Methods of estimation in log odds ratio regression models.

McCullagh's (1984, Journal of the Royal Statistical Society, Series B 46, 250-256) approximation to the conditional maximum likelihood estimator in log odds ratio regression models is shown to have negligible asymptotic bias unless the odds ratios are large and the sample sizes in individual 2 X 2 tables are very small. In application to two sets of case-control data, it yields results virtually indistinguishable from those of the conditional analysis. A generalization of the Mantel-Haenszel estimator proposed by Davis (1985, Biometrics 41, 487-495) does not approximate the conditional results nearly as well.