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Epidemiologic Methods

Edited by faculty of the Harvard School of Public Health

Ed. by Tchetgen Tchetgen, Eric J / VanderWeele, Tyler J. / Daniel, Rhian

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2161-962X
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A Note on the Mantel-Haenszel Estimators When the Common Effect Assumptions Are Violated

Hisashi NomaORCID iD: http://orcid.org/0000-0002-2520-9949 / Kengo NagashimaORCID iD: http://orcid.org/0000-0003-4529-9045
Published Online: 2016-05-06 | DOI: https://doi.org/10.1515/em-2015-0004

Abstract

The Mantel-Haenszel estimators for the common effect parameters of stratified 2×2 tables have been widely adopted in epidemiological and clinical studies for controlling the effects of confounding factors. Although the Mantel-Haenszel estimators are simple and effective estimating methods, the correctness of the common effect assumptions cannot be justified in general practices. Also then, the targeted “common effect parameters” do not exist. Under these settings, even if the Mantel-Haenszel estimators have desirable properties, it is quite uncertain what they estimate and how the estimates are interpreted. In this article, we conducted theoretical evaluations for their asymptotic behaviors when the common effect assumptions are violated. We explicitly showed that the Mantel-Haenszel estimators converge to weighted averages of stratum-specific effect parameters and they can be interpreted as intuitive summaries of the stratum-specific effect measures. Also, the Mantel-Haenszel estimators correspond to the standardized effect measures on standard distributions of stratification variables to be the total cohort, approximately. In addition, the ordinary sandwich-type variance estimators are still valid for quantifying variabilities of the Mantel-Haenszel estimators. We implemented numerical studies based on two epidemiologic studies of breast cancer and schizophrenia for evaluating empirical properties of these estimators, and confirmed general validities of these theoretical results.

Keywords: stratified analysis; Mantel-Haenszel estimators; common effect parameters; standardization; model misspecification

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About the article

Published Online: 2016-05-06

Published in Print: 2016-12-01


Funding: This work was supported by Grant-in-Aid for Scientific Research from the Ministry of Education, Culture, Sports, Science and Technology of Japan (Grant numbers: 25280008, 15K15954).


Citation Information: Epidemiologic Methods, ISSN (Online) 2161-962X, ISSN (Print) 2194-9263, DOI: https://doi.org/10.1515/em-2015-0004.

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