Exercise 7: Bayesian meta-analysis

In 2014, Crins et al. ¹ published a meta-analysis assessing the incidence of acute rejection (AR) with or without Interleukin-2 receptor antagonists. In this exercise we will recreate this analysis.

0. Load the package bayesmeta ² and the data from Crins et al. (2014) with the R command data("CrinsEtAl2014").

   library(bayesmeta)
   data(CrinsEtAl2014)

1. Play around with the companion shiny app at: https://rshiny.gwdg.de/apps/bayesmeta/.
   If the website is unavailable, you can launch the app locally by running the 2 following commands from :

   library("shiny")
   install.packages("rhandsontable")
   runUrl("http://www.gwdg.de/~croever/bayesmeta/bayesmeta-app.zip")

2. Directly in the console now, using the escalc() function from the package metafor, compute the estimated log odds ratios from the 6 considered studies alongside their sampling variances (ProTip: read the Measures for Dichotomous Variables section from the help of the escalc() function). Check that those are the same as the one on the online shiny app (ProTip: ‘sigma’ is the standard error, i.e. the square root of the sampling variance vi)

   library("metafor")
   crins.es <- escalc(measure = "OR", ai = exp.AR.events, n1i = exp.total, ci = cont.AR.events,
       n2i = cont.total, slab = publication, data = CrinsEtAl2014)
   crins.es[, c("publication", "yi", "vi")]

   publication	yi	vi
   Heffron (2003)	-2.3097026	0.3593718
   Gibelli (2004)	-0.4595323	0.3095760
   Schuller (2005)	-2.3025851	0.7750000
   Ganschow (2005)	-1.7578579	0.2078161
   Spada (2006)	-1.2584610	0.4121591
   Gras (2008)	-2.4178959	2.3372623

   NB: Log-odds ratios are symmetric around zero and have a sampling distribution closer to the normal distibution than the natural OR scale. For this reason, they are usually prefered for meta-analyses. Their sample variance is then computed as the sum of the inverse of all the counts in the \(2 \times 2\) associated contingency table³.

3. Perform a random-effect meta-analysis of those data using the bayesmeta() function from the package bayesmeta, within . Use a uniform prior on \([0,4]\) for \(\tau\) and a Gaussian prior for \(\mu\) centered around \(0\) and with a standard deviation of \(4\).

4. Write the corresponding random-effects Bayesian meta-analysis model (using math, not – yet).

5. Use rjags to estimate the same model, saving the BUGS model in a .txt file (called crinsBUGSmodel.txt for instance).