Odds ratio estimators when the data are sparse

Abstract

The properties of four commonly used estimators of the odds ratio are studied under a large-sample scheme in which the number of 2 × 2 tables increases but the possible marginal configurations remain fixed. Neither the unconditional maximum likelihood nor the empirical logit estimators converge to the true odds ratio; their asymptotic bias is computed for certain special cases of interest. The conditional maximum likelihood and Mantel-Haenszel estimators, which are consistent, have asymptotic variances whose ratio tends to one under the null hypothesis. Even for moderately large odds ratios the simple Mantel-Haenszel estimator maintains remarkably good efficiency.