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Biostatistics Advance Access published online on April 14, 2005
Biostatistics, doi:10.1093/biostatistics/kxi022
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© The Author 2005. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oupjournals.org.
Received February 3, 2004
Revised October 11, 2004
Accepted February 7, 2005

Article

Reduced Rank Proportional Hazards Model for Competing Risks

M. Fiocco 1*, H. Putter 1, and J.C. van Houwelingen 1

1 Department of Medical Statistics and Bioinformatics, Leiden University Medical Center, PO Box 9604, 2300 RC Leiden, The Netherlands

* To whom correspondence should be addressed.
M. Fiocco, E-mail: m.fiocco{at}lumc.nl


  Abstract

Competing events concerning individual subjects are of interest in many medical studies. For example, leukemia-free patients surviving a bone marrow transplant are at risk of developing acute or chronic graft-versus-host disease, or they might develop infections. In this situation competing risks models provide a natural framework to describe the disease. When incorporating covariates influencing the transition intensities, an obvious approach is to use Cox's proportional hazards model for each of the transitions separately. A practical problem then is how to deal with the abundance of regression parameters. Our objective is to describe the competing risks model in fewer parameters, both in order to avoid imprecise estimation in transitions with rare events and in order to facilitate interpretation of these estimates.

Suppose that the regression parameters are gathered into a pxK matrix B, with p and K the number of covariates and transitions respectively. We propose the use of reduced rank models, where B is required to be of lower rank R, smaller than both p and K. One way to achieve this is to write B = A{Gamma}{intcal} with A and {Gamma} matrices of dimensions p x R and K x R respectively.

We shall outline an algorithm to obtain estimates and their standard errors in a reduced rank proportional hazards model for competing risks and illustrate the approach on a competing risks model applied to 8966 leukemia patients from the European Group for Blood and Marrow Transplantation (EBMT).

Keywords: competing risks; survival analysis; reduced rank; prognostic factors; biplot.
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