Exact inference for fixed effects meta‐analysis of 2×2$$ 2\times 2 $$ tables

Abstract

Meta‐analysis of associations between rare outcomes and binary exposures are particularly important in studies of a drug's potential side‐effects. But meta‐analysis of the resulting contingency tables presents substantial practical difficulties, as analysts are currently forced to pick between “exact” inference—that eliminates concern over using large‐sample approximations with small cell counts—and explicitly allowing for heterogeneity of the underlying effects. A controversial example is given by the Avandia meta‐analysis (Nissen and Wolski. N Engl J Med. 2007;356(24):2457–2471) of rosiglitazone's effects on myocardial infarction and death. While the initial Avandia analysis—using simple methods—found a significant effect, its results conflict with subsequent re‐analyses that use either exact methods, or that explicitly acknowledge the plausible heterogeneity. In this article, we aim to resolve these difficulties, by providing an exact (albeit conservative) method that is valid under heterogeneity. We also provide a measure of the degree of conservatism, that indicates the approximate extent of the excess coverage. Applied to the Avandia data, we find support for Nissen and Wolski 2007's original results. Given that our method does not require strong assumptions or large cell counts, and provides intervals around the well‐known conditional maximum likelihood estimate, we anticipate that it could be an attractive default method for meta‐analysis of tables featuring rare events.