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Meta-analysis framework for exact inferences with application to the analysis of rare events. (English) Zbl 1390.62321
Summary: The usefulness of meta-analysis has been recognized in the evaluation of drug safety, as a single trial usually yields few adverse events and offers limited information. For rare events, conventional meta-analysis methods may yield an invalid inference, as they often rely on large sample theories and require empirical corrections for zero events. These problems motivate research in developing exact methods, including L. Tian et al.’s method of combining confidence intervals [“Exact and efficient inference procedure for meta-analysis and its application to the analysis of independent \(2\times2\) tables with all available data but without artificial continuity correction”, Biostatistics 10, No. 2, 275–281 (2009; doi:10.1093/biostatistics/kxn034)] and D. Liu et al.’s method of combining \(p\)-value functions [J. Am. Stat. Assoc. 109, No. 508, 1450–1465 (2014; Zbl 1368.62113)]. This article shows that these two exact methods can be unified under the framework of combining confidence distributions (CDs). Furthermore, we show that the CD method generalizes Tian et al.’s method in several aspects. Given that the CD framework also subsumes the Mantel-Haenszel and Peto methods, we conclude that the CD method offers a general framework for meta-analysis of rare events. We illustrate the CD framework using two real data sets collected for the safety analysis of diabetes drugs.

62P10 Applications of statistics to biology and medical sciences; meta analysis
62G10 Nonparametric hypothesis testing
62H17 Contingency tables
62G15 Nonparametric tolerance and confidence regions
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