BIAS-CORRECTED MAXIMUM-LIKELIHOOD ESTIMATOR OF A LOG COMMON ODDS RATIO

A bias-correction factor for the maximum likelihood estimator of the l og common odds ratio for sparse data is derived, which is applicable w hen the design is balanced and/or when the number of strata is large. The corrected maximum likelihood estimator is practically unbiased and its mean squared error is smaller than that of the uncorrected maximu m likelihood estimator. The correction factor for the maximum likeliho od estimator approaches one as strata sizes increase. Examples demonst rate that the corrected maximum likelihood estimator and the exact con ditional maximum likelihood estimator are essentially identical althou gh the standard error of the former tends to be slightly smaller than that of the latter. It is also demonstrated that a simple version of t he correction factor is a satisfactory approximation. The bias-correct ed maximum likelihood estimator proposed in this paper is the extensio n of Breslow's (1981) and it can be useful particularly when the compu tational burden of the exact conditional method is excessive.