R/glm_pp.R

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

#' Posterior of power prior (PP) with fixed \eqn{a_0}
#'
#' Sample from the posterior distribution of a GLM using the power prior (PP) by Ibrahim and Chen (2000) <doi:10.1214/ss/1009212673>.
#'
#' The power prior parameters (\eqn{a_0}'s) are treated as fixed. The initial priors on the regression coefficients
#' are independent normal priors. The current and historical data sets are assumed to have a common dispersion parameter
#' with a half-normal prior (if applicable).
#'
#' @include data_checks.R
#' @include get_stan_data.R
#'
#' @export
#'
#' @param formula           a two-sided formula giving the relationship between the response variable and covariates.
#' @param family            an object of class `family`. See \code{\link[stats:family]{?stats::family}}.
#' @param data.list         a list of `data.frame`s. The first element in the list is the current data, and the rest
#'                          are the historical data sets.
#' @param offset.list       a list of vectors giving the offsets for each data. The length of `offset.list` is equal to
#'                          the length of `data.list`. The length of each element of `offset.list` is equal to the number
#'                          of rows in the corresponding element of `data.list`. Defaults to a list of vectors of 0s.
#' @param 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.
#' @param 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.
#' @param a0.vals           a scalar between 0 and 1 or a vector whose dimension is equal to the number of historical
#'                          data sets giving the (fixed) power prior parameter for each historical data set. Each element of
#'                          vector should be between 0 and 1. If a scalar is provided, same as for `beta.mean`.
#' @param disp.mean         location parameter for the half-normal prior on dispersion parameter. Defaults to 0.
#' @param disp.sd           scale parameter for the half-normal prior on dispersion parameter. Defaults to 10.
#' @param iter_warmup       number of warmup iterations to run per chain. Defaults to 1000. See the argument `iter_warmup` in
#'                          `sample()` method in cmdstanr package.
#' @param 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.
#' @param chains            number of Markov chains to run. Defaults to 4. See the argument `chains` in `sample()` method in
#'                          cmdstanr package.
#' @param ...               arguments passed to `sample()` method in cmdstanr package (e.g., `seed`, `refresh`, `init`).
#'
#' @return
#'  The function returns an object of class `draws_df` giving posterior samples, with an attribute called 'data' which includes
#'  the list of variables specified in the data block of the Stan program.
#'
#' @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()) {
#'   data(actg019)
#'   data(actg036)
#'   ## take subset for speed purposes
#'   actg019 = actg019[1:100, ]
#'   actg036 = actg036[1:50, ]
#'   data_list = list(currdata = actg019, histdata = actg036)
#'   glm.pp(
#'     formula = cd4 ~ treatment + age + race,
#'     family = poisson('log'),
#'     data.list = data_list,
#'     a0.vals = 0.5,
#'     chains = 1, iter_warmup = 500, iter_sampling = 1000
#'   )
#' }
glm.pp = function(
    formula,
    family,
    data.list,
    a0.vals,
    offset.list       = NULL,
    beta.mean         = NULL,
    beta.sd           = NULL,
    disp.mean         = NULL,
    disp.sd           = NULL,
    iter_warmup       = 1000,
    iter_sampling     = 1000,
    chains            = 4,
    ...
) {
  ## get Stan data for PP
  standat = get.stan.data.pp(
    formula     = formula,
    family      = family,
    data.list   = data.list,
    a0.vals     = a0.vals,
    offset.list = offset.list,
    beta.mean   = beta.mean,
    beta.sd     = beta.sd,
    disp.mean   = disp.mean,
    disp.sd     = disp.sd
  )

  glm_pp     = instantiate::stan_package_model(
    name = "glm_pp",
    package = "hdbayes"
  )

  ## fit model in cmdstanr
  fit = glm_pp$sample(data = standat,
                      iter_warmup = iter_warmup, iter_sampling = iter_sampling, chains = chains,
                      ...)

  ## rename parameters
  p        = standat$p
  X        = standat$X
  oldnames = paste0("beta[", 1:p, "]")
  newnames = colnames(X)

  if ( !family$family %in% c('binomial', 'poisson') ) {
    oldnames = c(oldnames, 'dispersion[1]')
    newnames = c(newnames, 'dispersion')
  }
  d = rename.params(fit = fit, oldnames = oldnames, newnames = newnames)
  ## add data used for the variables specified in the data block of the Stan program as an attribute
  attr(x = d, which = 'data') = standat
  return(d)
}