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American Journal of Epidemiology Advance Access originally published online on June 3, 2009
American Journal of Epidemiology 2009 170(2):244-256; doi:10.1093/aje/kwp107
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American Journal of Epidemiology © The Author 2009. Published by the Johns Hopkins Bloomberg School of Public Health. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org.

PRACTICE OF EPIDEMIOLOGY

Competing Risk Regression Models for Epidemiologic Data

Bryan Lau, Stephen R. Cole and Stephen J. Gange

Correspondence to Dr. Bryan Lau, Department of Medicine, Johns Hopkins School of Medicine, 1830 East Monument Street, Room 8070, Baltimore, MD 21287 (e-mail: blau1{at}jhmi.edu).

Received for publication August 2, 2008. Accepted for publication April 6, 2009.

Competing events can preclude the event of interest from occurring in epidemiologic data and can be analyzed by using extensions of survival analysis methods. In this paper, the authors outline 3 regression approaches for estimating 2 key quantities in competing risks analysis: the cause-specific relative hazard (csRH) and the subdistribution relative hazard (sdRH). They compare and contrast the structure of the risk sets and the interpretation of parameters obtained with these methods. They also demonstrate the use of these methods with data from the Women's Interagency HIV Study established in 1993, treating time to initiation of highly active antiretroviral therapy or to clinical disease progression as competing events. In our example, women with an injection drug use history were less likely than those without a history of injection drug use to initiate therapy prior to progression to acquired immunodeficiency syndrome or death by both measures of association (csRH = 0.67, 95% confidence interval: 0.57, 0.80 and sdRH = 0.60, 95% confidence interval: 0.50, 0.71). Moreover, the relative hazards for disease progression prior to treatment were elevated (csRH = 1.71, 95% confidence interval: 1.37, 2.13 and sdRH = 2.01, 95% confidence interval: 1.62, 2.51). Methods for competing risks should be used by epidemiologists, with the choice of method guided by the scientific question.

competing risks; epidemiologic methods; mixture model; proportional hazards; regression; survival analysis

Abbreviations: AIDS, acquired immunodeficiency syndrome; CIF, cumulative incidence function; csCIF, cause-specific cumulative incidence function; csRH, cause-specific relative hazard; HIV, human immunodeficiency virus; sdCIF, subdistribution cumulative incidence function; sdRH, subdistribution relative hazard; WIHS, Women's Interagency HIV Study


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