The Asymptotic Relative Efficiency of the Mantel-Haenszel Estimator in the Increasing-Number-of-Strata Case

The asymptotic relative efficiency (ARE) of the Mantel-Haenszel estimator of a common odds ratio, At, is determined for the case in which the number of strata increases indefinitely for fixed withinstratum sample sizes. The ARE remains above 90% over a very wide range of cases and above 93% for .2 < A < 5. These results support consideration of the relatively easily calculated Mantel-Haenszel estimator rather than the conditional maximum likelihood estimator in these increasing-strata cases.