hdbayes (version 0.2.0)

pwe.pp: Posterior of 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) by Ibrahim and Chen (2000) doi:10.1214/ss/1009212673.

Usage

pwe.pp(
  formula,
  data.list,
  breaks,
  a0,
  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,
  ...
)

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

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.

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

a scalar between 0 and 1 giving the (fixed) power prior parameter for the historical data.

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. The initial priors on the regression coefficients are independent normal priors. The current and historical data models are assumed to share the baseline hazard parameters with half-normal priors.

References

Chen, M.-H. and Ibrahim, J. G. (2000). Power prior distributions for Regression Models. Statistical Science, 15(1).

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
    E1684$cage = as.numeric(scale(E1684$age))
    E1690$cage = as.numeric(scale(E1690$age))
    data_list = list(currdata = E1690, histdata = E1684)
    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.pp(
      formula = survival::Surv(failtime, failcens) ~ treatment + sex + cage + node_bin,
      data.list = data_list,
      breaks = breaks,
      a0 = 0.5,
      chains = 1, iter_warmup = 500, iter_sampling = 1000
    )
  }
}