piecewise exponential outcome distribution

[mattsecrest]

• [ ] Specifying fixed cutpoints?
• [ ] specify different priors for periods
• [ ] transforming data
  • [ ] Something like as.matrix(survSplit(data = data.frame(example_matrix), cut = c(5, 10), end = "time", event = "cnsr"))

[gravesti]

Using the Poisson trick it's quite easy actually. We can also process the data in Stan for the cuts.

## Stan
pem <- cmdstanr::cmdstan_model(stan_file = write_stan_file(
"
data {
  int<lower=0> N;
  vector[N] trt;
  vector[N] time;
  vector[N] cens;
  int<lower = 1> M;
  vector[M] starts;
  vector[M] durations;
}

transformed data {
  matrix[N,M] T;
  matrix[N,M] D;
  for(j in 1:M) {
    T[,j] = fmin(fdim(time, starts[j]), durations[j]);
  }
  for(j in 1:M) {
    for(i in 1:N) {
      D[i,j] = (starts[j] <= time[i] && time[i] < starts[j] + durations[j]) * (1 - cens[i]);
    }
  }
}

parameters {
  real beta_trt;
  vector[M] alpha;
}

transformed parameters {
  real HR_trt = exp(beta_trt);
}

model {
  vector[N] lp;
  beta_trt ~ normal(0, 1e+05);
  alpha ~ normal(0, 1e+05);

  for (j in 1:M){
    lp = alpha[j] + trt * beta_trt;
    target += (lp' * D[,j]) - (exp(lp)' * T[,j]);
  }
}
"))
pem_samples <- pem$sample(
  data = list(
    N = nrow(example_matrix),
    trt = example_matrix[,"trt"],
    cens = example_matrix[,"cnsr"],
    time = example_matrix[,"time"],
    M = 4,
    starts = c(0, 1.83, 6, 23),
    durations = diff(c(c(0, 1.83, 6, 23), max(example_matrix[,"time"])))
  ))

pem_results <- pem_samples$summary(
  variables = c("beta_trt", "alpha[1]", "alpha[2]", "alpha[3]", "alpha[4]"),
  mean = mean,
  median = median
)
pem_results$exp_mean <- exp(pem_results$mean)
pem_results$exp_median <- exp(pem_results$median)
pem_results

## Comparison
em <- as.data.frame(example_matrix)
em$event <- 1 - em$cnsr
res_eha_pchreg <- eha::pchreg(
  Surv(time, event) ~ trt,
  cuts = c(0, 1.83, 6, 23, 50),
  data = em
)
summary(res_eha_pchreg)
res_eha_pchreg$hazards

[mattsecrest]

Closing in favor of newer issue https://github.com/Genentech/psborrow2/issues/223