Analyzing Matched 2 × 2 Tables from all Corners

Abstract

Squared 2 × 2 tables with binary data from matched pairs are typically analyzed using Cochran-Mantel-Haenszel methodology, conditional logistic regression, or random intercepts logistic regression. These are all “pair-specific” type of approaches. However, many more methods and models for clustered binary data, including marginal models and marginalizable pair-specific models, can be applied. We provide a comprehensive overview of methods and apply them all to two well-known example datasets, the prime minister’s performance and the myocardial infarction datasets. The simple setting of matched binary data allows us to compare and relate different models, methods and their estimates. A technical explanation is given for why in some settings boundary estimates are obtained. Supplementary materials for this article are available online.

KEYWORDS:

• Bahadur model
• Binary clustered data
• Generalized estimating equations
• Likelihood
• Marginal model
• Matched pair
• Random effects

Supplementary Materials

Supplementary materials include: (A) a derivation of the point and variance estimators for GEE, prospective pairs, (B) a derivation of the point and variance estimators for GEE, retrospective pairs, (C) a derivation of the point estimators for BLR, retrospective pairs, (D) a figure of ${\widehat{\alpha }}_M$ and ${\widehat{\beta }}_M$ for which (9) holds, (E) SAS code for the reversed MP data.

Acknowledgments

We thank the American Public Health Association and Sheridan Content Solutions for the kind permission to reproduce Table 2 (MI data) from Table 3 in Coulehan et al. (1986). We also would like to thank the editor and referees for very helpful feedback and suggestions. Any remaining errors are the responsibility of the authors.

Disclosure Statement

This article did not receive specific funding, and the authors have no competing interests to declare.