Therema (rare event meta-analysis) package implements apermutation-based approach for binary meta-analyses of 2x2 tables,founded on conditional logistic regression, that provides more reliablestatistical tests when heterogeneity is observed in rare event data(Zabriskie et al. 2021). To adjust for the effect of heterogeneity, thismethod conditions on the sufficient statistic of a proxy for theheterogeneity effect as opposed to estimating the heterogeneityvariance. While this results in the model not strictly falling under therandom-effects framework, it is akin to a random-effects approach inthat it assumes differences in variability due to treatment. Further,this method does not rely on large-sample approximations or continuitycorrections for rare event data.
This method uses the permutational distribution of the test statisticinstead of asymptotic approximations for inference. The number ofobserved events drives the computation complexity for creating thispermutational distribution. Accordingly, for this method to becomputationally feasible, it should only be applied to meta-analyseswith a relatively low number of observed events. To create thispermutational distribution, a network algorithm, based on the work ofMehta et al. (1992) and Corcoran et al. (2001), is employed using C++and integrated into the package.
You can install the released version ofrema fromCRAN with
install.packages("rema")and the development version fromGitHub through thedevtoolspackage with
# install.packages("devtools")devtools::install_github("ZabStatLab/rema")Here is an example usingrema for a rare eventmeta-analysis on a small example data set. For more detailed analyses,please refer to the package vignette.
library(rema)trt.events<-c(2,4,6,7,7,11)trt.total<-c(39,44,107,103,110,154)ctrl.events<-c(1,4,4,5,3,4)ctrl.total<-c(43,44,110,100,106,146)rema(trt.events, trt.total, ctrl.events, ctrl.total)#> Call:#> rema(trt.events = trt.events, trt.total = trt.total, ctrl.events = ctrl.events,#> ctrl.total = ctrl.total)#>#> OR 95%-CI p-value#> 0.6457 [0.1512; 3.2015] 0.2423#>#> Details on meta-analytical method:#> - Rare event, heterogeneous meta-analysis method#> - Two-sided p-value returned (mid.p = TRUE)#> - Conditional Maximum Likelihood Estimate (CMLE) used when computing the odds ratioCorcoran C, Ryan L, Senchaudhuri P, Mehta C, Patel N, Molenberghs G(2001). “An Exact Trend Test for Correlated Binary Data.”Biometrics, 57, 941–948,doi:10.1111/j.0006-341x.2001.00941.x.
Mehta CR, Patel N, Senchaudhuri P (1992). “Exact Stratified LinearRank Tests for Ordered Categorical and Binary Data.”Journal ofComputational and Graphical Statistics, 1(1), 21–40,doi:10.2307/1390598.
Zabriskie BN, Corcoran C, Senchaudhuri P (2021). “A Permutation-BasedApproach for Heterogeneous Meta-Analyses of Rare Events.”Statisticsin Medicine, 40(25), 5587-5604, doi:10.1002/sim.9142.