pwe.stratified.pp: Posterior of stratified power prior (PP) with fixed a_0

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

Posterior of stratified power prior (PP) with fixed a_0

Description

Sample from the posterior distribution of a piecewise exponential (PWE) model (i.e., a proportional hazards model with a piecewise constant baseline hazard) using the power prior (PP) within predefined strata. If the strata and power prior parameters (a_0's) are determined based on propensity scores, this function can be used to sample from the posterior of a PWE model under the propensity score-integrated power prior (PSIPP) by Wang et al. (2019) doi:10.1080/10543406.2019.1657133.

Usage

pwe.stratified.pp(
  formula,
  data.list,
  strata.list,
  breaks,
  a0.strata,
  beta.mean = NULL,
  beta.sd = NULL,
  base.hazard.mean = NULL,
  base.hazard.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. 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 of data.frames. The first element in the list is the current data, and the rest are the historical data sets. For fitting piecewise exponential (PWE) models, all historical data sets will be stacked into one historical data set.
strata.list	a list of vectors specifying the stratum ID for each observation in the corresponding data set in data.list. The first element in the list corresponds to the current data, and the rest correspond to the historical data sets. Each vector should have the same length as the number of rows in the respective data set in data.list, with values representing stratum labels as positive integers (e.g., 1, 2, 3, ...).
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.
a0.strata	A scalar or a vector of fixed power prior parameters (a_0's) for each stratum, with values between 0 and 1. If a scalar is provided, it will be replicated for all strata. If a vector is provided, its length must match the total number of unique strata across all data sets. The first element of a0.strata corresponds to stratum 1, the second to stratum 2, and so on.
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.
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 power prior parameters (a_0's) are treated as fixed and must be provided for each stratum. Users must also specify the stratum ID for each observation. Within each stratum, the initial priors on the regression coefficients are independent normal priors, and the current and historical data models are assumed to share the baseline hazard parameters with half-normal priors.

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

References

Wang, C., Li, H., Chen, W.-C., Lu, N., Tiwari, R., Xu, Y., & Yue, L. Q. (2019). Propensity score-integrated power prior approach for incorporating real-world evidence in single-arm clinical studies. Journal of Biopharmaceutical Statistics, 29(5), 731–748.

Examples

if (instantiate::stan_cmdstan_exists()) {
  if(requireNamespace("survival")){
    library(survival)
    data(E1684)
    data(E1690)
    ## take subset for speed purposes
    E1684 = E1684[1:100, ]
    E1690 = E1690[1:50, ]
    ## replace 0 failure times with 0.50 days
    E1684$failtime[E1684$failtime == 0] = 0.50/365.25
    E1690$failtime[E1690$failtime == 0] = 0.50/365.25
    data_list = list(currdata = E1690, histdata = E1684)
    strata_list = list(rep(1:2, each = 25), rep(1:2, each = 50))
    # Alternatively, we can determine the strata based on propensity scores
    # using the psrwe package, which is available on GitHub
    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)])
    pwe.stratified.pp(
      formula = survival::Surv(failtime, failcens) ~ treatment,
      data.list = data_list,
      strata.list = strata_list,
      breaks = breaks,
      a0.strata = c(0.3, 0.5),
      chains = 1, iter_warmup = 500, iter_sampling = 1000
    )
  }
}

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