Alternative Estimators of The Odds Ratio
The sample odds ratio n11n00 / n10n01 is easy to calculate, and for moderate and large samples performs well as an estimator of the population odds ratio. When one or more of the cells in the contingency table can have a small value, the sample odds ratio can be biased and exhibit high variance. A number of alternative estimators of the odds ratio have been proposed to address this issue. One alternative estimator is the conditional maximum likelihood estimator, which conditions on the row and column margins when forming the likelihood to maximize (as in Fisher's exact test). Another alternative estimator is the Mantel-Haenszel estimator.
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