Pseudotable methods for the analysis of 2 x 2 tables

Abstract Epidemiologists often use the log odds ratio regression model to analyze sets of 2 × 2 tables. The estimation of a common odds ratio is based on this model. The classical estimation procedures for this problem are maximum likelihood, conditional maximum likelihood, and Mantel-Haenszel estimation. This paper proposes new estimators which augment the data by pseudotables of a particular form to reduce the bias and mean squared error of the estimation. The estimators can be motivated by Bayes and empirical Bayes methodology or as penalized likelihood estimators. A simulation study demonstrates that the proposed estimators have improved operating characteristics over large portions of the parameter space compared to the classical estimators. Applications are given to estimating the common odds ration of tumor in two examples, one involving “large strata” and one involving “sparse strata”.

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