pwe.npp: Posterior of normalized power prior (NPP)

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

Posterior of normalized power prior (NPP)

Description

Sample from the posterior distribution of a piecewise exponential (PWE) model using the normalized power prior (NPP) by Duan et al. (2006) doi:10.1002/env.752.

Usage

pwe.npp(
  formula,
  data.list,
  a0.lognc,
  lognc,
  breaks,
  beta.mean = NULL,
  beta.sd = NULL,
  base.hazard.mean = NULL,
  base.hazard.sd = NULL,
  a0.shape1 = 1,
  a0.shape2 = 1,
  a0.lower = 0,
  a0.upper = 1,
  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.
a0.lognc	a vector giving values of the power prior parameter for which the logarithm of the normalizing constant has been evaluated.
lognc	a vector giving the logarithm of the normalizing constant (as estimated by pwe.npp.lognc() for each value of a0.lognc using the 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.
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.
a0.shape1	first shape parameter for the beta prior on the power prior parameter (a_0). When a0.shape1 == 1 and a0.shape2 == 1, a uniform prior is used.
a0.shape2	second shape parameter for the beta prior on the power prior parameter (a_0). When a0.shape1 == 1 and a0.shape2 == 1, a uniform prior is used.
a0.lower	a scalar giving the lower bound for a_0. Defaults to 0.
a0.upper	a scalar giving the upper bound for a_0. Defaults to 1.
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

Before using this function, users must estimate the logarithm of the normalizing constant across a range of different values for the power prior parameter (a_0), possibly smoothing techniques over a find grid. The power prior parameters (a_0's) are treated as random with independent beta priors. 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.

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

Duan, Y., Ye, K., and Smith, E. P. (2005). Evaluating water quality using power priors to incorporate historical information. Environmetrics, 17(1), 95–106.

See Also

pwe.npp.lognc()

Examples

  if(requireNamespace("parallel")){
    library(parallel)
    ncores    = 2

    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)])
      formula = survival::Surv(failtime, failcens) ~ treatment + sex + cage + node_bin
    }

    a0 = seq(0, 1, length.out = 11)
    if (instantiate::stan_cmdstan_exists()) {
      ## call created function
      ## wrapper to obtain log normalizing constant in parallel package
      logncfun = function(a0, ...){
        hdbayes::pwe.npp.lognc(
          formula = formula, histdata = data_list[[2]], breaks = breaks, a0 = a0,
          ...
        )
      }

      cl = makeCluster(ncores)
      clusterSetRNGStream(cl, 123)
      clusterExport(cl, varlist = c('formula', 'data_list', 'breaks'))
      a0.lognc = parLapply(
        cl = cl, X = a0, fun = logncfun, iter_warmup = 500,
        iter_sampling = 1000, chains = 1, refresh = 0
      )
      stopCluster(cl)
      a0.lognc = data.frame( do.call(rbind, a0.lognc) )

      ## sample from normalized power prior
      pwe.npp(
        formula = formula,
        data.list = data_list,
        a0.lognc = a0.lognc$a0,
        lognc = a0.lognc$lognc,
        breaks = breaks,
        chains = 1, iter_warmup = 500, iter_sampling = 1000,
        refresh = 0
      )
    }
  }

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