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....
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Public Library of Science (PLoS)
2013-01-01
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| Series: | PLoS ONE |
| Online Access: | http://europepmc.org/articles/PMC3596394?pdf=render |
| _version_ | 1819146185812738048 |
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| author | Vaclav Fidler Nico Nagelkerke |
| author_facet | Vaclav Fidler Nico Nagelkerke |
| author_sort | Vaclav Fidler |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-12-22T13:09:55Z |
| format | Article |
| id | doaj.art-69b9693bc42648208fc9265f41986b26 |
| institution | Directory Open Access Journal |
| issn | 1932-6203 |
| language | English |
| last_indexed | 2024-12-22T13:09:55Z |
| publishDate | 2013-01-01 |
| publisher | Public Library of Science (PLoS) |
| record_format | Article |
| series | PLoS ONE |
| spelling | doaj.art-69b9693bc42648208fc9265f41986b262022-12-21T18:24:47ZengPublic Library of Science (PLoS)PLoS ONE1932-62032013-01-0183e5832710.1371/journal.pone.0058327The Mantel-Haenszel procedure revisited: models and generalizations.Vaclav FidlerNico NagelkerkeSeveral 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.http://europepmc.org/articles/PMC3596394?pdf=render |
| spellingShingle | Vaclav Fidler Nico Nagelkerke The Mantel-Haenszel procedure revisited: models and generalizations. PLoS ONE |
| 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 |
| url | http://europepmc.org/articles/PMC3596394?pdf=render |
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