Statistics and Its Interface

Volume 13 (2020)

Number 4

Statistical methods for quantifying between-study heterogeneity in meta-analysis with focus on rare binary events

Pages: 449 – 464



Chiyu Zhang (Department of Statistical Science, Southern Methodist University, Dallas, Texas, U.S.A.)

Min Chen (Department of Mathematical Sciences, University of Texas, Dallas, Tx., U.S.A.)

Xinlei Wang (Department of Statistical Science, Southern Methodist University, Dallas, Texas, U.S.A.)


Meta-analysis, the statistical procedure for combining results from multiple independent studies, has been widely used in medical research to evaluate intervention efficacy and drug safety. In many practical situations, treatment effects vary notably among the collected studies, and the variation, often modeled by the between-study variance parameter $\tau^2$, can greatly affect the inference of the overall effect size. In the past, comparative studies have been conducted for both point and interval estimation of $\tau^2$. However, most are incomplete, only including a limited subset of existing methods, and some are outdated. Further, none of the studies covers descriptive measures for assessing the level of heterogeneity. Nor are they focused on rare binary events that require special attention. We summarize by far the most comprehensive set including 11 descriptive measures, 23 estimators, and 16 confidence intervals. In addition to providing synthesized information, we further categorize these methods according to their key features. We then evaluate their performance based on simulation studies that examine various realistic scenarios for rare binary events, with an illustration using a data example of a gestational diabetes meta-analysis. We conclude that there is no uniformly “best” method. However, methods with consistently better performance do exist in the context of rare binary events, and we provide practical guidelines based on numerical evidences.


bias, confidence interval, coverage probability, DerSimonian and Laird, fixed effect, odds ratio, mean squared error, $Q$-statistic, random effects

The third-named author’s research was partially supported by NIH Grant R15GM131390.

Received 11 August 2019

Accepted 20 March 2020

Published 31 July 2020