 +1,171 @@ +library(survival) +library(survAUC) +library(SurvMetrics) + + +# function to get brier score +get_brier_score <- function(TR, TE, train.fit){ + + # survival data object + Surv.rsp <- survival::Surv(TR$time, TR$status) + Surv.rsp.new <- survival::Surv(TE$time, TE$status) + + # predictors train and test data + lp <- predict(train.fit, newdata = TR) + lpnew <- predict(train.fit, newdata = TE) + + # evaluation time + times <- sort(unique(TE$time[TE$status == 1])) + last_time_event = F + if(max(TE$time) %in% times){ + last_time_event = T + times <- times[times < max(TE$time)] + } + + # estimate of survival function + estimate = survival_function_weibull(train.fit, times, TE) + + # + # SurvMetrics + + brier_score_survMetrics <- vector(mode = 'numeric', length = length(times)) + for(i in seq_along(times)) + brier_score_survMetrics[i] <- Brier_SurvMetrics_DEBUG(Surv.rsp.new, estimate[,i], times[i]) + ibrier_score_survMetrics <- IBS_SurvMetrics_DEBUG(Surv.rsp.new, estimate, IBSrange = times) + + + # + # SurvAUC + + outputs_survAUC <- predErr(Surv.rsp, Surv.rsp.new, lp, lpnew, times, + type = "brier", int.type = "unweighted") + brier_score_survAUC <- outputs_survAUC$error + ibrier_score_survAUC <- outputs_survAUC$ierror + + + return(list(train_time = TR$time, train_status = TR$status, + test_time = TE$time, test_status = TE$status, + estimate = estimate, times = times, + brier_score_survMetrics = brier_score_survMetrics, + ibrier_score_survMetrics = ibrier_score_survMetrics, + brier_score_survAUC = brier_score_survAUC, + ibrier_score_survAUC = ibrier_score_survAUC + + )) + + +} + +# bugfix survMetrics brier score +bugfix_TimeROC_compute_iid_decomposition <- function(){ + + Brier_SurvMetrics_DEBUG <<- SurvMetrics::Brier + IBS_SurvMetrics_DEBUG <<- SurvMetrics::IBS + + # cases should be t <= t_star instead of t < t_star + print(body(Brier_SurvMetrics_DEBUG)[[21]][[4]][[2]][[2]]) + body(Brier_SurvMetrics_DEBUG)[[21]][[4]][[2]][[2]] <<- substitute(time[i] <= t_star & (status[i] == 1)) + print(body(Brier_SurvMetrics_DEBUG)[[21]][[4]][[2]][[2]]) + + # controls should be t > t_star instead of t >= t_star + print(body(Brier_SurvMetrics_DEBUG)[[21]][[4]][[3]][[2]]) + body(Brier_SurvMetrics_DEBUG)[[21]][[4]][[3]][[2]] <<- substitute(time[i] > t_star) + print(body(Brier_SurvMetrics_DEBUG)[[21]][[4]][[3]][[2]]) + + # use the Brier debug version in IBS + print(body(IBS_SurvMetrics_DEBUG)[[14]][[3]][[2]]) + body(IBS_SurvMetrics_DEBUG)[[14]][[3]][[2]] <<- substitute(bs <- Brier_SurvMetrics_DEBUG(object, sp_matrix, IBSrange)) + print(body(IBS_SurvMetrics_DEBUG)[[14]][[3]][[2]]) + + print(body(IBS_SurvMetrics_DEBUG)[[14]][[4]][[4]][[3]][[4]][[4]][[4]]) + body(IBS_SurvMetrics_DEBUG)[[14]][[4]][[4]][[3]][[4]][[4]][[4]] <<- substitute(t_brier[i] <- Brier_SurvMetrics_DEBUG(object, pre_sp, t_star)) + print(body(IBS_SurvMetrics_DEBUG)[[14]][[4]][[4]][[3]][[4]][[4]][[4]]) + + print(body(IBS_SurvMetrics_DEBUG)[[14]][[4]][[4]][[4]][[6]][[4]][[4]]) + body(IBS_SurvMetrics_DEBUG)[[14]][[4]][[4]][[4]][[6]][[4]][[4]] <<- substitute(t_brier[i] <- Brier_SurvMetrics_DEBUG(object, pre_sp, t_star)) + print(body(IBS_SurvMetrics_DEBUG)[[14]][[4]][[4]][[4]][[6]][[4]][[4]]) +} +bugfix_TimeROC_compute_iid_decomposition() + +# survival function weibull AFT model +survival_function_weibull <- function(fit, times, new_data){ + survreg.lp <- predict(fit, type = "lp", newdata = new_data) + survreg.scale <- fit$scale + shape <- 1/survreg.scale + scale <- exp(survreg.lp) + s <- matrix(ncol = length(times), nrow = length(scale), 0) + for(i in seq_along(times)){ + t = times[i] + s[,i] <- 1 - pweibull(t, shape = shape, scale = scale) + } + + return(s) +} + +# create list to save brier sores +brier_scores <- list() +i = 1 + + +# +# lung dataset +# + + +lung <- survival::lung +lung$sex = lung$sex == 1 +lung$status = lung$status == 2 +lung$age = (lung$age - mean(lung$age)) / sd(lung$age) + +midpoint = floor(nrow(lung) / 2) +mask = 1:nrow(lung) %in% 1:midpoint +TR <- lung[1:midpoint,] +TE <- lung[(midpoint + 1):nrow(lung),] +TR_complete <- TR[complete.cases(TR),] +TE_complete <- TE[complete.cases(TE),] + + +# one and two covariates and all covariates ignore missing values +train.fit_1 <- survreg(Surv(time, status) ~ age, data=TR, dist = 'weibull', scale = 1, x= T, y = T) +train.fit_2 <- survreg(Surv(time, status) ~ age+ sex, data=TR, dist = 'weibull', scale = 1, x= T, y = T) +train.fit_3 <- survreg(Surv(time, status) ~ age+ sex + ph.ecog + ph.karno + + pat.karno + meal.cal + wt.loss, data=TR_complete, dist = 'weibull', scale = 1, x= T, y = T) + +# save metrics +brier_scores[[i]] <- get_brier_score(TR, TE, train.fit_1); i = i + 1 +brier_scores[[i]] <- get_brier_score(TR, TE, train.fit_2); i = i + 1 +brier_scores[[i]] <- get_brier_score(TR_complete, TE_complete, train.fit_3); i = i + 1 + + +# +# gbsg dataset +# + +gbsg <- survival::gbsg +gbsg$age = (gbsg$age - mean(gbsg$age)) / sd(gbsg$age) +gbsg$size = (gbsg$size - mean(gbsg$size)) / sd(gbsg$size) +gbsg$time = gbsg$rfstime + +midpoint = floor(nrow(gbsg) / 2) +mask = 1:nrow(gbsg) %in% 1:midpoint +TR <- gbsg[1:midpoint,] +TE <- gbsg[(midpoint + 1):nrow(gbsg),] + +# one and two covariates and all covariates +train.fit_1 <- survreg(Surv(time, status) ~ age, data=TR, dist = 'weibull', scale = 1, x= T, y = T) +train.fit_2 <- survreg(Surv(time, status) ~ age+ size, data=TR, dist = 'weibull', scale = 1, x= T, y = T) +train.fit_3 <- survreg(Surv(time, status) ~ age+ size+ grade + + nodes + pgr + er + hormon, data=TR, dist = 'weibull', scale = 1, x= T, y = T) + +brier_scores[[i]] <- get_brier_score(TR, TE, train.fit_1); i = i + 1 +brier_scores[[i]] <- get_brier_score(TR, TE, train.fit_2); i = i + 1 +brier_scores[[i]] <- get_brier_score(TR, TE, train.fit_3); i = i + 1 + + +# +# Save +# + + +write_json(brier_scores, file.path("../benchmark_data/benchmark_brier_score.json")) + diff --git a/tests/benchmark_script/test_cindex.R b/tests/benchmark_script/test_cindex.R new file mode 100644 index 0000000..35278e2 --- /dev/null +++ b/tests/benchmark_script/test_cindex.R @@ -0,0 +1,184 @@ +library(survival) +library(survcomp) +library(jsonlite) +library(riskRegression) +library(survC1) +library(survAUC) + + +# function to get metrics +get_cindex <- function(TR, TE, train.fit){ + + # survival data object + Surv.rsp <- survival::Surv(TR$time, TR$status) + Surv.rsp.new <- survival::Surv(TE$time, TE$status) + + # survival probability KM estimate + surv.prob <- unique(survfit(Surv(TE$time,TE$status)~1)$surv) + surv.prob = surv.prob[-length(surv.prob)] + + # predictors train and test data + lp <- predict(train.fit, newdata = TR) + lpnew <- predict(train.fit, newdata = TE) + + # max time + times <- sort(unique(TE$time[TE$status == 1])) + last_time_event = F + if(max(TE$time) %in% times){ + last_time_event = T + times <- times[times < max(TE$time)] + } + max_times <- max(times) + + + # + # survival + + # survival: Harrell's C-index + c_Harrell_survival <- survival::concordance(train.fit, newdata = TE)$concordance + + + # + # SurvAUC + + # SurvAUC: Uno's c index + c_Uno_survAUC = survAUC::UnoC(Surv.rsp, Surv.rsp.new, lpnew, time = max_times) + + + # + # survC1 + + # survC1: Uno's C-index + c_Uno_survC1 = Est.Cval(cbind(TE$time, TE$status, lpnew), tau = max_times, nofit = TRUE)$Dhat + + # + # survcomp: + c_survcomp <- survcomp_concordance.index_modified(lpnew, TE$time, TE$status, method='noether') + c_survcomp_conservative <- survcomp_concordance.index_modified(lpnew, TE$time, TE$status, method='conservative') + + # Harrell's c-index + c_Harrell_survcomp = c_survcomp$c.index + + # Noether standard error + c_se_noether_survcomp = c_survcomp$se + ch_survcomp = c_survcomp$ch + dh_survcomp = c_survcomp$dh + weights_survcomp = c_survcomp$weights + + # conservative confidence interval (symmetric) + c_lower_conservative_survcomp = c_survcomp_conservative$lower + + + return(list(train_time = TR$time, train_status = TR$status, + test_time = TE$time, test_status = TE$status, + estimate = lpnew, times = times, + surv.prob = surv.prob, + c_Uno_survAUC = c_Uno_survAUC, + c_Uno_survC1 = c_Uno_survC1, + c_Harrell_survival = c_Harrell_survival, + c_Harrell_survcomp = c_Harrell_survcomp, + c_se_noether_survcomp = c_se_noether_survcomp, + c_lower_conservative_survcomp = c_lower_conservative_survcomp, + ch_survcomp = ch_survcomp, + dh_survcomp = dh_survcomp, + weights_survcomp = weights_survcomp + + )) + + +} + +# print more outputs from function +add_survcomp_ouputs <- function(){ + survcomp_concordance.index_modified <<- survcomp::concordance.index + + print(body(survcomp_concordance.index_modified)[[46]]) + body(survcomp_concordance.index_modified)[[46]] <<- substitute(return(list(c.index = cindex, + se = se, weights=weights, + lower = lower, upper = upper, + p.value = p, n = length(x2), + data = data, comppairs = cscount, + ch = ch, + dh = dh))) + print(body(survcomp_concordance.index_modified)[[46]]) +} + +add_survcomp_ouputs() + +# create list to save cindexs +cindexs <- list() +i = 1 + + +# +# lung dataset +# + + +lung <- survival::lung +lung$sex = lung$sex == 1 +lung$status = lung$status == 2 +lung$age = (lung$age - mean(lung$age)) / sd(lung$age) + +midpoint = floor(nrow(lung) / 2) +mask = 1:nrow(lung) %in% 1:midpoint +TR <- lung[1:midpoint,] +TE <- lung[(midpoint + 1):nrow(lung),] +TR_complete <- TR[complete.cases(TR),] +TE_complete <- TE[complete.cases(TE),] + + +# one and two covariates and all covariates ignore missing values +train.fit_1 <- coxph(Surv(time, status) ~ age, data = TR, method = 'efron', x= T, y = T) +train.fit_2 <- coxph(Surv(time, status) ~ age + sex, data = TR, method = 'efron', x= T, y = T) +train.fit_3 <- coxph(Surv(time, status) ~ age + sex + ph.ecog + ph.karno + + pat.karno + meal.cal + wt.loss, data = TR_complete, method = 'efron', x= T, y = T) + +# save metrics +cindexs[[i]] <- get_cindex(TR, TE, train.fit_1); i = i + 1 +cindexs[[i]] <- get_cindex(TR, TE, train.fit_2); i = i + 1 +cindexs[[i]] <- get_cindex(TR_complete, TE_complete, train.fit_3); i = i + 1 + + +# +# gbsg dataset +# + +gbsg <- survival::gbsg +gbsg$age = (gbsg$age - mean(gbsg$age)) / sd(gbsg$age) +gbsg$size = (gbsg$size - mean(gbsg$size)) / sd(gbsg$size) +gbsg$time = gbsg$rfstime + +midpoint = floor(nrow(gbsg) / 2) +mask = 1:nrow(gbsg) %in% 1:midpoint +TR <- gbsg[1:midpoint,] +TE <- gbsg[(midpoint + 1):nrow(gbsg),] + +# one and two covariates and all covariates +train.fit_1 <- coxph(Surv(rfstime, status) ~ age, data = TR, method = 'efron', x= T, y = T) +train.fit_2 <- coxph(Surv(rfstime, status) ~ age + size, data = TR, method = 'efron', x= T, y = T) +train.fit_3 <- coxph(Surv(rfstime, status) ~ age + size + grade + + nodes + pgr + er + hormon, data = TR, method = 'efron', x= T, y = T) + +cindexs[[i]] <- get_cindex(TR, TE, train.fit_1); i = i + 1 +cindexs[[i]] <- get_cindex(TR, TE, train.fit_2); i = i + 1 +cindexs[[i]] <- get_cindex(TR, TE, train.fit_3); i = i + 1 + + +# +# Save +# + + +write_json(cindexs, file.path("../benchmark_data/benchmark_cindex.json")) + + +# +# C-index +# Note: risksetROC::risksetAUC uses a smoothing methods to estimate AUC I/D that is integrated out to get the c-index +# --> not compared to torchsurv +# Note: pec::cindex and Hmisc::rcorr.cens C-index does not consider ties in the calculation of their C-index (https://stackoverflow.com/questions/24784203/r-differences-between-cindex-function-from-pec-package-and-coxph) +# --> not compared to torchsurv +# Note: SurvMetrics::Cindex does not consider ties but partial concordance metric (https://journal.r-project.org/articles/RJ-2023-009/RJ-2023-009.pdf) +# --> not compared to torchsurv + diff --git a/tests/benchmark_script/test_cox.R b/tests/benchmark_script/test_cox.R new file mode 100644 index 0000000..28677ff --- /dev/null +++ b/tests/benchmark_script/test_cox.R @@ -0,0 +1,152 @@ +library(survival) +library(jsonlite) + +# create function to extract log hazard and log likelihood +get_log_likelihood <- function(formula, data, x, no_ties){ + + time = data$time + status = data$status + + if(no_ties){ + # if no ties, standard cox partial likelihood is used + + fit <- coxph(formula, data = data) + log_hazard <- fit$coefficients %*% t(as.matrix(x, ncol = ncol(x))) + log_likelihood <- as.numeric(logLik(fit)) + + return(list(time = time, status = status, + log_hazard = log_hazard, + log_likelihood = log_likelihood, + no_ties = no_ties)) + }else{ + # with ties, use efrond and breslow method + + fit_efron <- coxph(formula, data = data, method = 'efron') + log_hazard_efron <- fit_efron$coefficients %*% t(as.matrix(x, ncol = ncol(x))) + log_likelihood_efron <- as.numeric(logLik(fit_efron)) + + fit_breslow <- coxph(formula, data = data, method = 'breslow') + log_hazard_breslow <- fit_breslow$coefficients %*% t(as.matrix(x, ncol = ncol(x))) + log_likelihood_breslow <- as.numeric(logLik(fit_breslow)) + + return(list(time = time, status = status, + log_hazard_efron = log_hazard_efron, + log_likelihood_efron = log_likelihood_efron, + log_hazard_breslow = log_hazard_breslow, + log_likelihood_breslow = log_likelihood_breslow, + no_ties = no_ties)) + } + +} + +# +# empty list to save log likelihoods +log_likelihoods <- list() +i = 1 + + +# +# lung dataset +# + +# load lung dataset +lung <- survival::lung +lung$sex = lung$sex == 1 +lung$status = lung$status == 2 +lung$age = (lung$age - mean(lung$age)) / sd(lung$age) + +# lung dataset without ties +index_duplicated <- which(duplicated(lung$time)) +lung_unique <- lung[-index_duplicated, ] + +# ignore missing values +lung_complete <- lung[complete.cases(lung),] +lung_unique_complete <- lung_unique[complete.cases(lung_unique),] + +# Cox: no ties +log_likelihoods[[i]] <- get_log_likelihood( + formula = Surv(time, status) ~ age, + data = lung_unique, + x = lung_unique[, c('age')], + no_ties = TRUE); i = i + 1 +log_likelihoods[[i]] <- get_log_likelihood( + formula = Surv(time, status) ~ age + sex, + data = lung_unique, + x = lung_unique[, c('age', 'sex')], + no_ties = TRUE); i = i + 1 +log_likelihoods[[i]] <- get_log_likelihood( + formula = Surv(time, status) ~ age + sex + ph.ecog + ph.karno + pat.karno + meal.cal + wt.loss, + data = lung_unique_complete, + x = lung_unique_complete[, c('age', 'sex', 'ph.ecog', 'ph.karno', 'pat.karno', 'meal.cal', 'wt.loss')], + no_ties = TRUE); i = i + 1 + +# Cox with ties +log_likelihoods[[i]] <- get_log_likelihood( + formula = Surv(time, status) ~ age, + data = lung, + x = lung[, c('age')], + no_ties = FALSE); i = i + 1 +log_likelihoods[[i]] <- get_log_likelihood( + formula = Surv(time, status) ~ age + sex, + data = lung, + x = lung[, c('age', 'sex')], + no_ties = FALSE); i = i + 1 +log_likelihoods[[i]] <- get_log_likelihood( + formula = Surv(time, status) ~ age + sex + ph.ecog + ph.karno + pat.karno + meal.cal + wt.loss, + data = lung_complete, + x = lung_complete[, c('age', 'sex', 'ph.ecog', 'ph.karno', 'pat.karno', 'meal.cal', 'wt.loss')], + no_ties = FALSE); i = i + 1 + + +# +# gbsg dataset +# + +gbsg <- survival::gbsg +gbsg$age = (gbsg$age - mean(gbsg$age)) / sd(gbsg$age) +gbsg$size = (gbsg$size - mean(gbsg$size)) / sd(gbsg$size) +gbsg$time = gbsg$rfstime + +# lung dataset without ties +index_duplicated <- which(duplicated(gbsg$time)) +gbsg_unique <- gbsg[-index_duplicated, ] + +# Cox: no ties +log_likelihoods[[i]] <- get_log_likelihood( + formula = Surv(time, status) ~ age, + data = gbsg_unique, + x = gbsg_unique[, c('age')], + no_ties = TRUE); i = i + 1 +log_likelihoods[[i]] <- get_log_likelihood( + formula = Surv(rfstime, status) ~ age + size, + data = gbsg_unique, + x = gbsg_unique[, c('age', 'size')], + no_ties = TRUE); i = i + 1 +log_likelihoods[[i]] <- get_log_likelihood( + formula = Surv(rfstime, status) ~ age + size + grade + nodes + pgr + er + hormon, + data = gbsg_unique, + x = gbsg_unique[, c('age', 'size', 'grade', 'nodes', 'pgr', 'er', 'hormon')], + no_ties = TRUE); i = i + 1 + +# Cox with ties +log_likelihoods[[i]] <- get_log_likelihood( + formula = Surv(time, status) ~ age, + data = gbsg, + x = gbsg[, c('age')], + no_ties = FALSE); i = i + 1 +log_likelihoods[[i]] <- get_log_likelihood( + formula = Surv(rfstime, status) ~ age + size, + data = gbsg, + x = gbsg[, c('age', 'size')], + no_ties = FALSE); i = i + 1 +log_likelihoods[[i]] <- get_log_likelihood( + formula = Surv(rfstime, status) ~ age + size + grade + nodes + pgr + er + hormon, + data = gbsg, + x = gbsg[, c('age', 'size', 'grade', 'nodes', 'pgr', 'er', 'hormon')], + no_ties = FALSE); i = i + 1 + + +# +# Save +write_json(log_likelihoods, file.path("../benchmark_data/benchmark_cox.json")) + diff --git a/tests/benchmark_script/test_ipcw.R b/tests/benchmark_script/test_ipcw.R new file mode 100644 index 0000000..80b0aba --- /dev/null +++ b/tests/benchmark_script/test_ipcw.R @@ -0,0 +1,54 @@ +library(pec) + +get_ipcw <- function(data){ + + sorted_indices <- order(data$time) + time = data$time[sorted_indices] + status = data$status[sorted_indices] + times <- quantile(time, probs=seq(0.2,0.8,0.1)) + + ipcw <- pec::ipcw(Surv(failure_time,status)~1, + data=data.frame(failure_time=time,status=as.numeric(status!=0)), + method="marginal", + times=times, + subjectTimes=T, + subjectTimesLag=0) + + ipcw_times <- 1/ipcw$IPCW.times + ipcw_subjectimes <- 1/ipcw$IPCW.subjectTimes + ipcw_subjectimes[ipcw_subjectimes == Inf] = 0 + + return(list(time=time, status=status, times=times, ipcw_times=ipcw_times, ipcw_subjectimes=ipcw_subjectimes)) +} + +# create list to save aucs +ipcws <- list() +i = 1 + +# +# lung dataset + +lung <- survival::lung +lung$sex = lung$sex == 1 +lung$status = lung$status == 2 +lung$age = (lung$age - mean(lung$age)) / sd(lung$age) + +ipcws[[1]] <- get_ipcw(lung) + +# +# gbsg dataset + +gbsg <- survival::gbsg +gbsg$age = (gbsg$age - mean(gbsg$age)) / sd(gbsg$age) +gbsg$size = (gbsg$size - mean(gbsg$size)) / sd(gbsg$size) +gbsg$time = gbsg$rfstime + +ipcws[[2]] <- get_ipcw(gbsg) + + +# +# Save + +write_json(ipcws, file.path("../benchmark_data/benchmark_ipcw.json")) + + diff --git a/tests/benchmark_script/test_kaplan_meier.R b/tests/benchmark_script/test_kaplan_meier.R new file mode 100644 index 0000000..ffe9d1a --- /dev/null +++ b/tests/benchmark_script/test_kaplan_meier.R @@ -0,0 +1,41 @@ +library(survival) + +get_kaplan_meier <- function(data){ + + surv_fit <- survfit(Surv(time, status) ~ 1, data=data) + times = surv_fit$time + surv_prob_survival <- surv_fit$surv + + return(list(time=data$time, status=data$status, + times = times, + surv_prob_survival=surv_prob_survival)) +} + +# create list to save aucs +kaplan_meiers <- list() +i = 1 + +# +# lung dataset + +lung <- survival::lung +lung$sex = lung$sex == 1 +lung$status = lung$status == 2 +lung$age = (lung$age - mean(lung$age)) / sd(lung$age) + +kaplan_meiers[[1]] <- get_kaplan_meier(lung) + +# +# gbsg dataset + +gbsg <- survival::gbsg +gbsg$age = (gbsg$age - mean(gbsg$age)) / sd(gbsg$age) +gbsg$size = (gbsg$size - mean(gbsg$size)) / sd(gbsg$size) +gbsg$time = gbsg$rfstime + +kaplan_meiers[[2]] <- get_kaplan_meier(gbsg) + +# +# Save + +write_json(kaplan_meiers, file.path("../benchmark_data/benchmark_kaplan_meier.json")) diff --git a/tests/benchmark_script/test_weibull.R b/tests/benchmark_script/test_weibull.R new file mode 100644 index 0000000..5626b10 --- /dev/null +++ b/tests/benchmark_script/test_weibull.R @@ -0,0 +1,89 @@ +library(survival) +library(jsonlite) + +# create function to extract log hazard and log likelihood +get_log_likelihood <- function(formula, data, x){ + + time = data$time + status = data$status + + fit <- survreg(formula, data=data, dist = 'weibull', scale = 1) # this is the survreg output model + log_shape = fit$coefficients %*% t(as.matrix(x, ncol = ncol(x))) + log_likelihood = fit$loglik[length(fit$loglik)] + + return(list(time = time, status = status, + log_shape = log_shape, + log_likelihood = log_likelihood)) + +} + +# +# empty list to save log likelihoods +log_likelihoods <- list() +i = 1 + + +# +# lung dataset +# + +# load lung dataset +lung <- survival::lung +lung$sex = lung$sex == 1 +lung$status = lung$status == 2 +lung$age = (lung$age - mean(lung$age)) / sd(lung$age) + +# lung dataset without ties +index_duplicated <- which(duplicated(lung$time)) + +# ignore missing values +lung_complete <- lung[complete.cases(lung),] + +log_likelihoods[[i]] <- get_log_likelihood( + formula = Surv(time, status) ~ age, + data = lung, + x = data.frame(rep(1, nrow(lung)), lung[, c('age')]) +); i = i + 1 +log_likelihoods[[i]] <- get_log_likelihood( + formula = Surv(time, status) ~ age + sex, + data = lung, + x = data.frame(rep(1, nrow(lung)), lung[, c('age', 'sex')]) +); i = i + 1 +log_likelihoods[[i]] <- get_log_likelihood( + formula = Surv(time, status) ~ age + sex + ph.ecog + ph.karno + pat.karno + meal.cal + wt.loss, + data = lung_complete, + x = data.frame(rep(1, nrow(lung_complete)),lung_complete[, c('age', 'sex', 'ph.ecog', 'ph.karno', 'pat.karno', 'meal.cal', 'wt.loss')]) +); i = i + 1 + + + +# +# gbsg dataset +# + +gbsg <- survival::gbsg +gbsg$age = (gbsg$age - mean(gbsg$age)) / sd(gbsg$age) +gbsg$size = (gbsg$size - mean(gbsg$size)) / sd(gbsg$size) +gbsg$time = gbsg$rfstime + +log_likelihoods[[i]] <- get_log_likelihood( + formula = Surv(time, status) ~ age, + data = gbsg, + x = data.frame(rep(1, nrow(gbsg)), gbsg[, c('age')]) +); i = i + 1 +log_likelihoods[[i]] <- get_log_likelihood( + formula = Surv(rfstime, status) ~ age + size, + data = gbsg, + x = data.frame(rep(1, nrow(gbsg)), gbsg[, c('age', 'size')]) +); i = i + 1 +log_likelihoods[[i]] <- get_log_likelihood( + formula = Surv(rfstime, status) ~ age + size + grade + nodes + pgr + er + hormon, + data = gbsg, + x = data.frame(rep(1, nrow(gbsg)), gbsg[, c('age', 'size', 'grade', 'nodes', 'pgr', 'er', 'hormon')]) +); i = i + 1 + + +# +# Save +write_json(log_likelihoods, file.path("../benchmark_data/benchmark_weibull.json")) + diff --git a/tests/test_auc.py b/tests/test_auc.py new file mode 100644 index 0000000..4d705a0 --- /dev/null +++ b/tests/test_auc.py @@ -0,0 +1,346 @@ +# global modules +import json +import unittest + +import numpy as np +import torch +from sksurv.metrics import cumulative_dynamic_auc +from utils import DataBatchContainer, conditions_ci, conditions_p_value + +# Local modules +from torchsurv.metrics.auc import Auc +from torchsurv.stats.ipcw import get_ipcw + +torch.manual_seed(23) + +# Load the benchmark metrics from R +with open("tests/benchmark_data/benchmark_auc.json", "r") as file: + benchmark_aucs = json.load(file) + +auc = Auc() + + +class TestAUC(unittest.TestCase): + """_summary_ + List of packages compared + - survAUC (R): AUC C/D with IPCW + Integral of AUC C/D + Integral of AUC I/D + - RiskRegression (R): AUC C/D with IPCW + Standard error of AUC C/D with IPCW + - timeROC (R): AUC C/D with IPCW + Standard error of AUC C/D with IPCW + - sksurv (Python): AUC C/D with IPCW + """ + + def test_auc_cd_real_data(self): + """test point estimate of auc cumulative/dynamic with ipcw on lung and gbsg datasets""" + for benchmark_auc in benchmark_aucs: + train_event = torch.tensor(benchmark_auc["train_status"]).bool() + train_time = torch.tensor(benchmark_auc["train_time"], dtype=torch.float32) + test_event = torch.tensor(benchmark_auc["test_status"]).bool() + test_time = torch.tensor(benchmark_auc["test_time"], dtype=torch.float32) + estimate = torch.tensor(benchmark_auc["estimate"], dtype=torch.float32) + new_time = torch.tensor(benchmark_auc["times"], dtype=torch.float32) + + # ipcw obtained using censoring distribution estimated on train data + ipcw = get_ipcw(train_event, train_time, test_time) + ipcw_new_time = get_ipcw(train_event, train_time, new_time) + auc_cd = auc( + estimate, + test_event, + test_time, + auc_type="cumulative", + weight=ipcw, + weight_new_time=ipcw_new_time, + new_time=new_time, + ) + + auc_cd_survAUC = benchmark_auc["auc_cd_survAUC"] # survAUC + auc_cd_Uno_riskRegression = benchmark_auc[ + "auc_cd_Uno_riskRegression" + ] # riskRegression + + self.assertTrue( + np.allclose( + auc_cd.numpy(), np.array(auc_cd_survAUC), rtol=1e-1, atol=1e-8 + ) + ) + self.assertTrue( + np.allclose( + auc_cd.numpy(), + np.array(auc_cd_Uno_riskRegression), + rtol=1e-1, + atol=1e-2, + ) + ) + + # commented out: riskRegression does not match other R packages + # auc_cd_se = auc._auc_se() + + # auc_cd_Uno_se_riskRegression = benchmark_auc[ + # "auc_cd_Uno_se_riskRegression" + # ] # riskRegression + + # self.assertTrue( + # np.allclose( + # auc_cd_se.numpy(), + # np.array(auc_cd_Uno_se_riskRegression), + # rtol=1e-1, + # atol=1e-1, + # ) + # ) + + def test_auc_cd_se_real_data(self): + """test standard error of auc cumulative/dynamic with ipcw on lung and gbsg datasets""" + for benchmark_auc in benchmark_aucs: + test_event = torch.tensor(benchmark_auc["test_status"]).bool() + test_time = torch.tensor(benchmark_auc["test_time"], dtype=torch.float32) + estimate = torch.tensor(benchmark_auc["estimate"], dtype=torch.float32) + new_time = torch.tensor(benchmark_auc["times_se"], dtype=torch.float32) + + # ipcw obtained using censoring distribution estimated on test data + ipcw = get_ipcw(test_event, test_time, test_time) + ipcw_new_time = get_ipcw(test_event, test_time, new_time) + auc_cd = auc( + estimate, + test_event, + test_time, + auc_type="cumulative", + weight=ipcw, + weight_new_time=ipcw_new_time, + new_time=new_time, + ) # point estimate + auc_cd_se = auc._auc_se() # standard error + + # timeROC + auc_cd_Uno_timeROC = benchmark_auc["auc_cd_Uno_timeROC"] # point estimate + auc_cd_Uno_se_timeROC = benchmark_auc[ + "auc_cd_Uno_se_timeROC" + ] # standard error + + self.assertTrue( + np.allclose( + auc_cd.numpy(), + np.array(auc_cd_Uno_timeROC), + rtol=1e-1, + atol=1e-8, + ) + ) + + self.assertTrue( + np.allclose( + auc_cd_se.numpy(), + np.array(auc_cd_Uno_se_timeROC), + rtol=1e-1, + atol=1e-8, + ) + ) + + def test_i_auc_real_data(self): + """test integral of auc with survAUC on lung and gbsg datasets""" + for benchmark_auc in benchmark_aucs: + times = torch.tensor(benchmark_auc["times"], dtype=torch.float64) + S = torch.tensor(benchmark_auc["surv.prob"], dtype=torch.float64) + + # integral of auc cumulative/dynamic + auc_cd_survAUC = torch.tensor( + benchmark_auc["auc_cd_survAUC"], dtype=torch.float64 + ) + auc_ne = Auc() + auc_ne.auc = auc_cd_survAUC + auc_ne.new_time = times + i_auc_cd = auc_ne._integrate_AUC_cumulative(S, times.max()) + + i_auc_cd_survAUC = benchmark_auc["iauc_cd_survAUC"] # survAUC + + # integral of auc incident/dynamic + auc_id_sz_survAUC = torch.tensor( + benchmark_auc["auc_id_sz_survAUC"], dtype=torch.float64 + ) + auc_ne = Auc() + auc_ne.auc = auc_id_sz_survAUC + auc_ne.new_time = times + i_auc_id_sz = auc_ne._integrate_AUC_incident(S, times.max()) + i_auc_id_sz_survAUC = benchmark_auc["i_auc_id_sz_survAUC"] # survAUC + + self.assertTrue( + np.isclose( + i_auc_cd.numpy(), np.array(i_auc_cd_survAUC), rtol=1e-3, atol=1e-8 + ) + ) + self.assertTrue( + np.isclose( + i_auc_id_sz.numpy(), + np.array(i_auc_id_sz_survAUC), + rtol=1e-3, + atol=1e-8, + ) + ) + + def test_auc_cd_simulated_data(self): + """test auc cumulative/dynamic on simulated batches including edge cases""" + batch_container = DataBatchContainer() + batch_container.generate_batches( + n_batch=20, + flags_to_set=[ + "train_ties_time_event", + "test_ties_time_event", + "train_ties_time_censoring", + "test_ties_time_censoring", + "train_ties_time_event_censoring", + "test_ties_time_event_censoring", + "test_no_censoring", + #'train_no_censoring', cumulative_dynamic_auc from sksurv fails + "test_event_at_last_time", + "ties_score_events", + "ties_score_event_censoring", + "ties_score_censoring", + ], + ) + for batch in batch_container.batches: + ( + train_time, + train_event, + test_time, + test_event, + estimate, + new_time, + y_train_array, + y_test_array, + _, + new_time_array, + ) = batch + + ipcw = get_ipcw(train_event, train_time, test_time) + ipcw_new_time = get_ipcw(train_event, train_time, new_time) + + # expand in 2D + estimate = estimate.unsqueeze(1).expand((len(test_time), len(new_time))) + estimate = estimate + torch.randn_like(estimate) * 0.1 + + auc_cd = auc( + estimate, + test_event, + test_time, + auc_type="cumulative", + weight=ipcw, + weight_new_time=ipcw_new_time, + new_time=new_time, + ) + + auc_cd_sksurv, _ = cumulative_dynamic_auc( + y_train_array, y_test_array, estimate.numpy(), new_time_array + ) # sksurv + + self.assertTrue( + np.allclose(auc_cd.numpy(), auc_cd_sksurv, rtol=1e-5, atol=1e-8) + ) + + def test_auc_confidence_interval_pvalue(self): + """test auc confidence interval and p-value are as expected""" + batch_container = DataBatchContainer() + batch_container.generate_batches( + n_batch=20, + flags_to_set=[ + "test_ties_time_event", + "test_ties_time_censoring", + "test_ties_time_event_censoring", + #'test_no_censoring', concordance_index_censored fails + "test_event_at_last_time", + "ties_score_events", + "ties_score_event_censoring", + "ties_score_censoring", + ], + ) + for batch in batch_container.batches: + (_, _, time, event, estimate, *_) = batch + + # Run c-index + auc( + estimate, + event, + time, + ) + + n_bootstraps = 9 + + for method in ["blanche", "bootstrap"]: + for alternative in ["two_sided", "less", "greater"]: + auc_ci = auc.confidence_interval( + method=method, + alternative=alternative, + n_bootstraps=n_bootstraps, + ) + self.assertTrue( + all([conditions_ci(auc_ci[:, i]) for i in range(len(auc.auc))]) + ) + + for method in ["blanche", "bootstrap"]: + for alternative in ["two_sided", "less", "greater"]: + auc_p_value = auc.p_value( + method=method, + alternative=alternative, + n_bootstraps=n_bootstraps, + ) + + self.assertTrue( + all( + [ + conditions_p_value(auc_p_value[i]) + for i in range(len(auc.auc)) + ] + ) + ) + + def test_auc_compare(self): + "test compare function of auc behavesas expected." + _ = torch.manual_seed(42) + n = 128 + estimate_informative = torch.randn( + (n,) + ) # estimate used to define time-to-event + estimate_non_informative = torch.randn((n,)) # random estimate + event = torch.randint(low=0, high=2, size=(n,)).bool() + time = ( + torch.randn(size=(n,)) * 10 - estimate_informative * 5.0 + 200 + ) # + estimate for auc < 0.5 and - for auc > 0.5 + + Auc_informative = Auc() + auc_informative = Auc_informative(estimate_informative, event, time) + + Auc_non_informative = Auc() + auc_non_informative = Auc_non_informative(estimate_non_informative, event, time) + + p_value_compare_informative = Auc_informative.compare(Auc_non_informative) + p_value_compare_non_informative = Auc_non_informative.compare(Auc_informative) + + self.assertTrue(np.all(auc_informative.numpy() > auc_non_informative.numpy())) + self.assertTrue(np.any(p_value_compare_informative.numpy() < 0.05)) + self.assertTrue(np.all(p_value_compare_non_informative.numpy() > 0.05)) + + def test_auc_error_raised(self): + """test that errors are raised in not-accepted edge cases.""" + batch_container = DataBatchContainer() + batch_container.generate_batches( + n_batch=2, + flags_to_set=[ + "test_all_censored", + "test_max_time_in_new_time", + ], + ) + for batch in batch_container.batches: + _, _, test_time, test_event, estimate, new_time, *_ = batch + + self.assertRaises( + ValueError, + auc, + estimate, + test_event, + test_time, + new_time=new_time, + ) + + +if __name__ == "__main__": + unittest.main() diff --git a/tests/test_brier_score.py b/tests/test_brier_score.py new file mode 100644 index 0000000..4d8670c --- /dev/null +++ b/tests/test_brier_score.py @@ -0,0 +1,284 @@ +# global modules +import json +import unittest + +import numpy as np +import torch +from sksurv.metrics import brier_score as brier_score_sksurv +from sksurv.metrics import integrated_brier_score as integrated_brier_score_sksurv +from utils import DataBatchContainer, conditions_ci, conditions_p_value + +# Local modules +from torchsurv.metrics.brier_score import BrierScore +from torchsurv.stats.ipcw import get_ipcw + +torch.manual_seed(23) + +# Load the benchmark metrics from R +with open("tests/benchmark_data/benchmark_brier_score.json", "r") as file: + benchmark_brier_scores = json.load(file) + +brier_score = BrierScore() + + +class TestBrierScore(unittest.TestCase): + """ + List of packages compared + - survMetrics (R) + - survAUC (R) + - sksurv (Python) + """ + + def test_brier_score_real_data(self): + """test point estimate of brier score and integrated brier score on lung and gbsg datasets""" + for benchmark_brier_score in benchmark_brier_scores: + train_event = torch.tensor(benchmark_brier_score["train_status"]).bool() + train_time = torch.tensor( + benchmark_brier_score["train_time"], dtype=torch.float32 + ) + test_event = torch.tensor(benchmark_brier_score["test_status"]).bool() + test_time = torch.tensor( + benchmark_brier_score["test_time"], dtype=torch.float32 + ) + estimate = torch.tensor( + benchmark_brier_score["estimate"], dtype=torch.float32 + ) + new_time = torch.tensor(benchmark_brier_score["times"], dtype=torch.float32) + + # ipcw obtained using censoring distribution estimated on train data + ipcw = get_ipcw(train_event, train_time, test_time) + ipcw_new_time = get_ipcw(train_event, train_time, new_time) + + bs = brier_score( + estimate, + test_event, + test_time, + new_time=new_time, + weight=ipcw, + weight_new_time=ipcw_new_time, + ) + ibs = brier_score.integral() + + bs_survAUC = np.array(benchmark_brier_score["brier_score_survAUC"]) + ibs_survAUC = np.array(benchmark_brier_score["ibrier_score_survAUC"]) + + # commented out: values far off compared to other packages + # self.assertTrue(np.allclose(bs.numpy(), bs_survAUC, rtol=1e-5, atol=1e-8)) + # self.assertTrue(np.allclose(ibs.numpy(), ibs_survAUC, rtol=1e-5, atol=1e-8)) + + # ipcw obtained using censoring distribution estimated on test data + ipcw = get_ipcw(test_event, test_time) + ipcw_new_time = get_ipcw(test_event, test_time, new_time) + + bs = brier_score( + estimate, + test_event, + test_time, + new_time=new_time, + weight=ipcw, + weight_new_time=ipcw_new_time, + ) + ibs = brier_score.integral() + + bs_survMetrics = np.array(benchmark_brier_score["brier_score_survMetrics"]) + ibs_survMetrics = np.array( + benchmark_brier_score["ibrier_score_survMetrics"] + ) + + self.assertTrue( + np.allclose(bs.numpy(), bs_survMetrics, rtol=1e-2, atol=1e-3) + ) + self.assertTrue( + np.allclose(ibs.numpy(), ibs_survMetrics, rtol=1e-2, atol=1e-3) + ) + + def test_brier_score_simulated_data(self): + """test point estimate of brier score and integrated brier score on simulated batches including edge cases""" + batch_container = DataBatchContainer() + batch_container.generate_batches( + n_batch=20, + flags_to_set=[ + "train_ties_time_event", + "test_ties_time_event", + "train_ties_time_censoring", + "test_ties_time_censoring", + "train_ties_time_event_censoring", + "test_ties_time_event_censoring", + "test_no_censoring", + # "train_no_censoring", sksurv fails + "test_event_at_last_time", + "ties_score_events", + "ties_score_event_censoring", + "ties_score_censoring", + ], + ) + for batch in batch_container.batches: + ( + train_time, + train_event, + test_time, + test_event, + _, + new_time, + y_train_array, + y_test_array, + _, + new_time_array, + ) = batch + + estimate = torch.rand((len(test_time), len(new_time))) + + ipcw = get_ipcw(train_event, train_time, test_time) + ipcw_new_time = get_ipcw(train_event, train_time, new_time) + bs = brier_score( + estimate, + test_event, + test_time, + new_time=new_time, + weight=ipcw, + weight_new_time=ipcw_new_time, + ) + + _, bs_sksurv = brier_score_sksurv( + y_train_array, y_test_array, estimate.numpy(), new_time_array + ) + + self.assertTrue(np.allclose(bs.numpy(), bs_sksurv, rtol=1e-5, atol=1e-8)) + + if len(new_time) > 2: + ibs = brier_score.integral() + ibs_sksurv = integrated_brier_score_sksurv( + y_train_array, y_test_array, estimate.numpy(), new_time_array + ) + self.assertTrue( + np.allclose(ibs.numpy(), ibs_sksurv, rtol=1e-5, atol=1e-8) + ) + + def test_brier_score_confidence_interval_pvalue(self): + """test brier score confidence interval and p value are as expected""" + batch_container = DataBatchContainer() + batch_container.generate_batches( + n_batch=20, + flags_to_set=[ + "test_ties_time_event", + "test_ties_time_censoring", + "test_ties_time_event_censoring", + #'test_no_censoring', concordance_index_censored fails + "test_event_at_last_time", + "ties_score_events", + "ties_score_event_censoring", + "ties_score_censoring", + ], + ) + for batch in batch_container.batches: + (_, _, time, event, _, new_time, *_) = batch + + estimate = torch.rand((len(time), len(new_time))) + + # Run c-index + brier_score(estimate, event, time, new_time) + + n_bootstraps = 9 + + for method in ["parametric", "bootstrap"]: + for alternative in ["two_sided", "less", "greater"]: + brier_score_ci = brier_score.confidence_interval( + method=method, + alternative=alternative, + n_bootstraps=n_bootstraps, + ) + self.assertTrue( + all( + [ + conditions_ci(brier_score_ci[:, i]) + for i in range(len(brier_score.brier_score)) + ] + ) + ) + + for alternative in ["two_sided", "less", "greater"]: + brier_score_pvalue = brier_score.p_value( + method="bootstrap", + alternative=alternative, + n_bootstraps=n_bootstraps, + ) + self.assertTrue( + all( + [ + conditions_p_value(brier_score_pvalue[i]) + for i in range(len(brier_score.brier_score)) + ] + ) + ) + brier_score_pvalue = brier_score.p_value( + method="parametric", + alternative=alternative, + n_bootstraps=n_bootstraps, + null_value=0.3, + ) + self.assertTrue( + all( + [ + conditions_p_value(brier_score_pvalue[i]) + for i in range(len(brier_score.brier_score)) + ] + ) + ) + + def test_brier_score_compare(self): + """test compare function of brier score behaves as expected""" + + _ = torch.manual_seed(42) + n = 128 + m = 100 + estimate_informative = torch.rand((n,)) # estimate used to define time-to-event + estimate_non_informative = ( + torch.rand((n,)).unsqueeze(1).expand(n, n) + ) # random estimate + event = torch.randint(low=0, high=2, size=(n,)).bool() + time = torch.randn(size=(n,)) + estimate_informative * 20.0 + 200 + + estimate_informative = estimate_informative.unsqueeze(1).expand(n, n) + + mask = event & (time < torch.max(time)) + new_time, inverse_indices, counts = torch.unique( + time[mask], sorted=True, return_inverse=True, return_counts=True + ) + sorted_unique_indices = BrierScore._find_torch_unique_indices( + inverse_indices, counts + ) + estimate_informative = (estimate_informative[:, mask])[:, sorted_unique_indices] + estimate_non_informative = (estimate_non_informative[:, mask])[ + :, sorted_unique_indices + ] + + ipcw = get_ipcw(event, time) # ipcw weights at subject event time + ipcw_new_time = get_ipcw(event, time, new_time) # ipcw weights at new_time + + brier_score_informative = BrierScore() + bs_informative = brier_score_informative( + estimate_informative, event, time, new_time, ipcw, ipcw_new_time + )[0:-1] + ibs_informative = brier_score_informative.integral() + + brier_score_non_informative = BrierScore() + bs_non_informative = brier_score_non_informative( + estimate_non_informative, event, time, new_time, ipcw, ipcw_new_time + )[0:-1] + ibs_non_informative = brier_score_non_informative.integral() + + p_value_compare_informative = brier_score_informative.compare( + brier_score_non_informative + ) + p_value_compare_non_informative = brier_score_non_informative.compare( + brier_score_informative + ) + + self.assertTrue(np.all(bs_informative.numpy() < bs_non_informative.numpy())) + self.assertTrue(np.all(ibs_informative.numpy() < ibs_non_informative.numpy())) + self.assertTrue(np.any(p_value_compare_informative.numpy() < 0.05)) + self.assertTrue(np.all(p_value_compare_non_informative.numpy() > 0.05)) + + +if __name__ == "__main__": + unittest.main() diff --git a/tests/test_cindex.py b/tests/test_cindex.py new file mode 100644 index 0000000..a4ec9b8 --- /dev/null +++ b/tests/test_cindex.py @@ -0,0 +1,295 @@ +# global modules +import json +import unittest + +import numpy as np +import torch +from sksurv.metrics import concordance_index_censored, concordance_index_ipcw +from utils import DataBatchContainer, conditions_ci, conditions_p_value + +# Local modules +from torchsurv.metrics.cindex import ConcordanceIndex +from torchsurv.stats.ipcw import get_ipcw + +torch.manual_seed(23) + +# Load the benchmark metrics from R +with open("tests/benchmark_data/benchmark_cindex.json", "r") as file: + benchmark_cindexs = json.load(file) + + +cindex = ConcordanceIndex() + + +class TestCIndex(unittest.TestCase): + """ + List of packages compared + - survival (R): Harrell's C index + - survcomp (R): Harrell's C index + - survAUC (R): Uno's C-index + - survC1 (R): Uno's C-index + - sksurv (Python): Harrell's C index and Uno's C-index + """ + + def test_cindex_real_data(self): + """test point estimate concordance index on lung and gbsg datasets""" + for benchmark_cindex in benchmark_cindexs: + train_event = torch.tensor(benchmark_cindex["train_status"]).bool() + train_time = torch.tensor( + benchmark_cindex["train_time"], dtype=torch.float32 + ) + test_event = torch.tensor(benchmark_cindex["test_status"]).bool() + test_time = torch.tensor(benchmark_cindex["test_time"], dtype=torch.float32) + estimate = torch.tensor(benchmark_cindex["estimate"], dtype=torch.float32) + new_time = torch.tensor(benchmark_cindex["times"], dtype=torch.float32) + + # harrell's c-index + c_harrell = cindex( + estimate, + test_event, + test_time, + ).numpy() + + c_harrell_survival = np.array( + benchmark_cindex["c_Harrell_survival"] + ) # survival + c_harrell_survcomp = np.array( + benchmark_cindex["c_Harrell_survcomp"] + ) # survcomp + + # uno's c-index + ipcw = get_ipcw(train_event, train_time, test_time) + c_uno = cindex( + estimate, test_event, test_time, weight=ipcw, tmax=new_time[-1] + ) + + c_uno_survAUC = benchmark_cindex["c_Uno_survAUC"] # survAUC + c_uno_survC1 = benchmark_cindex["c_Uno_survC1"] # survC1 + + self.assertTrue( + np.isclose( + c_harrell, + c_harrell_survival, + rtol=1e-4, + atol=1e-8, + ) + ) + + self.assertTrue( + np.isclose( + c_harrell, + c_harrell_survcomp, + rtol=1e-2, + atol=1e-8, + ) + ) + + self.assertTrue( + np.isclose(c_uno.numpy(), np.array(c_uno_survAUC), rtol=1e-1, atol=1e-8) + ) + + self.assertTrue( + np.isclose(c_uno.numpy(), np.array(c_uno_survC1), rtol=1e-1, atol=1e-8) + ) + + def test_cindex_se_real_data(self): + """test standard error of concordance index on lung and gbsg datasets""" + for benchmark_cindex in benchmark_cindexs: + concordant = torch.tensor(benchmark_cindex["ch_survcomp"], dtype=torch.int) + discordant = torch.tensor(benchmark_cindex["dh_survcomp"], dtype=torch.int) + weight = torch.tensor( + benchmark_cindex["weights_survcomp"], dtype=torch.float32 + ) + c_harrell_survcomp = torch.tensor( + benchmark_cindex["c_Harrell_survcomp"], dtype=torch.float32 + ) + + # overwrite objects used to calculate standard error + cindex.concordant = concordant + cindex.discordant = discordant + cindex.weight = weight + cindex.cindex = c_harrell_survcomp + + # Noether standard error + cindex_se = cindex._concordance_index_se() + cindex_se_survcomp = np.array( + benchmark_cindex["c_se_noether_survcomp"] + ) # survcomp + + # conservative confidence interval + cindex_lower = cindex._confidence_interval_conservative( + alpha=0.05, alternative="two_sided" + )[0] + cindex_lower_survcomp = np.array( + benchmark_cindex["c_lower_conservative_survcomp"] + ) # survcomp + + self.assertTrue( + np.isclose( + cindex_se.numpy(), + np.array(cindex_se_survcomp), + rtol=1e-1, + atol=1e-8, + ) + ) + + self.assertTrue( + np.isclose( + cindex_lower.numpy(), + np.array(cindex_lower_survcomp), + rtol=1e-1, + atol=1e-8, + ) + ) + + def test_cindex_simulated_data(self): + """test estimate of concordance index on simulated batches including edge cases""" + batch_container = DataBatchContainer() + batch_container.generate_batches( + n_batch=20, + flags_to_set=[ + "train_ties_time_event", + "test_ties_time_event", + "train_ties_time_censoring", + # "test_ties_time_censoring", + "train_ties_time_event_censoring", + "test_ties_time_event_censoring", + "test_no_censoring", + #'train_no_censoring', concordance_index_ipcw from sksurv fails + "test_event_at_last_time", + "ties_score_events", + "ties_score_event_censoring", + "ties_score_censoring", + ], + ) + for i, batch in enumerate(batch_container.batches): + ( + train_time, + train_event, + test_time, + test_event, + estimate, + new_time, + y_train_array, + y_test_array, + estimate_array, + new_time_array, + ) = batch + + # harrell's c index + c_harrell = cindex( + estimate, + test_event, + test_time, + ) + c_harrell_sksurv = concordance_index_censored( + y_test_array["survival"], y_test_array["futime"], estimate_array + )[0] + + # uno's c-index + ipcw = get_ipcw(train_event, train_time, test_time) + c_uno = cindex( + estimate, test_event, test_time, weight=ipcw, tmax=new_time[-1] + ).numpy() + + c_uno_sksurv = concordance_index_ipcw( + y_train_array, y_test_array, estimate_array, tau=new_time_array[-1] + )[0] + + self.assertTrue( + np.isclose(c_harrell.numpy(), c_harrell_sksurv, rtol=1e-2, atol=1e-8) + ) + self.assertTrue(np.isclose(c_uno, c_uno_sksurv, rtol=1e-2, atol=1e-8)) + + def test_cindex_confidence_interval_pvalue(self): + """test concordance index confidence interval and p value are as expected""" + batch_container = DataBatchContainer() + batch_container.generate_batches( + n_batch=20, + flags_to_set=[ + "test_ties_time_event", + "test_ties_time_censoring", + "test_ties_time_event_censoring", + #'test_no_censoring', concordance_index_censored fails + "test_event_at_last_time", + "ties_score_events", + "ties_score_event_censoring", + "ties_score_censoring", + ], + ) + for batch in batch_container.batches: + (_, _, time, event, estimate, *_) = batch + + # Run c-index + cindex( + estimate, + event, + time, + ) + + n_bootstraps = 9 + + for method in ["noether", "conservative", "bootstrap"]: + for alternative in ["two_sided", "less", "greater"]: + self.assertTrue( + conditions_ci( + cindex.confidence_interval( + method=method, + alternative=alternative, + n_bootstraps=n_bootstraps, + ) + ) + ) + + for method in ["noether", "bootstrap"]: + for alternative in ["two_sided", "less", "greater"]: + self.assertTrue( + conditions_p_value( + cindex.p_value( + method=method, + alternative=alternative, + n_bootstraps=n_bootstraps, + ) + ) + ) + + def test_cindex_compare(self): + "test compare function of cindex behaves as expected" + + _ = torch.manual_seed(42) + n = 128 + estimate_informative = torch.randn( + (n,) + ) # estimate used to define time-to-event + estimate_non_informative = torch.randn((n,)) # random estimate + event = torch.randint(low=0, high=2, size=(n,)).bool() + time = ( + torch.randn(size=(n,)) * 10 - estimate_informative * 5.0 + 200 + ) # + estimate for cindex < 0.5 and - for cindex > 0.5 + + cindex_informative = ConcordanceIndex() + c1 = cindex_informative(estimate_informative, event, time) + + cindex_non_informative = ConcordanceIndex() + c2 = cindex_non_informative(estimate_non_informative, event, time) + + p_value_compare = cindex_informative.compare(cindex_non_informative) + + self.assertTrue(c1.numpy() > c2.numpy()) + self.assertTrue(p_value_compare < 0.05) + + def test_cindex_error_raised(self): + """test that error are raised in not-accepted edge cases.""" + batch_container = DataBatchContainer() + batch_container.generate_batches( + n_batch=1, + flags_to_set=["test_all_censored"], + ) + for batch in batch_container.batches: + (_, _, test_time, test_event, estimate, *_) = batch + + self.assertRaises(ValueError, cindex, estimate, test_event, test_time) + + +if __name__ == "__main__": + unittest.main() diff --git a/tests/test_cox.py b/tests/test_cox.py new file mode 100644 index 0000000..b8cdbfa --- /dev/null +++ b/tests/test_cox.py @@ -0,0 +1,134 @@ +# global modules +import json +import unittest + +import numpy as np +import torch + +# Local modules +from torchsurv.loss.cox import neg_partial_log_likelihood as cox + +# Load the benchmark cox log likelihoods from R +with open("tests/benchmark_data/benchmark_cox.json", "r") as file: + benchmark_cox_logliks = json.load(file) + +# set seed for reproducibility +torch.manual_seed(42) + + +class TestCoxSurvivalLoss(unittest.TestCase): + """ + List of packages compared + - survival (R) + """ + + # random data and parameters + N = 32 + log_hz = torch.randn(N) + event = torch.randint(low=0, high=2, size=(N,)).bool() + time = torch.randint(low=1, high=100, size=(N,)) + + def test_y_tensor(self): + event_np_array = np.random.randint(0, 1 + 1, size=(self.N,), dtype="bool") + self.assertRaises(TypeError, cox, self.log_hz, event_np_array, self.time) + + def test_t_tensor(self): + time_np_array = np.random.randint(0, 100, size=(self.N,)) + self.assertRaises(TypeError, cox, self.log_hz, self.event, time_np_array) + + def test_log_hz_tensor(self): + log_hz_np_array = np.random.randn( + self.N, + ) + self.assertRaises(TypeError, cox, log_hz_np_array, self.event, self.time) + + def test_len_data(self): + time_wrong_len = torch.randint(low=1, high=100, size=(self.N + 1,)) + self.assertRaises(ValueError, cox, self.log_hz, self.event, time_wrong_len) + + def test_positive_t(self): + time_negative = torch.randint(low=-100, high=100, size=(self.N,)) + self.assertRaises(ValueError, cox, self.log_hz, self.event, time_negative) + + def test_boolean_y(self): + event_non_boolean = torch.randint(low=0, high=3, size=(self.N,)) + self.assertRaises(ValueError, cox, self.log_hz, event_non_boolean, self.time) + + def test_log_likelihood_without_ties(self): + """test cox partial log likelihood without ties on lung and gbsg datasets""" + for benchmark_cox_loglik in benchmark_cox_logliks: + + if benchmark_cox_loglik["no_ties"][0] == True: + + log_lik = -cox( + torch.tensor( + benchmark_cox_loglik["log_hazard"], dtype=torch.float32 + ).squeeze(0), + torch.tensor(benchmark_cox_loglik["status"]).bool(), + torch.tensor(benchmark_cox_loglik["time"], dtype=torch.float32), + reduction="sum", + ) + log_lik_survival = benchmark_cox_loglik["log_likelihood"] + + self.assertTrue( + np.allclose( + log_lik.numpy(), + np.array(log_lik_survival), + rtol=1e-5, + atol=1e-8, + ) + ) + + def test_log_likelihood_with_ties(self): + """test Efron and Breslow's approximation of cox partial log likelihood with ties on lung and gbsg data""" + for benchmark_cox_loglik in benchmark_cox_logliks: + + if benchmark_cox_loglik["no_ties"][0] == False: + + # efron approximation of partial log likelihood + log_lik_efron = -cox( + torch.tensor( + benchmark_cox_loglik["log_hazard_efron"], dtype=torch.float32 + ).squeeze(0), + torch.tensor(benchmark_cox_loglik["status"]).bool(), + torch.tensor(benchmark_cox_loglik["time"], dtype=torch.float32), + ties_method="efron", + reduction="sum", + ) + log_lik_efron_survival = benchmark_cox_loglik["log_likelihood_efron"] + + # breslow approximation of partial log likelihood + log_lik_breslow = -cox( + torch.tensor( + benchmark_cox_loglik["log_hazard_breslow"], dtype=torch.float32 + ).squeeze(0), + torch.tensor(benchmark_cox_loglik["status"]).bool(), + torch.tensor(benchmark_cox_loglik["time"], dtype=torch.float32), + ties_method="breslow", + reduction="sum", + ) + log_lik_breslow_survival = benchmark_cox_loglik[ + "log_likelihood_breslow" + ] + + self.assertTrue( + np.allclose( + log_lik_efron.numpy(), + np.array(log_lik_efron_survival), + rtol=1e-5, + atol=1e-8, + ) + ) + + self.assertTrue( + np.allclose( + log_lik_breslow.numpy(), + np.array(log_lik_breslow_survival), + rtol=1e-5, + atol=1e-8, + ) + ) + + +if __name__ == "__main__": + unittest.main() diff --git a/tests/test_ipcw.py b/tests/test_ipcw.py new file mode 100644 index 0000000..106100c --- /dev/null +++ b/tests/test_ipcw.py @@ -0,0 +1,111 @@ +# global modules +import json +import unittest + +import numpy as np +import torch +from sksurv.nonparametric import CensoringDistributionEstimator +from utils import DataBatchContainer + +# Local modules +from torchsurv.stats.ipcw import get_ipcw + +# Load the benchmark cox log likelihoods from R +with open("tests/benchmark_data/benchmark_ipcw.json", "r") as file: + benchmark_ipcws = json.load(file) + +# set seed for reproducibility +torch.manual_seed(42) + + +class TestIPCW(unittest.TestCase): + """ + List of packages compared + - pec (R) + - sksurv (Python) + """ + + def test_ipcw_real_data(self): + """test ipcw values on lung and gbsg data""" + + for benchmark_ipcw in benchmark_ipcws: + event = torch.tensor(benchmark_ipcw["status"]).bool() + time = torch.tensor(benchmark_ipcw["time"], dtype=torch.float32) + new_time = torch.tensor(benchmark_ipcw["times"], dtype=torch.float32) + + # ipcw evaluated at subject time + ipcw_subject_time = get_ipcw(event, time) + ipcw_subject_time_pec = np.array(benchmark_ipcw["ipcw_subjectimes"]) + + # ipcw evaluated at new time + ipcw_new_time = get_ipcw(event, time, new_time) + ipcw_new_time_pec = np.array(benchmark_ipcw["ipcw_times"]) + + self.assertTrue( + np.allclose( + ipcw_subject_time.numpy(), + ipcw_subject_time_pec, + rtol=1e-4, + atol=1e-8, + ) + ) + + self.assertTrue( + np.allclose( + ipcw_new_time.numpy(), ipcw_new_time_pec, rtol=1e-4, atol=1e-8 + ) + ) + + def test_ipcw_simulated_data(self): + """test ipcw on simulated batches including edge cases""" + batch_container = DataBatchContainer() + batch_container.generate_batches( + n_batch=20, + flags_to_set=[ + "train_ties_time_event", + "test_ties_time_event", + "train_ties_time_censoring", + # "test_ties_time_censoring", + "train_ties_time_event_censoring", + "test_ties_time_event_censoring", + "test_no_censoring", + #'train_no_censoring', concordance_index_ipcw from sksurv fails + "test_event_at_last_time", + "ties_score_events", + "ties_score_event_censoring", + "ties_score_censoring", + ], + ) + for i, batch in enumerate(batch_container.batches): + ( + train_time, + train_event, + test_time, + test_event, + _, + _, + y_train_array, + y_test_array, + _, + _, + ) = batch + + # ipcw + ipcw = get_ipcw(train_event, train_time, test_time) + + # sksurv imposes survival data (event and time) for ipcw prediction + # instead of just time. And then force icpw to be 0 if event == False + ipcw[test_event == False] = 0.0 + + # ipcw with sksurv + cens = CensoringDistributionEstimator() + cens.fit(y_train_array) + ipcw_sksurv = cens.predict_ipcw(y_test_array) + + self.assertTrue( + np.all(np.isclose(ipcw.numpy(), ipcw_sksurv, rtol=1e-4, atol=1e-8)) + ) + + +if __name__ == "__main__": + unittest.main() diff --git a/tests/test_kaplan_meier.py b/tests/test_kaplan_meier.py new file mode 100644 index 0000000..a7d555c --- /dev/null +++ b/tests/test_kaplan_meier.py @@ -0,0 +1,222 @@ +import json +import unittest + +import numpy as np +import torch +from sksurv.metrics import CensoringDistributionEstimator, SurvivalFunctionEstimator +from utils import DataBatchContainer + +# local +from torchsurv.stats.kaplan_meier import KaplanMeierEstimator + +# Load the benchmark cox log likelihoods from R +with open("tests/benchmark_data/benchmark_kaplan_meier.json", "r") as file: + benchmark_kaplan_meiers = json.load(file) + +torch.manual_seed(23) + + +class TestNonParametric(unittest.TestCase): + """ + List of packages compared + - survival (R) + - sksurv (Python) + """ + + def test_kaplan_meier_survival_distribution_real_data(self): + """test Kaplan Meier survival distribution estimate on lung and gbsg datasets""" + + for benchmark_kaplan_meier in benchmark_kaplan_meiers: + + event = torch.tensor(benchmark_kaplan_meier["status"]).bool() + time = torch.tensor(benchmark_kaplan_meier["time"], dtype=torch.float32) + new_time = torch.tensor( + benchmark_kaplan_meier["times"], dtype=torch.float32 + ) + + km = KaplanMeierEstimator() + km(event, time, censoring_dist=False) + st = km.predict(new_time) + + st_survival = np.array(benchmark_kaplan_meier["surv_prob_survival"]) + + self.assertTrue( + np.allclose( + st.numpy(), + st_survival, + rtol=1e-3, + atol=1e-8, + ) + ) + + def test_kaplan_meier_censoring_distribution_simulated_data(self): + """test Kaplan Meier estimate of censoring distribution on simulated batches including edge cases""" + batch_container = DataBatchContainer() + batch_container.generate_batches( + n_batch=20, + flags_to_set=[ + "train_ties_time_event", + "train_ties_time_censoring", + "train_ties_time_event_censoring", + "train_no_censoring", + ], + ) + for batch in batch_container.batches: + (time, event, _, _, _, _, y_array, *_) = batch + + km = KaplanMeierEstimator() + km(event, time, censoring_dist=True) + ct = km.km_est + + cens = CensoringDistributionEstimator() + cens.fit(y_array) + ct_sksurv = cens.prob_ + if not event.all(): + ct_sksurv = ct_sksurv[1:] + + self.assertTrue(np.allclose(ct.numpy(), ct_sksurv, rtol=1e-5, atol=1e-8)) + + def test_kaplan_meier_survival_distribution_simulated_data(self): + """test Kaplan Meier estimate of survival distribution on simulated batches including edge cases""" + batch_container = DataBatchContainer() + batch_container.generate_batches( + n_batch=20, + flags_to_set=[ + "train_ties_time_event", + "train_ties_time_censoring", + "train_ties_time_event_censoring", + "train_no_censoring", + ], + ) + for batch in batch_container.batches: + (time, event, _, _, _, _, y_array, *_) = batch + + km = KaplanMeierEstimator() + km(event, time, censoring_dist=False) + st = km.km_est + + surv = SurvivalFunctionEstimator() + surv.fit(y_array) + st_sksurv = surv.prob_[1:] + + self.assertTrue(np.allclose(st.numpy(), st_sksurv, rtol=1e-5, atol=1e-8)) + + def test_kaplan_meier_predict_censoring_distribution_simulated_data(self): + """test Kaplan Meier prediction of censoring distribution on simulated batches including edge cases""" + batch_container = DataBatchContainer() + batch_container.generate_batches( + n_batch=20, + flags_to_set=[ + "train_ties_time_event", + "test_ties_time_event", + "train_ties_time_censoring", + "test_ties_time_censoring", + "train_ties_time_event_censoring", + "test_ties_time_event_censoring", + "test_no_censoring", + #'train_no_censoring', CensoringDistributionEstimator from sksurv fails + "test_event_at_last_time", + ], + ) + for batch in batch_container.batches: + ( + train_time, + train_event, + test_time, + _, + _, + _, + y_train_array, + y_test_array, + *_, + ) = batch + + km = KaplanMeierEstimator() + km(train_event, train_time, censoring_dist=True) + ct_pred = km.predict(test_time) + + cens = CensoringDistributionEstimator() + cens.fit(y_train_array) + ct_pred_sksurv = cens.predict_proba(y_test_array["futime"]) + + self.assertTrue( + np.allclose(ct_pred.numpy(), ct_pred_sksurv, rtol=1e-5, atol=1e-8) + ) + + def test_kaplan_meier_predict_survival_distribution_simulated_data(self): + """test Kaplan Meier prediction of survival distribution on simulated batches including edge cases""" + batch_container = DataBatchContainer() + batch_container.generate_batches( + n_batch=20, + flags_to_set=[ + "train_ties_time_event", + "test_ties_time_event", + "train_ties_time_censoring", + "test_ties_time_censoring", + "train_ties_time_event_censoring", + "test_ties_time_event_censoring", + "test_no_censoring", + #'train_no_censoring', CensoringDistributionEstimator from sksurv fails + "test_event_at_last_time", + ], + ) + for batch in batch_container.batches: + ( + train_time, + train_event, + test_time, + _, + _, + _, + y_train_array, + y_test_array, + *_, + ) = batch + + km = KaplanMeierEstimator() + km(train_event, train_time, censoring_dist=False) + st_pred = km.predict(test_time) + + surv = SurvivalFunctionEstimator() + surv.fit(y_train_array) + st_pred_sksurv = surv.predict_proba(y_test_array["futime"]) + + self.assertTrue( + np.allclose(st_pred.numpy(), st_pred_sksurv, rtol=1e-5, atol=1e-8) + ) + + def test_kaplan_meier_estimate_error_raised(self): + """test that errors are raised for estimation in not-accepted edge cases.""" + batch_container = DataBatchContainer() + batch_container.generate_batches( + n_batch=1, + flags_to_set=["train_all_censored"], + ) + for batch in batch_container.batches: + (train_time, train_event, *_) = batch + + self.assertRaises( + ValueError, KaplanMeierEstimator(), train_event, train_time + ) + + def test_kaplan_meier_prediction_error_raised(self): + """test that errors are raised for prediction in not-accepted edge cases.""" + batch_container = DataBatchContainer() + batch_container.generate_batches( + n_batch=1, + flags_to_set=["test_max_time_gt_train_max_time"], + ) + for batch in batch_container.batches: + (train_time, train_event, test_time, *_) = batch + + train_event[-1] = ( + False # if last event is censoring, the last KM is > 0 and it cannot predict beyond this time + ) + km = KaplanMeierEstimator() + km(train_event, train_time, censoring_dist=False) + + self.assertRaises(ValueError, km.predict, test_time) + + +if __name__ == "__main__": + unittest.main() diff --git a/tests/test_mnist.py b/tests/test_mnist.py new file mode 100644 index 0000000..1c98713 --- /dev/null +++ b/tests/test_mnist.py @@ -0,0 +1,155 @@ +import unittest + +import torch +from pytorch_lightning import LightningModule, Trainer +from torch import nn +from torch.utils.data import DataLoader, random_split +from torchvision.datasets import MNIST +from torchvision.transforms import v2 + +from torchsurv.loss.cox import neg_partial_log_likelihood +from torchsurv.metrics.cindex import ConcordanceIndex + + +class LitMNIST(LightningModule): + def __init__(self, hidden_size=128, learning_rate=5e-4): + super().__init__() + + # Set our init args as class attributes + self.data_dir = "." + self.hidden_size = hidden_size + self.learning_rate = learning_rate + self.batch_size = 256 + self.num_workers = 4 + + # Model optimizisation + self.loss = neg_partial_log_likelihood + self.cindex = ConcordanceIndex() + + # Hardcode some dataset specific attributes + self.dims = (1, 28, 28) + channels, width, height = self.dims + self.transform = v2.Compose( + [ + v2.ToImage(), + v2.ToDtype(torch.float32, scale=True), + v2.Normalize(mean=(0,), std=(1,)), + v2.ColorJitter(brightness=0.2, contrast=0.2, saturation=0, hue=0), + ] + ) + + # Define PyTorch model + self.model = nn.Sequential( + nn.Flatten(), + nn.Linear(channels * width * height, hidden_size), + nn.ReLU(), + nn.Dropout(0.1), + nn.Linear(hidden_size, hidden_size), + nn.ReLU(), + nn.Dropout(0.1), + nn.Linear(hidden_size, 1), + ) + + def forward(self, x): + return self.model(x) + + def training_step(self, batch, batch_idx): + x, y = batch + y[y == 0] = 10.0 # Offset 0 to prevent log(0) + params = self(x) + loss = self.loss(params, torch.ones_like(y, device=y.device).bool(), y) + self.log("loss", loss, prog_bar=True, on_step=True, on_epoch=True) + return loss + + def validation_step(self, batch, batch_idx): + x, y = batch + y[y == 0] = 10 # Offset 0 to prevent log(0) + params = self(x) + loss = self.loss(params, torch.ones_like(y, device=y.device).bool(), y) + cindex = self.cindex( + params, torch.ones_like(y, device=y.device).bool(), y.float() + ) + self.log("val_loss", loss, prog_bar=True, on_step=True, on_epoch=True) + self.log( + "cindex", + cindex, + prog_bar=True, + on_step=True, + on_epoch=True, + ) + return loss + + def test_step(self, batch, batch_idx): + # Here we just reuse the validation_step for testing + return self.validation_step(batch, batch_idx) + + def configure_optimizers(self): + optimizer = torch.optim.Adam(self.parameters(), lr=self.learning_rate) + return optimizer + + #################### + # DATA RELATED HOOKS + #################### + + def prepare_data(self): + # download + MNIST(self.data_dir, train=True, download=True) + MNIST(self.data_dir, train=False, download=True) + + def setup(self, stage=None): + # Assign train/val datasets for use in dataloaders + if stage == "fit" or stage is None: + mnist_full = MNIST(self.data_dir, train=True, transform=self.transform) + self.mnist_train, self.mnist_val = random_split(mnist_full, [55000, 5000]) + + # Assign test dataset for use in dataloader(s) + if stage == "test" or stage is None: + self.mnist_test = MNIST( + self.data_dir, train=False, transform=self.transform + ) + + def train_dataloader(self): + return DataLoader( + self.mnist_train, + batch_size=self.batch_size, + num_workers=self.num_workers, + persistent_workers=True, + ) + + def val_dataloader(self): + return DataLoader( + self.mnist_val, + batch_size=self.batch_size, + num_workers=self.num_workers, + persistent_workers=True, + ) + + def test_dataloader(self): + return DataLoader( + self.mnist_test, + batch_size=self.batch_size, + num_workers=self.num_workers, + persistent_workers=True, + ) + + +class TestMetrics(unittest.TestCase): + def test_training(self): + model = LitMNIST() + trainer = Trainer( + logger=False, + enable_checkpointing=False, + accelerator="auto", + fast_dev_run=2, + ) + trainer.fit(model) + results = trainer.validate(model)[0] + values = list(results.values()) + names = list(results.keys()) + self.assertTrue(names == ["val_loss_epoch", "cindex_epoch"]) + self.assertTrue(values[0] > 0) # Loss + self.assertTrue(all([values[1] <= 1, values[1] >= 0])) # Cindex + + +if __name__ == "__main__": + unittest.main() diff --git a/tests/test_train.py b/tests/test_train.py new file mode 100644 index 0000000..60d72e4 --- /dev/null +++ b/tests/test_train.py @@ -0,0 +1,91 @@ +import unittest + +# Global +import lightning as L +import torch +from loguru import logger +from utils import ( + LitSurvival, + LitSurvivalTwins, + SimpleLinearNNOneParameter, + SimpleLinearNNTwoParameters, +) + +from torchsurv.loss.weibull import neg_log_likelihood as weibull + +# Set a seed for reproducibility +seed_value = 45 +torch.manual_seed(seed_value) +BATCH_N = 10 + + +trainer = L.Trainer(max_epochs=2, log_every_n_steps=5) + + +class TestLitTraining(unittest.TestCase): + def run_training(self, trainer, model): + logger.critical(f"Loading {model.dataname} dataset") + trainer.fit(model) + return model + + def test_one_param(self): + """One parameter Weibull""" + model = self.run_training( + trainer, + LitSurvival( + backbone=SimpleLinearNNOneParameter(input_size=2), + loss=weibull, + dataname="lung", + batch_size=248 // BATCH_N, + ), + ) + with torch.no_grad(): + params = model(torch.randn(1, 2)) + self.assertEqual(params.size(), (1, 1)) + + def test_two_params(self): + """Two parameters Weibull""" + model = self.run_training( + trainer, + LitSurvival( + backbone=SimpleLinearNNTwoParameters(input_size=2), + loss=weibull, + dataname="gbsb", + batch_size=686 // BATCH_N, + ), + ) + with torch.no_grad(): + params = model(torch.randn(1, 2)) + self.assertEqual(params.size(), (1, 2)) + + def test_twins(self): + """Two parameters Weibull""" + model = LitSurvivalTwins( + backbone=SimpleLinearNNOneParameter(input_size=2), + loss=weibull, + n=2, + dataname="gbsb", + batch_size=686 // BATCH_N, + ) + res = self.run_training( + trainer, + model, + ) + + with torch.no_grad(): + x = torch.randn(1, 2) + # logger.info(f"No training: {res.twinnets.backbone(x)}") + # logger.info(f"Student (Q): {res.twinnets.encoder_q(x)}") + # logger.info(f"Teacher (K): {res.twinnets.encoder_k(x)}") + + # Model parameters (sanity checks) + # for params in model.twinnets.backbone.parameters(): + # logger.info(f"No training: {params}") + # for params in model.twinnets.encoder_q.parameters(): + # logger.info(f"Student (Q): {params}") + # for params in model.twinnets.encoder_k.parameters(): + # logger.info(f"Teacher (K): {params}") + + +if __name__ == "__main__": + unittest.main() diff --git a/tests/test_weibull.py b/tests/test_weibull.py new file mode 100644 index 0000000..e3f3734 --- /dev/null +++ b/tests/test_weibull.py @@ -0,0 +1,274 @@ +# global modules +import json +import unittest + +import numpy as np +import torch +from lifelines import WeibullAFTFitter +from lifelines.datasets import load_gbsg2, load_lung + +# Local modules +from torchsurv.loss.weibull import neg_log_likelihood as weibull + +# Load the benchmark cox log likelihoods from R +with open("tests/benchmark_data/benchmark_weibull.json", "r") as file: + benchmark_weibull_logliks = json.load(file) + +# set seed for reproducibility +torch.manual_seed(42) + + +class TestWeibullSurvivalLoss(unittest.TestCase): + """ + List of packages compared + - survival (R) + - lifelines (python) + """ + + # random data and parameters + N = 32 + log_params = torch.randn(N, 2) + y = torch.randint(low=0, high=2, size=(N, 1)).bool() + t = torch.randint(low=1, high=100, size=(N, 1)) + + # prepare data + lung = load_lung() + lung["sex"] = (lung["sex"] == 1).astype(float) + lung["age"] = (lung["age"] - lung["age"].mean()) / lung["age"].std() + + gbsg = load_gbsg2() + gbsg["age"] = (gbsg["age"] - gbsg["age"].mean()) / gbsg["age"].std() + gbsg["tsize"] = (gbsg["tsize"] - gbsg["tsize"].mean()) / gbsg["tsize"].std() + + def test_y_tensor(self): + y_np_array = np.random.randint(0, 1 + 1, size=(self.N, 1), dtype="bool") + self.assertRaises(TypeError, weibull, self.log_params, y_np_array, self.t) + + def test_t_tensor(self): + t_np_array = np.random.randint(0, 100, size=(self.N, 1)) + self.assertRaises(TypeError, weibull, self.log_params, self.y, t_np_array) + + def test_log_params_tensor(self): + log_params_np_array = np.random.randn(self.N, 2) + self.assertRaises(TypeError, weibull, log_params_np_array, self.y, self.t) + + def test_nrow_log_params(self): + log_params_wrong_nrow = torch.randn(self.N + 1, 2) + self.assertRaises(ValueError, weibull, log_params_wrong_nrow, self.y, self.t) + + def test_len_data(self): + t_wrong_len = torch.randint(low=1, high=100, size=(self.N + 1, 1)) + self.assertRaises(ValueError, weibull, self.log_params, self.y, t_wrong_len) + + def test_positive_t(self): + t_negative = torch.randint(low=-100, high=100, size=(self.N, 1)) + self.assertRaises(ValueError, weibull, self.log_params, self.y, t_negative) + + def test_boolean_y(self): + y_non_boolean = torch.randint(low=0, high=3, size=(self.N, 1)) + self.assertRaises(ValueError, weibull, self.log_params, y_non_boolean, self.t) + + def test_log_likelihood_1_param(self): + """test weibull log likelihood with only 1 param (log scale) on lung and gbsg data""" + for benchmark_weibull_loglik in benchmark_weibull_logliks: + log_lik = -weibull( + torch.tensor( + benchmark_weibull_loglik["log_shape"], dtype=torch.float32 + ).squeeze(0), + torch.tensor(benchmark_weibull_loglik["status"]).bool(), + torch.tensor(benchmark_weibull_loglik["time"], dtype=torch.float32), + reduction="sum", + ) + + log_lik_survival = benchmark_weibull_loglik["log_likelihood"] + + self.assertTrue( + np.allclose( + log_lik.numpy(), + np.array(log_lik_survival), + rtol=1e-5, + atol=1e-8, + ) + ) + + def test_log_likelihood_2_params_lung(self): + """test value of weibull log likelihood with 2 params (log scale and log shape) on lung data""" + + event = torch.tensor(self.lung["status"]).bool() + time = torch.tensor(self.lung["time"], dtype=torch.float32) + + # intercept only + wbf = WeibullAFTFitter() + wbf.fit(self.lung[["time", "status"]], duration_col="time", event_col="status") + log_params = np.ones((len(event), 1)) * wbf.summary.loc[:, "coef"].values + log_likelihood_lifelines = wbf.log_likelihood_ + log_likelihood = -weibull( + torch.tensor(log_params, dtype=torch.float32), + event, + time, + reduction="sum", + ) + self.assertTrue( + np.allclose( + log_likelihood.numpy(), + np.array(log_likelihood_lifelines), + rtol=1e-5, + atol=1e-8, + ) + ) + + # one covariate + wbf = WeibullAFTFitter() + wbf.fit( + self.lung[["time", "status", "age"]], + duration_col="time", + event_col="status", + ) + log_scale = ( + wbf.summary.loc[:, "coef"].lambda_.Intercept + + np.array(self.lung["age"]) * wbf.summary.loc[:, "coef"].lambda_.age + ) + log_shape = ( + np.ones((self.lung.shape[0],)) * wbf.summary.loc[:, "coef"].rho_.Intercept + ) + log_params = np.column_stack((log_scale, log_shape)) + log_likelihood_lifelines = wbf.log_likelihood_ + log_likelihood = -weibull( + torch.tensor(log_params, dtype=torch.float32), + event, + time, + reduction="sum", + ) + self.assertTrue( + np.allclose( + log_likelihood.numpy(), + np.array(log_likelihood_lifelines), + rtol=1e-5, + atol=1e-8, + ) + ) + + # two covariates + wbf = WeibullAFTFitter() + wbf.fit( + self.lung[["time", "status", "age", "sex"]], + duration_col="time", + event_col="status", + ) + log_scale = ( + wbf.summary.loc[:, "coef"].lambda_.Intercept + + np.array(self.lung["age"]) * wbf.summary.loc[:, "coef"].lambda_.age + + np.array(self.lung["sex"]) * wbf.summary.loc[:, "coef"].lambda_.sex + ) + log_shape = ( + np.ones((self.lung.shape[0],)) * wbf.summary.loc[:, "coef"].rho_.Intercept + ) + log_params = np.column_stack((log_scale, log_shape)) + log_likelihood_lifelines = wbf.log_likelihood_ + log_likelihood = -weibull( + torch.tensor(log_params, dtype=torch.float32), + event, + time, + reduction="sum", + ) + self.assertTrue( + np.allclose( + log_likelihood.numpy(), + np.array(log_likelihood_lifelines), + rtol=1e-5, + atol=1e-8, + ) + ) + + def test_log_likelihood_2_params(self): + """test value of weibull log likelihood with 2 params (log scale and log shape) on gbsg data""" + + event = torch.tensor(self.gbsg["cens"]).bool() + time = torch.tensor(self.gbsg["time"], dtype=torch.float32) + + # intercept only + wbf = WeibullAFTFitter() + wbf.fit(self.gbsg[["time", "cens"]], duration_col="time", event_col="cens") + log_params = np.ones((len(event), 1)) * wbf.summary.loc[:, "coef"].values + log_likelihood_lifelines = wbf.log_likelihood_ + log_likelihood = -weibull( + torch.tensor(log_params, dtype=torch.float32), + event, + time, + reduction="sum", + ) + self.assertTrue( + np.allclose( + log_likelihood.numpy(), + np.array(log_likelihood_lifelines), + rtol=1e-5, + atol=1e-8, + ) + ) + + # one covariate + wbf = WeibullAFTFitter() + wbf.fit( + self.gbsg[["time", "cens", "age"]], + duration_col="time", + event_col="cens", + ) + log_scale = ( + wbf.summary.loc[:, "coef"].lambda_.Intercept + + np.array(self.gbsg["age"]) * wbf.summary.loc[:, "coef"].lambda_.age + ) + log_shape = ( + np.ones((self.gbsg.shape[0],)) * wbf.summary.loc[:, "coef"].rho_.Intercept + ) + log_params = np.column_stack((log_scale, log_shape)) + log_likelihood_lifelines = wbf.log_likelihood_ + log_likelihood = -weibull( + torch.tensor(log_params, dtype=torch.float32), + event, + time, + reduction="sum", + ) + self.assertTrue( + np.allclose( + log_likelihood.numpy(), + np.array(log_likelihood_lifelines), + rtol=1e-5, + atol=1e-8, + ) + ) + + # two covariates + wbf = WeibullAFTFitter() + wbf.fit( + self.gbsg[["time", "cens", "age", "tsize"]], + duration_col="time", + event_col="cens", + ) + log_scale = ( + wbf.summary.loc[:, "coef"].lambda_.Intercept + + np.array(self.gbsg["age"]) * wbf.summary.loc[:, "coef"].lambda_.age + + np.array(self.gbsg["tsize"]) * wbf.summary.loc[:, "coef"].lambda_.tsize + ) + log_shape = ( + np.ones((self.gbsg.shape[0],)) * wbf.summary.loc[:, "coef"].rho_.Intercept + ) + log_params = np.column_stack((log_scale, log_shape)) + log_likelihood_lifelines = wbf.log_likelihood_ + log_likelihood = -weibull( + torch.tensor(log_params, dtype=torch.float32), + event, + time, + reduction="sum", + ) + self.assertTrue( + np.allclose( + log_likelihood.numpy(), + np.array(log_likelihood_lifelines), + rtol=1e-5, + atol=1e-8, + ) + ) + + +if __name__ == "__main__": + unittest.main() diff --git a/tests/utils.py b/tests/utils.py new file mode 100644 index 0000000..4562d53 --- /dev/null +++ b/tests/utils.py @@ -0,0 +1,673 @@ +from typing import Tuple + +import lifelines +import lightning as L +import numpy as np +import torch +import torch.nn as nn +from torch.utils.data import DataLoader, Dataset + +# Local module +from torchsurv.loss.momentum import Momentum + + +class LitSurvival(L.LightningModule): + """Survival Model Fitter""" + + def __init__(self, backbone, loss, batch_size: int = 64, dataname: str = "lung"): + super().__init__() + self.backbone = backbone + self.loss = loss + self.batch_size = batch_size + self.dataname = dataname + + def forward(self, x): + return self.backbone(x) + + def training_step(self, batch, batch_idx): + # Can be anything + x, y, t = batch + params = self(x) + loss = self.loss(params, y, t) + self.log("loss", loss, on_step=True, on_epoch=True, prog_bar=True, logger=True) + return loss + + def configure_optimizers(self): + optimizer = torch.optim.Adam(self.parameters(), lr=1e-3) + return optimizer + + def setup(self, stage: str): + self.dataset = SurvivalDataset(self.dataname) + + def train_dataloader(self): + return DataLoader( + self.dataset, batch_size=self.batch_size, shuffle=True, drop_last=True + ) + + +class LitSurvivalTwins(LitSurvival): + """Survival Model Fitter""" + + def __init__(self, n: int = 5, **kw): + super(LitSurvivalTwins, self).__init__(**kw) + self.momentum = Momentum( + backbone=self.backbone, + loss=self.loss, + n=n, + batchsize=self.batch_size, + m=0.999, + ) + + def forward(self, x, y, t): + return self.momentum(x, y, t) + + def training_step(self, batch, batch_idx): + # Can be anything + x, y, t = batch + loss = self(x, y, t) + self.log("loss", loss, on_step=True, on_epoch=True, prog_bar=True, logger=True) + return loss + + +class SimpleLinearNNOneParameter(L.LightningModule): + """Neural network with output = bias + weight * x""" + + def __init__(self, input_size: int): + super(SimpleLinearNNOneParameter, self).__init__() + self.linear = nn.Linear(input_size, 1) + + def forward(self, x: torch.Tensor): + return self.linear(x) + + +class SimpleLinearNNTwoParameters(L.LightningModule): + """Neural network with output1 = bias_2 + weight_2 * x and output2 = bias_1 + 0 * x""" + + def __init__(self, input_size: int): + super(SimpleLinearNNTwoParameters, self).__init__() + self.linear1 = nn.Linear(input_size, 1) + self.linear2 = nn.Linear(input_size, 1) + self.freeze_linear2_weights() + + def forward(self, x: torch.Tensor): + output1 = self.linear1(x) + output2 = self.linear2(torch.zeros_like(x)) # Use zeros as input for output2 + return torch.hstack((output1, output2)) + + def freeze_linear2_weights(self): + # Set requires_grad to False for the weights parameters of linear2 + for param_name, param in self.linear2.named_parameters(): + if "weight" in param_name: + param.requires_grad = False + elif "bias" in param_name: + param.requires_grad = True + + +class SurvivalDataset(Dataset): + def __init__(self, name: str = "lung"): + self.name = name + self.df = ( + lifelines.datasets.load_lung() + if "lung" in name + else lifelines.datasets.load_gbsg2() + ) + + def __len__(self): + return len(self.df) + + def __getitem__(self, idx): + row = self.df.iloc[idx] + if "lung" in self.name: + x = torch.tensor(row[["sex", "age"]].values, dtype=torch.float32) + y = torch.tensor(row["status"], dtype=torch.float32) + t = torch.tensor(row["time"], dtype=torch.float32) + else: + x = torch.tensor(row[["age", "tsize"]].tolist(), dtype=torch.float32) + t = torch.tensor(row["time"], dtype=torch.float32) + y = torch.tensor(row["cens"], dtype=torch.float32) + + return x, y, t + + +class SurvivalDataGenerator: + def __init__( + self, + test_ties_time_event: bool = False, + test_ties_time_censoring: bool = False, + test_ties_time_event_censoring: bool = False, + train_ties_time_event: bool = False, + train_ties_time_censoring: bool = False, + train_ties_time_event_censoring: bool = False, + ties_score_events: bool = False, + ties_score_censoring: bool = False, + ties_score_event_censoring: bool = False, + test_event_at_last_time: bool = False, + test_no_censoring: bool = False, + test_all_censored: bool = False, + train_no_censoring: bool = False, + train_all_censored: bool = False, + test_max_time_gt_train_max_time: bool = False, + test_max_time_in_new_time: bool = False, + ): + """Simulate survival data with specified characteristics. + + Args: + test_ties_time_event (bool, optional): + Whether there should be at least one tie in event times in the test set. + Defaults to False. + test_ties_time_censoring (bool, optional): + Whether there should be at least one tie in censoring times in the test set. + Defaults to False. + test_ties_time_event_censoring (bool, optional): + Whether there should be at least one tie between the event time and censoring time in the test set. + Defaults to False. + train_ties_time_event (bool, optional): + Whether there should be at least one tie in event times in the train set. + Defaults to False. + train_ties_time_censoring (bool, optional): + Whether there should be at least one tie in censoring times in the train set. + Defaults to False. + train_ties_time_event_censoring (bool, optional): + Whether there should be at least one tie between the event time and censoring time in the train set. + Defaults to False. + ties_score_events (bool, optional): + Whether there should be at least one tie in the risk score associated to patients with event. + Defaults to False. + ties_score_censoring (bool, optional): + Whether there should be at least one tie in the risk score associated to patients with censoring. + Defaults to False. + ties_score_event_censoring (bool, optional): + Whether there should be at least one tie in the risk score associated to a patient with event and a patient with censoring. + Defaults to False. + test_event_at_last_time (bool, optional): + Whether the last time should be associated to an event in test set. + Defaults to False. + test_no_censoring (bool, optional): + Whether there should be no patients censored in test set. + Defaults to False. + test_all_censored (bool, optional): + Whether all patient should be censored in test set. + Defaults to False. + train_no_censoring (bool, optional): + Whether there should be no patients censored in train set. + Defaults to False. + train_all_censored (bool, optional): + Whether all patient should be censored in train set. + Defaults to False. + test_max_time_gt_train_max_time (bool, optional): + Whether the maximum time in the test set should be greater than that in the train set. + Defaults to False. + test_max_time_in_new_time (bool, optional): + Whether the maximum time in the test set should be included in the evaluation times. + Defaults to False. + """ + + # Create internal attributes states + self.test_ties_time_event = test_ties_time_event + self.test_ties_time_censoring = test_ties_time_censoring + self.test_ties_time_event_censoring = test_ties_time_event_censoring + self.train_ties_time_event = train_ties_time_event + self.train_ties_time_censoring = train_ties_time_censoring + self.train_ties_time_event_censoring = train_ties_time_event_censoring + self.test_event_at_last_time = test_event_at_last_time + self.test_no_censoring = test_no_censoring + self.test_all_censored = test_all_censored + self.train_no_censoring = train_no_censoring + self.train_all_censored = train_all_censored + self.test_max_time_gt_train_max_time = test_max_time_gt_train_max_time + self.test_max_time_in_new_time = test_max_time_in_new_time + self.ties_score_events = ties_score_events + self.ties_score_censoring = ties_score_censoring + self.ties_score_event_censoring = ties_score_event_censoring + + # generate simulated survival data + self._generate_input() + + # given simulated data, evaluate value of conditions. + self._evaluate_conditions() + + # check that the conditions set by the flags are met. + self._check_conditions() + + def get_input( + self, + ) -> Tuple[ + torch.Tensor, + torch.Tensor, + torch.Tensor, + torch.Tensor, + torch.Tensor, + torch.Tensor, + ]: + """Returns simulated data as tensors. + + Returns (Tuple, torch.tensor): + time-to-event or censoring in train set, + event indicator in train test, + time-to-event or censoring in test set, + event indicator in test test, + estimated risk score, + evaluation time + """ + return ( + self.train_time, + self.train_event, + self.test_time, + self.test_event, + self.estimate, + self.new_time, + ) + + def get_input_array(self) -> Tuple[np.array, np.array, np.array, np.array]: + """Returns simulated data as np array. + + Returns (Tuple, np.array): + Array containing the event indicator, and time-to-event or censoring of train set, + Array containing the event indicator, and time-to-event or censoring of test set, + Array containing estimated risk score, + Array containing evaluation time. + """ + + # convert simulated input to arrays + self._convert_to_arrays() + + return ( + self.y_train_array, + self.y_test_array, + self.estimate_array, + self.new_time_array, + ) + + def _generate_input(self): + + # random maximum time in observational period + tmax = torch.randint(5, 500, (1,)).item() + + # random number samples in train and number of samples in test + n_train = torch.randint(20, 101, (1,)).item() + n_test = torch.randint(20, 101, (1,)).item() + + # generate random train and test time-to-event or censoring and event indicator + self._generate_data(tmax, n_train, n_test) + + # generate random estimate + self._generate_estimate() + + # generate random evaluation time + self._generate_new_time() + + def _generate_data(self, tmax: int, n_train: int, n_test: int): + + # time-to-event or censoring in train + train_time = torch.randint(1, tmax + 1, (n_train,)).float() + + # event status (1: event, 0: censored) in train + train_event = torch.randint(0, 1 + 1, (n_train,)).float() + while train_event.sum() == 0: + train_event = torch.randint(0, 1 + 1, (n_train,)) + + # enforce conditions + train_time, train_event = self._enforce_conditions_data( + train_time, train_event, "train" + ) + + # order by time and create internal attributes + index = torch.sort(train_time)[1] + self.train_time = train_time[index] + self.train_event = train_event[index].bool() + + # time-to-event or censoring in test + test_time = torch.randint(1, tmax + 1, (n_test,)).float() + + # event status (1: event, 0: censored) in test + test_event = torch.randint(0, 1 + 1, (len(test_time),)).float() + + # order by time + index_test = torch.sort(test_time)[1] + test_time = test_time[index_test] + test_event = test_event[index_test] + + # enforce conditions + test_time, test_event = self._enforce_conditions_data( + test_time, test_event, "test" + ) + + # order by time and create internal attributes + index = torch.sort(test_time)[1] + self.test_time = test_time[index] + self.test_event = test_event[index].bool() + + def _enforce_conditions_data( + self, time: torch.tensor, event: torch.tensor, dataset_type: str + ) -> Tuple[torch.tensor, torch.tensor]: + + # if test max time should be greater than train max time + if dataset_type == "test": + if self.test_max_time_gt_train_max_time: + time[torch.where(event == 1.0)[0][0]] = self.train_time.max() + 1 + else: + index_time = (time > self.train_time.min()) & ( + time < self.train_time.max() + ) + time = time[index_time] + event = event[index_time] + + # if there should be ties in two event times + if (dataset_type == "train" and self.train_ties_time_event) or ( + dataset_type == "test" and self.test_ties_time_event + ): + time[torch.where(event == 1.0)[0][0]] = time[ + torch.where(event == 1.0)[0][1] + ] + + # if there should be ties in two censoring times + if (dataset_type == "train" and self.train_ties_time_censoring) or ( + dataset_type == "test" and self.test_ties_time_censoring + ): + time[torch.where(event == 0.0)[0][0]] = time[ + torch.where(event == 0.0)[0][1] + ] + + # if there should be a tie in an event time and a censoring time + if (dataset_type == "train" and self.train_ties_time_event_censoring) or ( + dataset_type == "test" and self.test_ties_time_event_censoring + ): + time[torch.where(event == 1.0)[0][0]] = time[ + torch.where(event == 0.0)[0][0] + ] + + # if there should be an event at the last time + if dataset_type == "test" and self.test_event_at_last_time: + event[-1] = 1 + + # if there should be no censoring + if (dataset_type == "train" and self.train_no_censoring) or ( + dataset_type == "test" and self.test_no_censoring + ): + event = event.fill_(1.0) + + # if all patients should be censored + if (dataset_type == "train" and self.train_all_censored) or ( + dataset_type == "test" and self.test_all_censored + ): + event = event.fill_(0.0) + + return time, event + + def _generate_estimate(self): + + # random risk score for observations in test + estimate = torch.randn(len(self.test_event)) + + # enforce conditions risk score + self.estimate = self._enforce_conditions_estimate(estimate) + + def _enforce_conditions_estimate(self, estimate: torch.tensor) -> torch.tensor: + + # if there should be ties in risk score associated to patients with event + if self.ties_score_events: + estimate[torch.where(self.test_event == 1.0)[0][0]] = estimate[ + torch.where(self.test_event == 1.0)[0][1] + ] + + # if there should be ties in risk score associated to patients with censoring + if self.ties_score_censoring: + estimate[torch.where(self.test_event == 0.0)[0][0]] = estimate[ + torch.where(self.test_event == 0.0)[0][1] + ] + + # if there should be ties in risk score associated to patients with event and with censoring + if self.ties_score_event_censoring: + estimate[torch.where(self.test_event == 1.0)[0][0]] = estimate[ + torch.where(self.test_event == 0.0)[0][0] + ] + + return estimate + + def _generate_new_time(self): + + if torch.all(self.test_event == False): + # if all patients are censored in test, no evaluation time + new_time = torch.tensor([]) + + else: + # random number of evaluation time + n = torch.randint(low=1, high=int(len(self.test_time) / 2), size=(1,)) + + # generate random evaluation time within test event time + new_time = torch.unique( + torch.randint( + low=self.test_time[self.test_event == 1].min().long(), + high=self.test_time[self.test_event == 1].max().long(), + size=(n,), + ).float() + ) + + # enforce conditions + self.new_time = self._enforce_conditions_time(new_time) + + def _enforce_conditions_time(self, new_time: torch.tensor) -> torch.tensor: + + # if the test max time should be included in evaluation time + if self.test_max_time_in_new_time: + new_time = torch.cat( + [new_time, torch.tensor([self.test_time.max()])], dim=0 + ) + + return new_time + + def _evaluate_conditions(self): + + # are there ties in event times + self.has_train_ties_time_event = self._has_ties( + self.train_time[self.train_event == 1] + ) + self.has_test_ties_time_event = self._has_ties( + self.test_time[self.test_event == 1] + ) + + # are there ties in censoring times + self.has_train_ties_time_censoring = self._has_ties( + self.train_time[self.train_event == 0] + ) + self.has_test_ties_time_censoring = self._has_ties( + self.test_time[self.test_event == 0] + ) + + # are there ties in event and censoring times + self.has_test_ties_time_event_censoring = self._has_ties( + self.test_time[self.test_event == 1], + self.test_time[self.test_event == 0], + ) + self.has_train_ties_time_event_censoring = self._has_ties( + self.train_time[self.train_event == 1], + self.train_time[self.train_event == 0], + ) + + # is last time is event + self.has_test_event_at_last_time = (self.test_event[-1] == 1.0).item() + + # is there no censoring + self.has_train_no_censoring = torch.all(self.train_event).item() + self.has_test_no_censoring = torch.all(self.test_event).item() + + # is all patients all censored + self.has_train_all_censored = torch.all(self.train_event == False).item() + self.has_test_all_censored = torch.all(self.test_event == False).item() + + # is test time greater than train time + self.has_test_max_time_gt_train_max_time = ( + self.test_time.max() > self.train_time.max() + ).item() + + # is max test time included in evaluation time + self.has_test_max_time_in_new_time = torch.any( + self.new_time == self.test_time.max() + ).item() + + # is there ties in risk score associated to patients with event + self.has_ties_score_events = self._has_ties( + self.estimate[self.test_event == 1.0] + ) + + # is there ties in risk score associated to patients with censoring + self.has_ties_score_event_censoring = self._has_ties( + self.estimate[self.test_event == 1.0], + self.estimate[self.test_event == 0.0], + ) + + # is there ties in risk score associated to patients with event and censoring + self.has_ties_score_censoring = self._has_ties( + self.estimate[self.test_event == 0.0] + ) + + def _check_conditions(self): + """Compare condition evaluated on simulated to condition required.""" + + self._check_condition(self.test_ties_time_event, self.has_test_ties_time_event) + self._check_condition( + self.test_ties_time_censoring, self.has_test_ties_time_censoring + ) + self._check_condition( + self.test_ties_time_event_censoring, self.has_test_ties_time_event_censoring + ) + self._check_condition( + self.train_ties_time_event, self.has_train_ties_time_event + ) + self._check_condition( + self.train_ties_time_censoring, self.has_train_ties_time_censoring + ) + self._check_condition( + self.train_ties_time_event_censoring, + self.has_train_ties_time_event_censoring, + ) + self._check_condition( + self.test_event_at_last_time, self.has_test_event_at_last_time + ) + self._check_condition(self.test_no_censoring, self.has_test_no_censoring) + self._check_condition(self.train_no_censoring, self.has_train_no_censoring) + self._check_condition(self.train_all_censored, self.has_train_all_censored) + self._check_condition(self.test_all_censored, self.has_test_all_censored) + self._check_condition( + self.test_max_time_gt_train_max_time, + self.has_test_max_time_gt_train_max_time, + ) + self._check_condition( + self.test_max_time_in_new_time, self.has_test_max_time_in_new_time + ) + self._check_condition(self.ties_score_events, self.has_ties_score_events) + self._check_condition( + self.has_ties_score_event_censoring, self.has_ties_score_event_censoring + ) + self._check_condition( + self.has_ties_score_censoring, self.has_ties_score_censoring + ) + + def _check_condition(self, condition, flag): + if condition == True and flag == False: + raise ValueError("Condition is not met.") + + def _has_ties(self, tensor, tensor2=None): + # check if there are ties within tensor or with tensor2 if specified + if tensor2 is None: + return len(tensor) > len(torch.unique(tensor)) + else: + cat, counts = torch.cat([tensor, tensor2]).unique(return_counts=True) + intersection = cat[torch.where(counts.gt(1))] + return intersection.numel() > 0 + + def _convert_to_arrays(self): + # train time and survival as numpy array + self.y_train_array = np.array( + list(zip(self.train_event.numpy(), self.train_time.numpy())), + dtype=[("survival", "?"), ("futime", " n_batch: + n_batch = len(flags_to_set) + + for i in range(n_batch): + + if i >= len(flags_to_set): + # simulate data without flag + self.generate_one_batch() + else: + # simulate data given one flag + self.generate_one_batch(flags_to_set[i]) + + def generate_one_batch(self, flag_to_set: str = None, **kwargs): + """Simulate one batch. + + Args: + flag_to_set (str, optional): Name of condition. Defaults to None. + """ + + if flag_to_set is not None: + kwargs[flag_to_set] = True + + data_batch = SurvivalDataGenerator(**kwargs) + self.add_batch(data_batch.get_input() + data_batch.get_input_array()) + + +def conditions_ci(output): + # Lower < Upper, lower >= 0, upper <= 1 + return all([output[0] <= output[1], output[0] >= 0, output[1] <= 1]) + + +def conditions_p_value(output): + # p-value must be within [0-1] + return all([output <= 1, output >= 0]) + + +if __name__ == "__main__": + # generate random survival data + data = SurvivalDataGenerator(train_ties_time_event=True) + data = SurvivalDataGenerator(test_ties_time_event=True) + data = SurvivalDataGenerator(train_ties_time_censoring=True) + data = SurvivalDataGenerator(test_ties_time_censoring=True) + data = SurvivalDataGenerator(train_ties_time_event_censoring=True) + data = SurvivalDataGenerator(test_ties_time_event_censoring=True) + data = SurvivalDataGenerator(test_event_at_last_time=True) + data = SurvivalDataGenerator(test_no_censoring=True) + data = SurvivalDataGenerator(train_no_censoring=True) + data = SurvivalDataGenerator(test_all_censored=True) + data = SurvivalDataGenerator(train_all_censored=True) + data = SurvivalDataGenerator(test_max_time_gt_train_max_time=True) + data = SurvivalDataGenerator(test_max_time_in_new_time=True) + data = SurvivalDataGenerator(ties_score_events=True) + data = SurvivalDataGenerator(ties_score_event_censoring=True) + data = SurvivalDataGenerator(ties_score_censoring=True) + + # batch of randomly generate data + batch_container = DataBatchContainer() + batch_container.generate_batches( + n_batch=10, flags_to_set=["train_ties_time_event", "test_ties_time_event"] + ) + batches = batch_container.batches