Fix Claret Unit test (#441)

design/debug-cb/.gitignore

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+
+**/claret_bruno

design/debug-cb/A/README.md

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+
+
+
+
+
+## Model Specification
+
+Fixed effects only model, that is we have no patient level random effects. We have no study or arm level hierarchical effects. There is no censoring and we only account for strictly positive time.
+
+
+$$
+\begin{align*}
+y_i &\sim \mathcal{N} \left( \mu_i, \mu_i^2 \sigma^2 \right) \\
+\\
+\mu_i =
+b \cdot &\exp \left( g t_{i} - \frac{p}{c} \left( 1 - e^{-c t_{i}} \right) \right) 
+\end{align*}
+$$
+
+- $i$ is the observation index
+
+### Priors
+
+$$
+\begin{align*}
+b &\sim \text{LogNormal} \left( \right) \\
+g &\sim \text{LogNormal} \left( \right) \\
+p &\sim \text{LogNormal} \left( \right) \\
+c &\sim \text{LogNormal} \left( \right) \\
+\sigma &\sim \text{LogNormal} \left( \right)
+\end{align*}
+$$
+
+
+
+
+

design/debug-cb/A/claret_bruno.R

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+
+
+library(cmdstanr)
+library(dplyr)
+library(ggplot2)
+library(bayesplot)
+
+
+get_sld <- function(t, b, g, c, p) {
+    b * exp((g * t) - (p/c) * (1 - exp(-c * t)))
+}
+
+pars <- list(
+    b = 60,
+    g = 0.5,
+    c = 0.4,
+    p = 0.7,
+    sigma = 0.002
+)
+
+dat <- tibble(
+    t = seq(1, 900, by = 5) / 365,
+    sld_mu = get_sld(t, pars$b, pars$g, pars$c, pars$p),
+    sld = rnorm(length(t), sld_mu, sld_mu * pars$sigma)
+)
+
+ggplot(data = dat, aes(x = t, y = sld)) +
+    geom_point() +
+    geom_line(aes(y = sld_mu), color = "red")
+
+
+mod <- cmdstan_model(
+    stan_file = here::here("design/debug-cb/A/claret_bruno.stan")
+)
+
+stan_data <- list(
+    N = nrow(dat),
+    values = dat$sld,
+    times = dat$t
+)
+
+fit <- mod$sample(
+    data = stan_data,
+    chains = 2,
+    parallel_chains = 2,
+    refresh = 200,
+    iter_warmup = 1000,
+    iter_sampling = 2000
+)
+
+fit$summary()
+
+
+
+
+
+
+

design/debug-cb/A/claret_bruno.stan

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+
+functions {
+    vector claret_bruno_mu(vector times, real b, real c, real p, real g) {
+        vector[rows(times)] values;
+        values = b * exp(
+            (g .* times) -  (
+                (p/c) .* (1 - exp(-c .* times))
+            )
+        );
+        return values;
+    }
+}
+
+
+data {
+    int <lower=0> N;
+    vector[N] values;
+    vector[N] times;
+}
+
+parameters {
+   real <lower=0>  b;
+   real <lower=0>  c;
+   real <lower=0>  p;
+   real <lower=0>  g;
+   real <lower=0> sigma;
+}
+
+transformed parameters {
+    vector[N] mu = claret_bruno_mu(times, b, c, p, g);
+}
+
+// pars <- list(
+//     b = 60,
+//     g = 0.5,
+//     c = 0.4,
+//     p = 0.7,
+//     sigma = 0.004
+// )
+
+model {
+    b ~ lognormal(log(60), 0.5);
+    c ~ lognormal(log(0.5), 0.5);
+    p ~ normal(log(0.4), 0.5);
+    g ~ lognormal(log(0.7), 0.5);
+    sigma ~ lognormal(log(0.004), 0.5);
+    values ~ normal(mu, mu * sigma);
+}
+
+
+
+

design/debug-cb/B/README.md

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+
+
+
+
+
+## Model Specification
+
+Simple by-patient Random effects model. We have no study or arm level hierarchical effects. There is no censoring and we only account for strictly positive time.
+
+
+$$
+\begin{align*}
+y_{ij} &\sim \mathcal{N} \left( \mu_{ij}, \mu_{ij}^2 \sigma^2 \right) \\
+\\
+\mu_{ij} &=
+b_i \cdot \exp \left( g_i t_{ij} - \frac{p_i}{c_i} \left( 1 - e^{-c_i t_{ij}} \right) \right) 
+\end{align*}
+$$
+
+
+- $i$ is the patient index
+- $j$ is the time index
+
+### Priors
+
+$$
+\begin{align*}
+b_i &\sim \text{LogNormal} \left( log(\mu_b) , \sigma_b \right) \\
+g_i &\sim \text{LogNormal} \left( log(\mu_g) , \sigma_g \right) \\
+p_i &\sim \text{LogNormal} \left( log(\mu_p) , \sigma_p \right) \\
+c_i &\sim \text{LogNormal} \left( log(\mu_c) , \sigma_c \right) \\
+\\
+\mu_b &\sim \text{LogNormal} \left( \right) \\
+\mu_g &\sim \text{LogNormal} \left( \right) \\
+\mu_p &\sim \text{LogNormal} \left( \right) \\
+\mu_c &\sim \text{LogNormal} \left( \right) \\
+\\
+\sigma_b &\sim \text{LogNormal} \left( \right) \\
+\sigma_g &\sim \text{LogNormal} \left( \right) \\
+\sigma_p &\sim \text{LogNormal} \left( \right) \\
+\sigma_c &\sim \text{LogNormal} \left( \right) \\
+\\
+\sigma &\sim \text{LogNormal} \left( \right) \\
+\end{align*}
+$$
+
+
+
+
+

design/debug-cb/B/claret_bruno.R

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+
+
+library(cmdstanr)
+library(dplyr)
+library(ggplot2)
+library(bayesplot)
+library(tidyr)
+library(brms)
+
+
+get_sld <- function(t, b, g, c, p) {
+    b * exp((g * t) - (p/c) * (1 - exp(-c * t)))
+}
+
+pars_mu <- list(
+    b = 60,
+    g = 0.5,
+    c = 0.4,
+    p = 0.7,
+    sigma = 0.02
+)
+
+pars_sigma <- list(
+    b = 0.1,
+    g = 0.1,
+    c = 0.1,
+    p = 0.1
+)
+
+N <- 120
+
+dat_baseline <- tibble(
+    pt = sprintf("pt%05d", 1:N),
+    b = exp(rnorm(N, log(pars_mu$b), pars_sigma$b)),
+    g = exp(rnorm(N, log(pars_mu$g), pars_sigma$g)),
+    c = exp(rnorm(N, log(pars_mu$c), pars_sigma$c)),
+    p = exp(rnorm(N, log(pars_mu$p), pars_sigma$p))
+)
+
+dat <- tidyr::crossing(
+    pt = dat_baseline$pt,
+    t = seq(1, 900, length.out = 8) / 365
+) |>
+    left_join(dat_baseline, by = "pt") |>
+    mutate(
+        sld_mu = get_sld(t, b, g, c, p),
+        sld = rnorm(n(), sld_mu, sld_mu * pars_mu$sigma)
+    ) |>
+    arrange(pt, t) |>
+    mutate(pt = factor(pt))
+
+
+mod <- cmdstan_model(
+    stan_file = here::here("design/debug-cb/B/claret_bruno.stan")
+)
+
+stan_data <- list(
+    N_obs = nrow(dat),
+    N_pt = N,
+    pt_index = as.numeric(dat$pt),
+    values = dat$sld,
+    times = dat$t
+)
+
+
+fit <- mod$sample(
+    data = stan_data,
+    chains = 3,
+    parallel_chains = 3,
+    refresh = 200,
+    iter_warmup = 1500,
+    iter_sampling = 2000
+)
+
+fit
+fit$summary()
+
+
+
+
+
+######################
+#
+# brms implementation
+#
+#
+
+
+# pars_mu <- list(
+#     b = 60,
+#     g = 0.5,
+#     c = 0.4,
+#     p = 0.7,
+#     sigma = 0.02
+# )
+
+bfit <- brm(
+    bf(
+        value ~ exp(b) * exp(  exp(g) * t - exp(p-c) * (1 - exp(- exp(c) * t))),
+        b ~ 1 + (1 | pt),
+        g ~ 1 + (1 | pt),
+        c ~ 1 + (1 | pt),
+        p ~ 1 + (1 | pt),
+        nl = TRUE
+    ),
+    data = dat |> select(pt, value = sld, t),
+    prior = c(
+        prior("normal(log(60), 0.3)", nlpar = "b"),   # b intercept
+        prior("normal(log(0.5), 0.3)", nlpar = "g"),  # g intercept
+        prior("normal(log(0.4), 0.3)", nlpar = "c"),  # c intercept
+        prior("normal(log(0.7), 0.3)", nlpar = "p"),  # p intercept
+        prior("lognormal(log(0.1), 0.3)", nlpar = "b", class = "sd"),  # b random effect sigma
+        prior("lognormal(log(0.1), 0.3)", nlpar = "g", class = "sd"),  # g random effect sigma
+        prior("lognormal(log(0.1), 0.3)", nlpar = "c", class = "sd"),  # c random effect sigma
+        prior("lognormal(log(0.1), 0.3)", nlpar = "p", class = "sd"),  # p random effect sigma
+        prior("lognormal(log(0.02), 0.3)", class = "sigma")   # overall sigma
+    ),
+    warmup = 1500,
+    iter = 2500,
+    chains = 3,
+    cores = 3,
+    backend = "cmdstanr",
+    control = list(adapt_delta = 0.95)
+)
+
+
+
+
+#####################
+#
+#  Debugging 
+#
+#
+
+
+
+# Plot patient profiles
+pdat <- dat |> filter(pt %in% sample(dat$pt, 5))
+
+ggplot(data = pdat, aes(x = t, y = sld, group = pt, col = pt)) +
+    geom_point() +
+    geom_line(aes(y = sld_mu))
+
+
+# Plottig priors
+plot(density(exp(rnorm(5000, log(0.6), 0.2))))
+
+
+# Plotting Joint Priors
+N <- 100000
+mu <- rnorm(N, log(0.6), 0.3)
+sigma <- exp(rnorm(N, log(0.1), 0.3))
+value <- exp(rnorm(N, mu, sigma))
+
+pdat <- tibble(
+    mu = mu,
+    sigma = sigma,
+    value = value
+)
+
+ggplot(data = pdat, aes(x =value, y = mu)) +
+    geom_bin2d(bins = 300)
+
+