glm.rmap: Posterior of robust meta-analytic predictive prior (RMAP)

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

Posterior of robust meta-analytic predictive prior (RMAP)

Description

Sample from the posterior distribution of a GLM using the robust meta-analytic predictive prior (RMAP) by Schmidli et al. (2014) doi:10.1111/biom.12242.

Usage

glm.rmap(
  formula,
  family,
  data.list,
  offset.list = NULL,
  w = 0.1,
  meta.mean.mean = NULL,
  meta.mean.sd = NULL,
  meta.sd.mean = NULL,
  meta.sd.sd = NULL,
  disp.mean = NULL,
  disp.sd = NULL,
  norm.vague.mean = NULL,
  norm.vague.sd = NULL,
  bridge.args = 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.
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.
w	a scalar between 0 and 1 giving how much weight to put on the historical data. Defaults to 0.1.
meta.mean.mean	same as meta.mean.mean in glm.bhm(). It is 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 in Bayesian hierarchical model (BHM). 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	same as meta.mean.sd in glm.bhm(). It is 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 in BHM. If a scalar is provided, same as for meta.mean.mean. Defaults to a vector of 10s.
meta.sd.mean	same as meta.sd.mean in glm.bhm(). It is 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 in BHM. If a scalar is provided, same as for meta.mean.mean. Defaults to a vector of 0s.
meta.sd.sd	same as meta.sd.sd in glm.bhm(). It is 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 in BHM. If a scalar is provided, same as for meta.mean.mean. Defaults to a vector of 1s.
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 meta.mean.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 meta.mean.mean. Defaults to a vector of 10s.
norm.vague.mean	same as beta.mean in glm.post(). It is a scalar or a vector whose dimension is equal to the number of regression coefficients giving the means for the vague normal prior on regression coefficients. If a scalar is provided, norm.vague.mean will be a vector of repeated elements of the given scalar. Defaults to a vector of 0s.
norm.vague.sd	same as beta.sd in glm.post(). It is a scalar or a vector whose dimension is equal to the number of regression coefficients giving the sds for the vague normal prior on regression coefficients. If a scalar is provided, same as for norm.vague.mean. Defaults to a vector of 10s.
bridge.args	a list giving arguments (other than samples, log_posterior, data, lb, ub) to pass onto bridgesampling::bridge_sampler().
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 robust meta-analytic predictive prior (RMAP) is a two-part mixture prior consisting of a meta-analytic predictive (MAP) prior (the prior induced by Bayesian hierarchical model (BHM)) and a vague (i.e., non-informative) prior (specifically, the normal/half-normal prior with large variances). Although Schmidli et al. (2014) recommends to use a finite mixture of conjugate priors to approximate the BHM, it can be difficult and time-consuming to come up with an appropriate approximation.

Instead, the approach taken by hdbayes is to use the marginal likelihood of the MAP and vague priors. Specifically, note that the posterior distribution of a GLM under RMAP is also a two-part mixture distribution. The updated mixture weight for posterior density under the MAP prior is

\widetilde{w} = \frac{w Z_I(D, D_0)}{w Z_I(D, D_0) + (1-w) Z_V(D)},

where w is the prior mixture weight for the MAP prior in RMAP, Z_I(D, D_0) is the marginal likelihood of the MAP prior, and Z_V(D) is the marginal likelihood of the vague prior.

Value

The function returns a list with the following objects

post.samples

an object of class draws_df giving posterior samples under the robust meta-analytic predictive prior (RMAP)

post.samples.bhm

an object of class draws_df giving posterior samples under the Bayesian hierarchical model (BHM), obtained from using glm.bhm()

post.samples.vague

an object of class draws_df giving posterior samples under the vague/non-informative prior, obtained from using glm.post()

bs.map

output from computing log marginal likelihood of the prior induced by the BHM (referred to as the meta-analytic predictive (MAP) prior) via glm.logml.map() function

bs.vague

output from computing log marginal likelihood of the vague prior via glm.logml.post() function

References

Schmidli, H., Gsteiger, S., Roychoudhury, S., O’Hagan, A., Spiegelhalter, D., and Neuenschwander, B. (2014). Robust meta‐analytic‐predictive priors in clinical trials with historical control information. Biometrics, 70(4), 1023–1032.

Gronau, Q. F., Singmann, H., and Wagenmakers, E.-J. (2020). bridgesampling: An r package for estimating normalizing constants. Journal of Statistical Software, 92(10).

Examples

  if (instantiate::stan_cmdstan_exists()) {
    data(actg019) ## current data
    data(actg036) ## historical data
    ## take subset for speed purposes
    actg019 = actg019[1:150, ]
    actg036 = actg036[1:100, ]
    data.list = list(actg019, actg036)
    glm.rmap(
      formula = outcome ~ scale(age) + race + treatment + scale(cd4),
      family = binomial('logit'),
      data.list = data.list,
      w = 0.1,
      chains = 1, iter_warmup = 1000, iter_sampling = 2000
    )
  }

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