Description
Bayesian Multivariate Meta-Analysis.
Description
Objective Bayesian inference procedures for the parameters of the multivariate random effects model with application to multivariate meta-analysis. The posterior for the model parameters, namely the overall mean vector and the between-study covariance matrix, are assessed by constructing Markov chains based on the Metropolis-Hastings algorithms as developed in Bodnar and Bodnar (2021) (<arXiv:2104.02105>). The Metropolis-Hastings algorithm is designed under the assumption of the normal distribution and the t-distribution when the Berger and Bernardo reference prior and the Jeffreys prior are assigned to the model parameters. Convergence properties of the generated Markov chains are investigated by the rank plots and the split hat-R estimate based on the rank normalization, which are proposed in Vehtari et al. (2021) (<DOI:10.1214/20-BA1221>).
README.md
BayesMultMeta - Bayesian Multivariate Meta-Analysis
This package implements the methods developed in [1]
To simulate samples from the posterior using the methods developed in the paper you simply need to run
set.seed(2021)
dataREM<-mvmeta::hyp
# Observation matrix X
X<-t(cbind(dataREM$sbp,dataREM$dbp))
p<-nrow(X) # model dimension
n<-ncol(X) # sample size
# Matrix U
U<-matrix(0,n*p,n*p)
for (i_n in 1:n) {
Use<-diag(c(dataREM$sbp_se[i_n],dataREM$dbp_se[i_n]))
Corr_mat<-matrix(c(1,dataREM$rho[i_n],dataREM$rho[i_n],1),p,p)
U[(p*(i_n-1)+1):(p*i_n),(p*(i_n-1)+1):(p*i_n)]<- Use%*%Corr_mat%*%Use
}
bmgmr_run <- BayesMultMeta(X, U, 1e4, burn_in = 100,
likelihood = "normal", prior="jeffrey",
algorithm_version = "A")
summary(bmgmr_run)
References
[1] Olha Bodnar, Taras Bodnar (2021). Objective Bayesian meta-analysis based on generalized multivariate random effects model. Under revision in Bayesian analysis.