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When zero cells occur, Haldane\u2010type (+0.5) corrections can further bias the estimated effects. To overcome these limitations, likelihood\u2010based approaches such as the hypergeometric\u2013normal (HGN) model have been developed to enable exact conditional likelihood\u2010based inference. However, ordinary Wald\u2010type inference may still be inaccurate in small and sparse data settings. In this article, we investigate likelihood\u2010ratio (LR)\u2010based inference for the HGN random\u2010effects model and propose two parametric bootstrap procedures for improving its finite\u2010sample 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\u2010event conditions demonstrate that the uncorrected LR\u2010based 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\u2010event settings, whereas direct bootstrap inference provided an alternative distribution\u2010based approach. An application to a meta\u2010analysis of rosiglitazone and myocardial infarction is also presented.<\/jats:p>","DOI":"10.1002\/sim.70776","type":"journal-article","created":{"date-parts":[[2026,10,14]],"date-time":"2026-10-14T01:20:52Z","timestamp":1791940852000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Bootstrap Calibration of Likelihood\u2010Ratio Inference for the Hypergeometric\u2013Normal Random\u2010Effects Model in Rare\u2010Event Meta\u2010Analysis"],"prefix":"10.1002","volume":"45","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2520-9949","authenticated-orcid":false,"given":"Hisashi","family":"Noma","sequence":"first","affiliation":[{"name":"Department of Interdisciplinary Statistical Mathematics The Institute of Statistical Mathematics  Tokyo Japan"},{"name":"The Graduate Institute for Advanced Studies, The Graduate University for Advanced Studies (SOKENDAI)  Tokyo 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