glm.commensurate {hdbayes}

Posterior of commensurate prior (CP)

Description

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

Usage

glm.commensurate(
  formula,
  family,
  data.list,
  tau,
  offset.list = NULL,
  beta0.mean = NULL,
  beta0.sd = NULL,
  disp.mean = NULL,
  disp.sd = NULL,
  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.

tau

a scalar or a vector whose dimension is equal to the number of regression coefficients giving the commensurate prior parameters. If a scalar is provided, tau will be a vector of repeated elements of the given scalar. Each element of tau must be positive, corresponding to a normal precision parameter.

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, same as for tau. 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 tau. 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 means for the half-normal priors on the dispersion parameters. If a scalar is provided, same as for tau. 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 sds for the half-normal priors on the dispersion parameters. If a scalar is provided, same as for tau. Defaults to a vector of 10s.

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 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 user-specified vector (tau) of precision parameters. 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.

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,
    tau = rep(5, 4),    ## 4 parameters including intercept
    chains = 1, iter_warmup = 500, iter_sampling = 1000
  )
}