Approximately Exact Inference for the Common Odds Ratio in Several 2 × 2 Tables

Abstract The conditional maximum likelihood estimator (MLE) of the common odds ratio in a sequence of independent 2 × 2 tables is known to be superior to the Mantel–Haenszel estimator in terms of asymptotic efficiency and has the further advantage that its exact distribution is known. However, a long-standing barrier to the widespread use of this estimator has been computational intractability; in particular, the calculation of significance levels, confidence sets, and power based on the exact distribution requires fast and efficient algorithms. An important class of such algorithms form the basis of StatXact, a software package able to solve various aspects of the exact inference problem for a sequence of several 2 × 2 tables in real time. We provide an alternative methodology by developing several useful saddlepoint approximations to the exact distribution of the conditional MLE. The approximations are derived from an interesting representation for hypergeometric random variables as a sum of independent...

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