Confidence intervals for heterogeneity in meta-analysis of the rare binary events based on empirical likelihood-type methods

Abstract

In meta-analysis, heterogeneity between independent studies is one of the important reference indicators for comprehensive analyses. It is usually described in terms of the variance between groups of the random-effect model. The existing methods are used to construct their confidence intervals based on the assumption of the normal distribution, but in reality, this assumption is often violated, especially in rare binary events. Recently, the method of the jackknife empirical likelihood was proposed to build confidence intervals; however, it tends to perform not as good as the parametric methods when the number of studies involved is small. Therefore, we propose to use the adjusted jackknife empirical likelihood, transformed jackknife empirical likelihood, and transformed adjusted jackknife empirical likelihood to construct confidence intervals for heterogeneity of the rare binary event. We investigate the performance of the proposed methods through the simulations based on different distributions, especially for skewed distributions and the small sample sizes. Applications to real data with the proposed methods are also provided.