On hazard ratio estimators by proportional hazards models in matchedpair cohort studies
Abstract Background In matchedpair cohort studies with censored events, the hazard ratio (HR) may be of main interest. However, it is lesser known in epidemiologic literature that the partial maximum likelihood estimator of a common HR conditional on matched pairs is written in a simple form, namel...
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20170601

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doaja68d806182db43e99eff215196daa17520201124T21:59:47ZengBMCEmerging Themes in Epidemiology174276222017060114111410.1186/s1298201700608On hazard ratio estimators by proportional hazards models in matchedpair cohort studiesTomohiro Shinozaki0Mohammad Ali Mansournia1Yutaka Matsuyama2Department of Biostatistics, School of Public Health, the University of TokyoDepartment of Epidemiology and Biostatistics, School of Public Health, Tehran University of Medical SciencesDepartment of Biostatistics, School of Public Health, the University of TokyoAbstract Background In matchedpair cohort studies with censored events, the hazard ratio (HR) may be of main interest. However, it is lesser known in epidemiologic literature that the partial maximum likelihood estimator of a common HR conditional on matched pairs is written in a simple form, namely, the ratio of the numbers of two pairtypes. Moreover, because HR is a noncollapsible measure and its constancy across matched pairs is a restrictive assumption, marginal HR as “average” HR may be targeted more than conditional HR in analysis. Methods Based on its simple expression, we provided an alternative interpretation of the common HR estimator as the odds of the matchedpair analog of Cstatistic for censored timetoevent data. Through simulations assuming proportional hazards within matched pairs, the influence of various censoring patterns on the marginal and common HR estimators of unstratified and stratified proportional hazards models, respectively, was evaluated. The methods were applied to a real propensityscore matched dataset from the Rotterdam tumor bank of primary breast cancer. Results We showed that stratified models unbiasedly estimated a common HR under the proportional hazards within matched pairs. However, the marginal HR estimator with robust variance estimator lacks interpretation as an “average” marginal HR even if censoring is unconditionally independent to event, unless no censoring occurs or no exposure effect is present. Furthermore, the exposuredependent censoring biased the marginal HR estimator away from both conditional HR and an “average” marginal HR irrespective of whether exposure effect is present. From the matched Rotterdam dataset, we estimated HR for relapsefree survival of absence versus presence of chemotherapy; estimates (95% confidence interval) were 1.47 (1.18–1.83) for common HR and 1.33 (1.13–1.57) for marginal HR. Conclusion The simple expression of the common HR estimator would be a useful summary of exposure effect, which is less sensitive to censoring patterns than the marginal HR estimator. The common and the marginal HR estimators, both relying on distinct assumptions and interpretations, are complementary alternatives for each other.http://link.springer.com/article/10.1186/s1298201700608CollapsibilityCstatisticHazard ratioMatchingProportional hazards model 
collection 
DOAJ 
language 
English 
format 
Article 
sources 
DOAJ 
author 
Tomohiro Shinozaki Mohammad Ali Mansournia Yutaka Matsuyama 
spellingShingle 
Tomohiro Shinozaki Mohammad Ali Mansournia Yutaka Matsuyama On hazard ratio estimators by proportional hazards models in matchedpair cohort studies Emerging Themes in Epidemiology Collapsibility Cstatistic Hazard ratio Matching Proportional hazards model 
author_facet 
Tomohiro Shinozaki Mohammad Ali Mansournia Yutaka Matsuyama 
author_sort 
Tomohiro Shinozaki 
title 
On hazard ratio estimators by proportional hazards models in matchedpair cohort studies 
title_short 
On hazard ratio estimators by proportional hazards models in matchedpair cohort studies 
title_full 
On hazard ratio estimators by proportional hazards models in matchedpair cohort studies 
title_fullStr 
On hazard ratio estimators by proportional hazards models in matchedpair cohort studies 
title_full_unstemmed 
On hazard ratio estimators by proportional hazards models in matchedpair cohort studies 
title_sort 
on hazard ratio estimators by proportional hazards models in matchedpair cohort studies 
publisher 
BMC 
series 
Emerging Themes in Epidemiology 
issn 
17427622 
publishDate 
20170601 
description 
Abstract Background In matchedpair cohort studies with censored events, the hazard ratio (HR) may be of main interest. However, it is lesser known in epidemiologic literature that the partial maximum likelihood estimator of a common HR conditional on matched pairs is written in a simple form, namely, the ratio of the numbers of two pairtypes. Moreover, because HR is a noncollapsible measure and its constancy across matched pairs is a restrictive assumption, marginal HR as “average” HR may be targeted more than conditional HR in analysis. Methods Based on its simple expression, we provided an alternative interpretation of the common HR estimator as the odds of the matchedpair analog of Cstatistic for censored timetoevent data. Through simulations assuming proportional hazards within matched pairs, the influence of various censoring patterns on the marginal and common HR estimators of unstratified and stratified proportional hazards models, respectively, was evaluated. The methods were applied to a real propensityscore matched dataset from the Rotterdam tumor bank of primary breast cancer. Results We showed that stratified models unbiasedly estimated a common HR under the proportional hazards within matched pairs. However, the marginal HR estimator with robust variance estimator lacks interpretation as an “average” marginal HR even if censoring is unconditionally independent to event, unless no censoring occurs or no exposure effect is present. Furthermore, the exposuredependent censoring biased the marginal HR estimator away from both conditional HR and an “average” marginal HR irrespective of whether exposure effect is present. From the matched Rotterdam dataset, we estimated HR for relapsefree survival of absence versus presence of chemotherapy; estimates (95% confidence interval) were 1.47 (1.18–1.83) for common HR and 1.33 (1.13–1.57) for marginal HR. Conclusion The simple expression of the common HR estimator would be a useful summary of exposure effect, which is less sensitive to censoring patterns than the marginal HR estimator. The common and the marginal HR estimators, both relying on distinct assumptions and interpretations, are complementary alternatives for each other. 
topic 
Collapsibility Cstatistic Hazard ratio Matching Proportional hazards model 
url 
http://link.springer.com/article/10.1186/s1298201700608 
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AT tomohiroshinozaki onhazardratioestimatorsbyproportionalhazardsmodelsinmatchedpaircohortstudies AT mohammadalimansournia onhazardratioestimatorsbyproportionalhazardsmodelsinmatchedpaircohortstudies AT yutakamatsuyama onhazardratioestimatorsbyproportionalhazardsmodelsinmatchedpaircohortstudies 
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