hdbayes (version 0.2.0)

pwe.commensurate: Posterior of commensurate prior (CP)

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 commensurate prior (CP) by Hobbs et al. (2011) doi:10.1111/j.1541-0420.2011.01564.x.

Usage

pwe.commensurate(
  formula,
  data.list,
  breaks,
  beta0.mean = NULL,
  beta0.sd = NULL,
  p.spike = 0.1,
  spike.mean = 200,
  spike.sd = 0.1,
  slab.mean = 0,
  slab.sd = 5,
  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.

beta0.mean

a scalar or a vector whose dimension is equal to the number of regression coefficients giving the mean parameters for the prior on the historical data regression coefficients. If a scalar is provided, beta0.mean will be a vector of repeated elements of the given scalar. Defaults to a vector of 0s.

beta0.sd

a scalar or a vector whose dimension is equal to the number of regression coefficients giving the sd parameters for the prior on the historical data regression coefficients. If a scalar is provided, same as for beta0.mean. Defaults to a vector of 10s.

p.spike

a scalar between 0 and 1 giving the probability of the spike component in spike-and-slab prior on commensurability parameter \(\tau\). Defaults to 0.1.

spike.mean

a scalar giving the location parameter for the half-normal prior (spike component) on \(\tau\). Defaults to 200.

spike.sd

a scalar giving the scale parameter for the half-normal prior (spike component) on \(\tau\). Defaults to 0.1.

slab.mean

a scalar giving the location parameter for the half-normal prior (slab component) on \(\tau\). Defaults to 0.

slab.sd

a scalar giving the scale parameter for the half-normal prior (slab component) on \(\tau\). Defaults to 5.

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 beta0.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 beta0.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 commensurate prior (CP) assumes that the regression coefficients for the current data model conditional on those for the historical data model are independent normal distributions with mean equal to the corresponding regression coefficients for the historical data and variance equal to the inverse of the corresponding elements of a vector of precision parameters (referred to as the commensurability parameter \(\tau\)). We regard \(\tau\) as random and elicit a spike-and-slab prior, which is specified as a mixture of two half-normal priors, on \(\tau\).

The number of current data regression coefficients is assumed to be the same as that of historical data regression coefficients. The baseline hazard parameters for both current and historical data models are assumed to be independent and identically distributed, each assigned a half-normal prior.

References

Hobbs, B. P., Carlin, B. P., Mandrekar, S. J., and Sargent, D. J. (2011). Hierarchical commensurate and power prior models for adaptive incorporation of historical information in clinical trials. Biometrics, 67(3), 1047–1056.

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.commensurate(
      formula = survival::Surv(failtime, failcens) ~ treatment + sex + cage + node_bin,
      data.list = data_list,
      breaks = breaks,
      p.spike = 0.1,
      chains = 1, iter_warmup = 500, iter_sampling = 1000
    )
  }
}