title: Meta-analysis framework for exact inferences with application to the analysis of rare events.
abstract: 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 Tian et al.'s method of combining confidence intervals (2009, Biostatistics, 10, 275-281) and Liu et al.'s method of combining p-value functions (2014, JASA, 109, 1450-1465). 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.
authors.affiliation: Business Analytics, Dun & Bradstreet Inc., Short Hills, New Jersey 07078, U.S.A.
authors.forename: Guang
authors.initials: G
authors.lastname: Yang
authors.affiliation: University of Cincinnati Lindner College of Business, Cincinnati, Ohio 45221, U.S.A.
authors.forename: Dungang
authors.initials: D
authors.lastname: Liu
authors.affiliation: Biostatistics and Programming, Merck Serono, Beijing 100022, China.
authors.forename: Junyuan
authors.initials: J
authors.lastname: Wang
authors.affiliation: Department of Statistics and Biostatistics, Rutgers University, New Brunswick, New Jersey 08854, U.S.A.
authors.forename: Min-Ge
authors.initials: MG
authors.lastname: Xie
mesh_terms: D001699:Biometry / Q000379:methods; D003198:Computer Simulation; D016001:Confidence Intervals; D006801:Humans; D007004:Hypoglycemic Agents / Q000009:adverse effects; D015201:Meta-Analysis as Topic
chemical_list: D007004:Hypoglycemic Agents
keywords: Clinical trial; Confidence distribution; Drug safety; Safety signal detecting; Zero event