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Biostatistics Advance Access originally published online on April 22, 2008
Biostatistics 2008 9(4):765-776; doi:10.1093/biostatistics/kxn009
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© The Author 2008. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org.

Time-dependent covariates in the proportional subdistribution hazards model for competing risks

Jan Beyersmann*

Freiburg Centre for Data Analysis and Modelling, University of Freiburg, Freiburg, Germany and Institute of Medical Biometry and Medical Informatics, University Medical Centre Freiburg, Freiburg, D-79104, Germany
jan{at}fdm.uni-freiburg.de

Martin Schumacher

Institute of Medical Biometry and Medical Informatics, University Medical Centre Freiburg, Freiburg, D-79104, Germany

* To whom correspondence should be addressed

Separate Cox analyses of all cause-specific hazards are the standard technique of choice to study the effect of a covariate in competing risks, but a synopsis of these results in terms of cumulative event probabilities is challenging. This difficulty has led to the development of the proportional subdistribution hazards model. If the covariate is known at baseline, the model allows for a summarizing assessment in terms of the cumulative incidence function. black Mathematically, the model also allows for including random time-dependent covariates, but practical implementation has remained unclear due to a certain risk set peculiarity. We use the intimate relationship of discrete covariates and multistate models to naturally treat time-dependent covariates within the subdistribution hazards framework. The methodology then straightforwardly translates to real-valued time-dependent covariates. As with classical survival analysis, including time-dependent covariates does not result in a model for probability functions anymore. Nevertheless, the proposed methodology provides a useful synthesis of separate cause-specific hazards analyses. We illustrate this with hospital infection data, where time-dependent covariates and competing risks are essential to the subject research question.

Keywords: Fine and Gray model; Hospital infection; Multistate model

Received June 15, 2007; revised February 26, 2008; accepted for publication March 21, 2008.


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H. Binder, A. Allignol, M. Schumacher, and J. Beyersmann
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Bioinformatics, April 1, 2009; 25(7): 890 - 896.
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