Estimators of the Variance of the Mantel-Haenszel Log-Odds-Ratio Estimate

A new approach to large-sample studies of the variance of the log-odds- ratio estimate of \textit{N. Mantel} and \textit{W. Haenszel} [J. Nat. Cancer Inst. 22, 719-748 (1959)] is developed and used to derive formulas that lead to useful standard error formulas for the Mantel-Haenszel estimate. The variance estimator of \textit{J. Robins}, \textit{N. E. Breslow}, and \textit{S. Greenland} [Biometrics 42, 311-323 (1986; Zbl 0619.62035)] is derived in a new way and a new variance estimator valid only for the case of (1,M)-matching is also derived using the new approach.

Keywords

Contingency tables, standard error formulas, Applications of statistics to biology and medical sciences; meta analysis, combination of two by two tables, matched pairs, variance estimator, large-sample studies, variance of the log-odds-ratio estimate, Mantel-Haenszel estimate, noncentral hypergeometric distribution

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