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Biometrika 1983 70(2):519-522; doi:10.1093/biomet/70.2.519
© 1983 by Biometrika Trust
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MISCELLANEA

On the asymptotic inefficiency of certain noniterative estimators of a common relative risk or odds ratio

ROBERT E. TARONE, JOHN J. GART and WALTER W. HAUCK

Biometry Branch, National Cancer Institute Bethesda, Maryland, U.S.A
Northwestern University Cancer Center Chicago, Illinois, U.S.A

Nurminen (1981) gives conditions for the asymptotic efficiency of general weighted mean estimators. His application is a noniterative estimator of a common relative risk for binomial variates. This summary estimator and, by implication, the Mantel-Haenszel summary odds ratio estimator are asserted to be asymptotically efficient. We examine conditions for the asymptotic efficiency in the unconditional sample space of the Mantel Haenszel estimator for a common odds ratio, the estimator of a common relative risk considered by Nurminen, and Tarone's (1981) estimator of a common relative risk for binomial variables. Contrary to Nurminen, we find that, except for a few degenerate cases, these estimators are inefficient whenever the common odds ratio or common relative risk is not equal to 1.

Key Words: Asymptotic efficiency • Combination of 2 × 2 tables • Odds ratio • Relative risk


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[Abstract] [PDF]


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