curepwe.post: Posterior of a normal/half-normal prior

In hdbayes: Bayesian Analysis of Generalized Linear Models with Historical Data

Posterior of a normal/half-normal prior

Description

Sample from the posterior distribution of a mixture cure rate model using a normal/half-normal prior. The model assumes that a fraction \pi of the population is "cured", while the remaining 1 - \pi are susceptible to the event of interest. The survival function for the entire population is given by:

S_{\text{pop}}(t) = \pi + (1 - \pi) S(t),

where S(t) represents the survival function of the non-cured individuals. We model S(t) using a piecewise exponential (PWE) model (i.e., a proportional hazards model with a piecewise constant baseline hazard). Covariates are incorporated through the PWE model. This cure rate model is referred to as the CurePWE model.

Usage

curepwe.post(
  formula,
  data.list,
  breaks,
  beta.mean = NULL,
  beta.sd = NULL,
  base.hazard.mean = NULL,
  base.hazard.sd = NULL,
  logit.pcured.mean = NULL,
  logit.pcured.sd = NULL,
  get.loglik = FALSE,
  iter_warmup = 1000,
  iter_sampling = 1000,
  chains = 4,
  ...
)

Arguments

formula	a two-sided formula giving the relationship between the response variable and covariates in the PWE model. The response is a survival object as returned by the survival::Surv(time, event) function, where event is a binary indicator for event (0 = no event, 1 = event has occurred). The type of censoring is assumed to be right-censoring.
data.list	a list consisting of one data.frame giving the current data. If data.list has more than one data.frame, only the first element will be used as the current data.
breaks	a numeric vector specifying the time points that define the boundaries of the piecewise intervals. The values should be in ascending order, with the final value being greater than or equal to the maximum observed time.
beta.mean	a scalar or a vector whose dimension is equal to the number of regression coefficients giving the mean parameters for the initial prior on regression coefficients. If a scalar is provided, beta.mean will be a vector of repeated elements of the given scalar. Defaults to a vector of 0s.
beta.sd	a scalar or a vector whose dimension is equal to the number of regression coefficients giving the sd parameters for the initial prior on regression coefficients. If a scalar is provided, same as for beta.mean. Defaults to a vector of 10s.
base.hazard.mean	a scalar or a vector whose dimension is equal to the number of intervals giving the location parameters for the half-normal priors on the baseline hazards of the PWE model. If a scalar is provided, same as for beta.mean. Defaults to 0.
base.hazard.sd	a scalar or a vector whose dimension is equal to the number of intervals giving the scale parameters for the half-normal priors on the baseline hazards of the PWE model. If a scalar is provided, same as for beta.mean. Defaults to 10.
logit.pcured.mean	mean parameter for the normal prior on the logit of the cure fraction \pi. Defaults to 0.
logit.pcured.sd	sd parameter for the normal prior on the logit of the cure fraction \pi. Defaults to 3.
get.loglik	whether to generate log-likelihood matrix. Defaults to FALSE.
iter_warmup	number of warmup iterations to run per chain. Defaults to 1000. See the argument iter_warmup in sample() method in cmdstanr package.
iter_sampling	number of post-warmup iterations to run per chain. Defaults to 1000. See the argument iter_sampling in sample() method in cmdstanr package.
chains	number of Markov chains to run. Defaults to 4. See the argument chains in sample() method in cmdstanr package.
...	arguments passed to sample() method in cmdstanr package (e.g., seed, refresh, init).

Details

The priors on the regression coefficients in the PWE model are independent normal distributions. When the normal priors are elicited with large variances, the prior is also referred to as the reference or vague prior. The baseline hazard parameters of the PWE model are assumed to be independent of the regression coefficients with half-normal priors. Additionally, a normal prior is specified for the logit of the cure fraction \pi.

Value

The function returns an object of class draws_df containing posterior samples. The object has two attributes:

data

a list of variables specified in the data block of the Stan program

model

a character string indicating the model name

Examples

if (instantiate::stan_cmdstan_exists()) {
  if(requireNamespace("survival")){
    library(survival)
    data(E1690)
    ## take subset for speed purposes
    E1690 = E1690[1:100, ]
    ## replace 0 failure times with 0.50 days
    E1690$failtime[E1690$failtime == 0] = 0.50/365.25
    E1690$cage = as.numeric(scale(E1690$age))
    data_list = list(currdata = E1690)
    nbreaks = 3
    probs   = 1:nbreaks / nbreaks
    breaks  = as.numeric(
      quantile(E1690[E1690$failcens==1, ]$failtime, probs = probs)
    )
    breaks  = c(0, breaks)
    breaks[length(breaks)] = max(10000, 1000 * breaks[length(breaks)])
    curepwe.post(
      formula = survival::Surv(failtime, failcens) ~ treatment + sex + cage + node_bin,
      data.list = data_list,
      breaks = breaks,
      logit.pcured.mean = 0, logit.pcured.sd = 3,
      chains = 1, iter_warmup = 500, iter_sampling = 1000
    )
  }
}

hdbayes documentation built on Nov. 21, 2025, 1:07 a.m.