Bootstrap Calibration of Likelihood-Ratio Inference for the Hypergeometric-Normal Random-Effects Model in Rare-Event Meta-Analysis.

Conventional random-effects models in meta-analysis rely on normal approximations and fixed within-study variance assumptions that are often violated in rare-event settings. When zero cells occur, Haldane-type (+0.5) corrections can further bias the estimated effects. To overcome these limitations, likelihood-based approaches such as the hypergeometric-normal (HGN) model have been developed to enable exact conditional likelihood-based inference. However, ordinary Wald-type inference may still be inaccurate in small and sparse data settings. In this article, we investigate likelihood-ratio (LR)-based inference for the HGN random-effects model and propose two parametric bootstrap procedures for improving its finite-sample calibration: (1) bootstrap mean calibration of the LR statistic and (2) bootstrap inference based directly on the empirical distribution of the LR statistic. Extensive simulation studies under rare-event conditions demonstrate that the uncorrected LR-based confidence interval already provides stable coverage, reflecting the favorable properties of the exact conditional likelihood. Bootstrap mean calibration generally provided the most consistent additional calibration under the most challenging extremely rare-event settings, whereas direct bootstrap inference provided an alternative distribution-based approach. An application to a meta-analysis of rosiglitazone and myocardial infarction is also presented.