hdbayes (version 0.2.0)

curepwe.bhm: Posterior of Bayesian hierarchical model (BHM)

Description

Sample from the posterior distribution of a mixture cure rate model (referred to as the CurePWE model) using the Bayesian hierarchical model (BHM). The CurePWE 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.

Usage

curepwe.bhm(
  formula,
  data.list,
  breaks,
  meta.mean.mean = NULL,
  meta.mean.sd = NULL,
  meta.sd.mean = NULL,
  meta.sd.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,
  ...
)

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 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 of data.frames. The first element in the list is the current data, and the rest are the historical data sets. For fitting CurePWE 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.

meta.mean.mean

a scalar or a vector whose dimension is equal to the number of regression coefficients giving the means for the normal hyperpriors on the mean hyperparameters of regression coefficients. If a scalar is provided, meta.mean.mean will be a vector of repeated elements of the given scalar. Defaults to a vector of 0s.

meta.mean.sd

a scalar or a vector whose dimension is equal to the number of regression coefficients giving the sds for the normal hyperpriors on the mean hyperparameters of regression coefficients. If a scalar is provided, same as for meta.mean.mean. Defaults to a vector of 10s.

meta.sd.mean

a scalar or a vector whose dimension is equal to the number of regression coefficients giving the means for the half-normal hyperpriors on the sd hyperparameters of regression coefficients. If a scalar is provided, same as for meta.mean.mean. Defaults to a vector of 0s.

meta.sd.sd

a scalar or a vector whose dimension is equal to the number of regression coefficients giving the sds for the half-normal hyperpriors on the sd hyperparameters of regression coefficients. If a scalar is provided, same as for meta.mean.mean. Defaults to a vector of 1s.

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 meta.mean.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 meta.mean.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 Bayesian hierarchical model (BHM) assumes that the regression coefficients in the PWE models for the historical and current data are different, but are correlated through a common distribution, whose hyperparameters (i.e., mean and standard deviation (sd) (the covariance matrix is assumed to have a diagonal structure)) are treated as random. The number of regression coefficients for the current data is assumed to be the same as that for the historical data.

The hyperpriors on the mean and the sd hyperparameters are independent normal and independent half-normal distributions, respectively. The baseline hazard parameters for both current and historical data models are assumed to be independent and identically distributed (i.i.d.), each assigned a half-normal prior. Similarly, the cure fractions for both models are treated as i.i.d., with a normal prior specified on the logit of the cure fraction.

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)])
    curepwe.bhm(
      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
    )
  }
}