glm.commensurate: Posterior of commensurate prior (CP)

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

Posterior of commensurate prior (CP)

Description

Sample from the posterior distribution of a GLM using the commensurate prior (CP) by Hobbs et al. (2011) doi:10.1111/j.1541-0420.2011.01564.x.

Usage

glm.commensurate(
  formula,
  family,
  data.list,
  offset.list = NULL,
  beta0.mean = NULL,
  beta0.sd = NULL,
  disp.mean = NULL,
  disp.sd = NULL,
  p.spike = 0.1,
  spike.mean = 200,
  spike.sd = 0.1,
  slab.mean = 0,
  slab.sd = 5,
  iter_warmup = 1000,
  iter_sampling = 1000,
  chains = 4,
  ...
)

Arguments

formula	a two-sided formula giving the relationship between the response variable and covariates
family	an object of class family. See ?stats::family
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.
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.
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.
disp.mean	a scalar or a vector whose dimension is equal to the number of data sets (including the current data) giving the location parameters for the half-normal priors on the dispersion parameters. If a scalar is provided, same as for beta0.mean. Defaults to a vector of 0s.
disp.sd	a scalar or a vector whose dimension is equal to the number of data sets (including the current data) giving the scale parameters for the half-normal priors on the dispersion parameters. 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.
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 conditional on those for the historical data 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 priors on the dispersion parameters (if applicable) for the current and historical data sets are independent half-normal distributions.

Value

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

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()) {
  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.commensurate(
    formula = cd4 ~ treatment + age + race,
    family = poisson(), data.list = data_list,
    p.spike = 0.1,
    chains = 1, iter_warmup = 500, iter_sampling = 1000
  )
}

hdbayes documentation built on Sept. 11, 2024, 5:34 p.m.