Extend Weibull Regression Examples (#256)

Updated Weibull Regression Examples namely:
- Added flexsurv and survreg examples for Weibull regression
- Added second weibull regression examples file showing it applied to a common dataset (not simulated data)
- Updated stan code to be more efficient (but other wise no changes in functionality nor interfaces)

design/examples/weibull.R

@@ -53,10 +53,43 @@ dat <- tibble(
 
 coxph(
     Surv(time, event) ~ age + sex + trt,
-    data =dat
+    data = dat
 )
 
 
+################################
+#
+# Flexsurv parametric Regression
+#
+
+
+flexsurvreg(
+    Surv(time, event) ~  sex + trt,
+    data = dat,
+    dist = "weibullPH"
+)
+
+
+################################
+#
+# Survreg parametric Regression
+#
+
+
+mod <- survreg(
+    Surv(time, event) ~ age + sex + trt,
+    data = dat,
+    dist = "weibull"
+)
+
+gamma <- 1 / mod$scale
+lambda <- exp(-mod$coefficients[1] * gamma)
+param_log_coefs <- -mod$coefficients[-1] * gamma
+c(gamma, lambda, param_log_coefs)
+## Need to use delta method to get standard errors
+
+
+
 ################################
 #
 # Bayesian Weibull Regression
@@ -67,12 +100,11 @@ mod <- cmdstan_model(
     exe_file = here("design/examples/models/weibull")
 )
 
-design_mat <- model.matrix(~ age + sex + trt, data = dat)
+design_mat <- model.matrix(~  sex + trt, data = dat)
 
 
 stan_data <- list(
     n = nrow(dat),
-    x = rnorm(50, 5, 2),
     design = design_mat,
     p = ncol(design_mat),
     times = dat$time,
@@ -133,3 +165,4 @@ vars <- c(
 )
 
 mp@results$summary(vars)
+

design/examples/weibull.stan

@@ -1,72 +1,52 @@
 
 
+functions {
+    // Stan's in-built weibull functions are for the AFT formulation
+    // so instead we define here the PH formulation
+    real weibull_ph_lpdf (real t, real lambda, real gamma) {
+        return log(lambda) + log(gamma) + (gamma -1)* log(t) -lambda * t^gamma;
+    }
+    real weibull_ph_lccdf (real t, real lambda, real gamma) {
+        return -lambda * t^gamma;
+    }
+}
+
+
 data {
-    int<lower=1> n;
-    int<lower=0> p;
-    vector[n] times;
-    vector[n] event_fl;
-    matrix[n, p] design;
+    int<lower=1> n;                          // Number of subjects
+    int<lower=0> p;                          // Number of covariates (including intercept)
+    vector<lower=0>[n] times;                // Event|Censor times
+    array[n] int<lower=0, upper=1> event_fl; // 1=event 0=censor
+    matrix[n, p] design;                     // Design matrix
 }
 
 transformed data {
-    // To make life easier for the user we manually derive the indices
-    // of the event and censoring times (this would be easier to implement
-    // on the R side but would require more code from the user).
-
-    // First we work out how many censoring and events there are each so that
-    // we can construct index vectors of the correct size
-    int n_event = 0;
-    for (i in 1:n) {
-        if (event_fl[i] == 1) {
-            n_event += 1;
-        }
-    }
-    int n_censor = n - n_event;
-
-    // Now we construct the index vectors
-    array[n_event] int event_idx;
-    array[n_censor] int censor_idx;
-    int j = 1;
-    int k = 1;
-    for (i in 1:n) {
-        if (event_fl[i] == 1) {
-            event_idx[j] = i;
-            j+=1;
-        } else {
-            censor_idx[k] = i;
-            k+=1;
-        }
-    }
+    // Assuming that the first term is an intercept column which
+    // will conflict with the lambda term so remove it
+    matrix[n, p-1] design_reduced = design[, 2:p];
 }
 
 parameters {
-    vector[p] beta;
-    // real<lower = 0> lambda;  // Lambda is represented via exp(intercept) term of the design matrix
-    real<lower = 0> gamma;
+    vector[p-1] beta;
+    real<lower=0> lambda_0;
+    real<lower=0> gamma_0;
 }
 
-
 model {
-    // Stans in built distributions use the AFT parameterisation of the Weibull distribution
-    // As such we need to convert our PH parameters to the AFT parameters
-    real d_alpha;
-    vector[n] d_beta;
-    d_beta = exp(design * beta)^(-1/gamma);
-    d_alpha = gamma;
-
+
+    vector[n] lambda = lambda_0 .* exp(design_reduced * beta);
+
     // Priors
-    beta ~ normal(0, 2);
-    gamma ~ normal(1, 0.5);
+    beta ~ normal(0, 3);
+    gamma_0 ~ lognormal(log(1), 1.5);
+    lambda_0 ~ lognormal(log(0.05), 1.5);
 
     // Likelihood
-    target += weibull_lpdf(times[event_idx] | d_alpha, d_beta[event_idx]);
-    target += weibull_lccdf(times[censor_idx] | d_alpha, d_beta[censor_idx]);
-}
-
-generated quantities {
-    // Reconstruct the baseline lambda value from the intercept
-    // of the design matrix
-    real lambda_0 = exp(beta[1]);
+    for (i in 1:n) {
+        if (event_fl[i] == 1) {
+            target += weibull_ph_lpdf(times[i] | lambda[i], gamma_0);
+        } else {
+            target += weibull_ph_lccdf(times[i] | lambda[i], gamma_0);
+        }
+    }
 }
-
-

design/examples/weibull_std.R

@@ -0,0 +1,141 @@
+
+
+library(dplyr)
+library(flexsurv)
+library(survival)
+library(cmdstanr)
+library(posterior)
+library(bayesplot)
+library(here)
+
+
+dat <- flexsurv::bc |>
+    as_tibble() |>
+    mutate(arm = "A", study = "S", pt = sprintf("pt-%05d", 1:n()))
+
+
+
+################################
+#
+# Cox Regression
+#
+
+coxph(
+    Surv(recyrs, censrec) ~ group,
+    data = dat
+)
+
+
+################################
+#
+# Flexsurv parametric Regression
+#
+
+
+flexsurvreg(
+    Surv(recyrs, censrec) ~ group,
+    data = dat,
+    dist = "weibullPH"
+)
+
+
+################################
+#
+# Survreg parametric Regression
+#
+
+
+mod <- survreg(
+    Surv(recyrs, censrec) ~ group,
+    data = dat,
+    dist = "weibull"
+)
+
+gamma <- 1 / mod$scale
+lambda <- exp(-mod$coefficients[1] * gamma)
+param_log_coefs <- -mod$coefficients[-1] * gamma
+
+c(gamma, lambda, param_log_coefs)
+## Need to use delta method to get standard errors
+
+
+
+################################
+#
+# Bayesian Weibull Regression
+#
+
+mod <- cmdstan_model(
+    stan_file = here("design/examples/weibull.stan"),
+    exe_file = here("design/examples/models/weibull")
+)
+
+design_mat <- model.matrix(~ group, data = dat)
+
+
+stan_data <- list(
+    n = nrow(dat),
+    design = design_mat,
+    p = ncol(design_mat),
+    times = dat$recyrs,
+    event_fl = dat$censrec
+)
+fit <- mod$sample(
+    data = stan_data,
+    chains = 2,
+    parallel_chains = 2,
+    refresh = 200,
+    iter_warmup = 1000,
+    iter_sampling = 1500
+)
+
+fit$summary()
+
+
+bayesplot::mcmc_pairs(fit$draws())
+
+################################
+#
+# JMpost
+#
+
+devtools::load_all()
+# library(jmpost)
+
+jm <- JointModel(
+    survival = SurvivalWeibullPH(
+        lambda = prior_lognormal(log(1/200), 1.3),
+        gamma = prior_lognormal(log(1), 1.3)
+    )
+)
+
+jdat <- DataJoint(
+    subject = DataSubject(
+        data = dat,
+        subject = "pt",
+        arm = "arm",
+        study = "study"
+    ),
+    survival = DataSurvival(
+        data = dat,
+        formula = Surv(recyrs, censrec) ~ group
+    )
+)
+
+mp <- sampleStanModel(
+    jm,
+    data = jdat,
+    iter_warmup = 1000,
+    iter_sampling = 1500,
+    chains = 2,
+    parallel_chains = 2
+)
+
+vars <- c(
+    "sm_weibull_ph_lambda",
+    "sm_weibull_ph_gamma",
+    "beta_os_cov"
+)
+
+mp@results$summary(vars)
+