knitr::opts_chunk$set( collapse = TRUE, comment = "#" )
To fit meta-analysis models using frequentist methods, there are many R packages available including metafor
. On the other hand, Bayesian estimation methods such as Markov chain Monte Carlo (MCMC) are very attractive for meta-analysis, especially because they can be used to fit more complicated models. These include binomial-normal hierarchical models and beta-binomial models which are based on the exact distributional assumptions unlike (commonly used) normal-normal hierarchical model. Another advantage of Bayesian methods to be able to use informative prior distributions for example to regularize heterogeneity estimates in case of low number of studies. Thus, we developed MetaStan
which uses Stan (a modern MCMC engine) to fit several pairwise meta-analysis models including binomial-normal hierarchical model and beta-binomial model. This package is also the accompanying package for Günhan, Röver, and Friede (2020).
The development version of MetaStan
is available on Github (https://github.com/gunhanb/MetaStan) and can be installed using devtools
package as follows:
devtools:::install_github("gunhanb/MetaStan")
The BCG trials example is available in the package, and it can be loaded as follows:
library("MetaStan") data("dat.Berkey1995", package = "MetaStan") head(dat.Berkey1995)
Additional information can be obtained by typing ?dat.Berkey1995
(for any dataset and function in the package).
We can visualize individual log odds ratio estimates plot using ggplot2
as follows:
library(ggplot2) # Calculating log odds ratios and variances from data logodds <- function(x) log((x[1] * (x[4] - x[3]))/((x[2] - x[1]) * x[3])) stdes <- function(x) sqrt(1/x[1] + 1/(x[2] - x[1]) + 1/x[3] + 1/(x[4] - x[3])) r_ind <- apply(cbind(dat.Berkey1995$r2, dat.Berkey1995$n2, dat.Berkey1995$r1, dat.Berkey1995$n1), 1, logodds) se_ind <- apply(cbind(dat.Berkey1995$r2, dat.Berkey1995$n2, dat.Berkey1995$r1, dat.Berkey1995$n1), 1, stdes) lower95_ind <- r_ind + qnorm(.025) * se_ind upper95_ind <- r_ind + qnorm(.975) * se_ind # Comparison of the results trials <- c("1", "2" ,"3", "4", "5", "6", "7", "8", "9", "10", "11", "12", "13") trials <- ordered(trials, levels = trials) d <- data.frame(x = trials, y = r_ind, ylo = lower95_ind, yhi = upper95_ind) forest.plot <- ggplot(d, aes(x = x, y = y, ymin = ylo, ymax = yhi)) + geom_pointrange() + coord_flip() + geom_hline(aes(yintercept=0), lty = 2) + xlab("Studies") + ggtitle("Forest Plot (BCG vaccines)") plot(forest.plot)
metastan
is the main fitting function of this package. The main computations are executed via the rstan
package's sampling
function. We can fit the binomial-normal hierarchical model (Günhan, Röver, and Friede, 2020) using a weakly informative prior for treatment effect as follows:
data('dat.Berkey1995', package = "MetaStan") ## Fitting a Binomial-Normal Hierarchical model using WIP priors data('dat.Berkey1995', package = "MetaStan") ## Fitting a Binomial-Normal Hierarchical model using WIP priors dat_MetaStan <- create_MetaStan_dat(dat = dat.Berkey1995, armVars = c(responders = "r", sampleSize = "n")) meta.BCG.stan <- meta_stan(data = dat_MetaStan, likelihood = "binomial", mu_prior = c(0, 10), theta_prior = c(0, 100), tau_prior = 0.5, tau_prior_dist = "half-normal")
Convergence diagnostics, very conveniently, obtained using shinystan
package as follows:
library("shinystan") ## Firstly convert "stan" object to a "shinystan" object bnhm1.BCG.shinystan = as.shinystan(meta.BCG.stan$fit) launch_shinystan(bnhm1.BCG.shinystan)
A simple summary of the fitted model is given by print
option:
print(meta.BCG.stan)
Note that this model corresponds to Model 4 in Jackson et al (2018).
Please see Günhan, Röver, and Friede (2020) and Jackson et al (2018) for complete model descriptions.
Günhan, BK, Röver, C, and Friede, T (2020). "Random-effects meta-analysis of few studies involving rare events". In: Research Synthesis Methods 11.1, pp. 74-90. DOI: 10.1002/jrsm.1370.
Jackson, D et al. (2018). "A comparison of seven random-effects models for meta-analyses that estimate the summary odds ratio". In: Statistics in Medicine 37.7, pp. 1059-1085. DOI: 10.1002/sim.7588.
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