Add categorical covariate model

[zhengp0]

Add CatCovModel in the mrtool.core.cov_model module, this is try to process the categorical risks and potentially network analysis.

Simple Example

Simulate data, here we simulate data with four categories, 10 studies and 10 observations per study.

import itertools

import numpy as np
import pandas as pd

from mrtool import MRData, LinearCatCovModel, MRBRT

np.random.seed(0)
num_studies = 10
num_obs_per_study = 10
gamma = 0.1
obs_se = np.sqrt(0.1)

effects = pd.DataFrame(dict(cat=["A", "B", "C", "D"], effect=[0, 1, 2, 3]))
all_pairs = list(itertools.combinations(effects.cat, 2))
# sample pairs for each observation
pairs = [
    all_pairs[np.random.randint(0, len(all_pairs))]
    for _ in range(num_studies * num_obs_per_study)
]

df = pd.DataFrame(pairs, columns=["ref_cat", "alt_cat"])
df["study_id"] = np.repeat(range(num_studies), num_obs_per_study)
df["re"] = np.repeat(
    np.random.normal(0, scale=np.sqrt(gamma), size=num_studies), num_obs_per_study
)
df["obs_se"] = obs_se
df["noise"] = np.random.normal(scale=df["obs_se"])

# merge with the true effect sizes
df = df.merge(
    effects.rename(columns={"cat": "ref_cat", "effect": "ref_effect"}),
    on="ref_cat",
).merge(
    effects.rename(columns={"cat": "alt_cat", "effect": "alt_effect"}),
    on="alt_cat",
)

df["obs"] = df.eval("alt_effect - ref_effect + noise + re")

df.head(5)

Fit model

data = MRData()
data.load_df(
    df,
    col_obs="obs",
    col_obs_se="obs_se",
    col_covs=["ref_cat", "alt_cat"],
    col_study_id="study_id",
)

covmodels = [
    LinearCatCovModel(
        alt_cov="alt_cat", ref_cov="ref_cat", ref_cat="A", use_re=True
    )
]

model = MRBRT(data, covmodels)

model.fit_model()

# check solution and compare with the truth
model.beta_soln # vs effects
model.gamma_soln # vs gamma