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The Mantel-Haenszel Procedure Revisited: Models and Generalizations

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....

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Detalles Bibliográficos
Autores principales: Fidler, Vaclav, Nagelkerke, Nico
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Public Library of Science 2013
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3596394/
https://www.ncbi.nlm.nih.gov/pubmed/23516463
http://dx.doi.org/10.1371/journal.pone.0058327
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author Fidler, Vaclav
Nagelkerke, Nico
author_facet Fidler, Vaclav
Nagelkerke, Nico
author_sort Fidler, Vaclav
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description 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.
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spelling pubmed-35963942013-03-20 The Mantel-Haenszel Procedure Revisited: Models and Generalizations Fidler, Vaclav Nagelkerke, Nico PLoS One Research Article 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. Public Library of Science 2013-03-13 /pmc/articles/PMC3596394/ /pubmed/23516463 http://dx.doi.org/10.1371/journal.pone.0058327 Text en © 2013 Fidler and Nagelkerke http://creativecommons.org/licenses/by/4.0/ This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are properly credited.
spellingShingle Research Article
Fidler, Vaclav
Nagelkerke, Nico
The Mantel-Haenszel Procedure Revisited: Models and Generalizations
title The Mantel-Haenszel Procedure Revisited: Models and Generalizations
title_full The Mantel-Haenszel Procedure Revisited: Models and Generalizations
title_fullStr The Mantel-Haenszel Procedure Revisited: Models and Generalizations
title_full_unstemmed The Mantel-Haenszel Procedure Revisited: Models and Generalizations
title_short The Mantel-Haenszel Procedure Revisited: Models and Generalizations
title_sort mantel-haenszel procedure revisited: models and generalizations
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3596394/
https://www.ncbi.nlm.nih.gov/pubmed/23516463
http://dx.doi.org/10.1371/journal.pone.0058327
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