ra4bayesmeta-package {ra4bayesmeta}R Documentation

Reference analysis for Bayesian meta-analysis

Description

Functionality for performing a principled reference analysis in the Bayesian normal-normal hierarchical model (NNHM) used for Bayesian meta-analysis. Focuses on the choice of the prior for the between-study (heterogeneity) standard deviation τ. Implements the methodology proposed in Ott et al. (2020).

The main posterior benchmark used is Jeffreys' reference posterior, induced by a minimally informative improper reference prior for heterogeneity. Two additional extreme (in terms of the relative latent model complexity (RLMC)) posterior benchmarks are also considered, which allow to assess if a heterogeneity prior is more informative for the τ=0 or the τ=∞ hypothesis. On the prior level, the impact of the improper Jeffreys' reference prior on the marginal posteriors is bounded by two proper prior benchmarks. In addition, the two extreme (in terms of RLMC) prior benchmarks are also included. All four benchmarks belong to two closely related parametric families, the so-called "square-root generalized conventional" (SGC) and "inverse square-root generalized conventional" (SIGC) distributions, which are derived from prior distributions for variance components described in Berger & Deely (1988). Note that most of these prior benchmarks also depend on the data set considered.

The posterior reference analysis applies the Hellinger distance to quantify the informativeness of an actual heterogeneity prior of interest by comparing the corresponding marginal posteriors (for different parameters in the NNHM) with posterior benchmarks. The prior reference analysis quantifies the informativeness of an actual heterogeneity prior given the data by computing its Hellinger distance to prior benchmarks.

The main functions post_RA and pri_RA perform the reference analysis at the posterior and prior level based on a data frame as input. The function fit_models_RA computes the benchmark heterogeneity priors and corresponding (marginal) posteriors for a given data frame. The more flexible functions post_RA_fits and pri_RA_fits perform the reference analysis at the posterior and prior level based on the provided benchmark and actual model fits (of class bayesmeta), so that alternative benchmarks heterogeneity priors can also be used. Functions for plotting the densities of the heterogeneity priors and marginal posteriors for different parameters are also provided. The functions operate on data frames which are compatible with the bayesmeta R package on CRAN.

Details

Package: ra4bayesmeta

Type: Package

Title: Reference analysis for Bayesian meta-analysis

Version: 0.1-2

Date: 2020-02-23

Author: Manuela Ott [aut, cre], Malgorzata Roos [aut]

Maintainer: Manuela Ott <manuela.c.ott@gmail.ch>

Depends: bayesmeta

License: GPL (>=2)

Author(s)

Manuela Ott, Malgorzata Roos Maintainer: Manuela Ott <manuela.c.ott@gmail.ch>

References

Ott, M., Plummer, M., Roos, M. How vague is vague? How informative is informative? Reference analysis for Bayesian meta-analysis. Manuscript submitted to Statistics in Medicine. 2020.

Berger, J. O., Deely, J. (1988). A Bayesian approach to ranking and selection of related means with alternatives to analysis-of-variance methodology. Journal of the American Statistical Association 83(402), 364–373.

Examples

# auricular acupuncture (AA) data set
data(aa)
# posterior reference analysis
# for standard HN and HC heterogeneity priors
post_RA(df=aa, tau.prior=
               list(function(t)dhalfnormal(t, scale=1),                                                                function(t)dhalfcauchy(t, scale=1)))
# prior reference analysis                                
pri_RA(df=aa, tau.prior=
              list(function(t)dhalfnormal(t, scale=1),
                   function(t)dhalfcauchy(t, scale=1))) 
          
# plot the marginal posterior for the effect mu
plot_RA(df=aa, tau.prior=
               list(function(t)dhalfnormal(t, scale=1),
                    function(t)dhalfcauchy(t, scale=1)),
        type="post.mu", xlim=c(-1,1.5), ylim=c(0,2.5),
        legend=TRUE, legend.tau.prior=c("HN(1)", "HC(1)"))   

[Package ra4bayesmeta version 0.1-2 Index]