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The Mantel-Haenszel Procedure Revisited: Models and Generalizations

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  • Vaclav Fidler
  • Nico Nagelkerke

Abstract

Several statistical methods have been developed for adjusting the Odds Ratio of the relation between two dichotomous variables X and Y for some confounders Z. With the exception of the Mantel-Haenszel method, commonly used methods, notably binary logistic regression, are not symmetrical in X and Y. The classical Mantel-Haenszel method however only works for confounders with a limited number of discrete strata, which limits its utility, and appears to have no basis in statistical models. Here we revisit the Mantel-Haenszel method and propose an extension to continuous and vector valued Z. The idea is to replace the observed cell entries in strata of the Mantel-Haenszel procedure by subject specific classification probabilities for the four possible values of (X,Y) predicted by a suitable statistical model. For situations where X and Y can be treated symmetrically we propose and explore the multinomial logistic model. Under the homogeneity hypothesis, which states that the odds ratio does not depend on Z, the logarithm of the odds ratio estimator can be expressed as a simple linear combination of three parameters of this model. Methods for testing the homogeneity hypothesis are proposed. The relationship between this method and binary logistic regression is explored. A numerical example using survey data is presented.

Suggested Citation

  • Vaclav Fidler & Nico Nagelkerke, 2013. "The Mantel-Haenszel Procedure Revisited: Models and Generalizations," PLOS ONE, Public Library of Science, vol. 8(3), pages 1-4, March.
    • Handle: RePEc:plo:pone00:0058327
    DOI: 10.1371/journal.pone.0058327
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    References listed on IDEAS

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    1. S. le Cessie & J. C. van Houwelingen, 1994. "Logistic Regression for Correlated Binary Data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 43(1), pages 95-108, March.
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    1. Dwivedi Alok Kumar & Mallawaarachchi Indika & Figueroa-Casas Juan B. & Morales Angel M. & Tarwater Patrick, 2015. "Multinomial Logistic Regression Approach for the Evaluation of Binary Diagnostic Test in Medical Research," Statistics in Transition New Series, Statistics Poland, vol. 16(2), pages 203-222, June.
    2. Angel M. Morales & Patrick Tarwater & Indika Mallawaarachchi & Alok Kumar Dwivedi & Juan B. Figueroa-Casas, 2015. "Multinomial logistic regression approach for the evaluation of binary diagnostic test in medical research," Statistics in Transition new series, Główny Urząd Statystyczny (Polska), vol. 16(2), pages 203-222, June.
    3. Alok Kumar Dwivedi & Indika Mallawaarachchi & Juan B. Figueroa-Casas & Angel M. Morales & Patrick Tarwater, 2015. "Multinomial Logistic Regression Approach For The Evaluation Of Binary Diagnostic Test In Medical Research," Statistics in Transition New Series, Polish Statistical Association, vol. 16(2), pages 203-222, June.

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