The `rema`

(rare event meta-analysis) package implements a permutation-based approach for binary meta-analyses of 2x2 tables, founded on conditional logistic regression, that provides more reliable statistical tests when heterogeneity is observed in rare event data (Zabriskie et al. 2021). To adjust for the effect of heterogeneity, this method conditions on the sufficient statistic of a proxy for the heterogeneity effect as opposed to estimating the heterogeneity variance. While this results in the model not strictly falling under the random-effects framework, it is akin to a random-effects approach in that it assumes differences in variability due to treatment. Further, this method does not rely on large-sample approximations or continuity corrections for rare event data.

This method uses the permutational distribution of the test statistic instead of asymptotic approximations for inference. The number of observed events drives the computation complexity for creating this permutational distribution. Accordingly, for this method to be computationally feasible, it should only be applied to meta-analyses with a relatively low number of observed events. To create this permutational distribution, a network algorithm, based on the work of Mehta et al. (1992) and Corcoran et al. (2001), is employed using C++ and integrated into the package.

You can install the released version of `rema`

from CRAN with

and the development version from GitHub through the `devtools`

package with

Here is an example using `rema`

for a rare event meta-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 ratio
```

Corcoran 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 Linear Rank Tests for Ordered Categorical and Binary Data.” *Journal of Computational and Graphical Statistics*, 1(1), 21–40, doi:10.2307/1390598.

Zabriskie BN, Corcoran C, Senchaudhuri P (2021). “A Permutation-Based Approach for Heterogeneous Meta-Analyses of Rare Events.” *Statistics in Medicine*, 40(25), 5587-5604, doi:10.1002/sim.9142.