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Biostatistics Advance Access published online on April 24, 2006
Biostatistics, doi:10.1093/biostatistics/kxj040
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© The Author 2006. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org
Received January 12, 2006
Revised April 19, 2006
Accepted April 21, 2006

Article

Parametric regression on cumulative incidence function

Jong-Hyeon Jeong 1 * and Jason P. Fine 2

1 Department of Biostatistics, University of Pittsburgh, Pittsburgh, PA 15261, USA
2 Department of Statistics and Department of Biostatistics & Medical Informatics, University of Wisconsin, Madison, WI 53706, USA

* To whom correspondence should be addressed.
Jong-Hyeon Jeong, E-mail: jeong{at}nsabp.pitt.edu


  Abstract

We propose parametric regression analysis of cumulative incidence function with competing risks data. A simple form of Gompertz distribution is used for the improper baseline subdistribution of the event of interest. Maximum likelihood inference on regression parameters and associated cumulative incidence function is developed for parametric models, including a flexible generalized odds rate model. Estimation of the long term proportion of patients with cause-specific events is straightforward in the parametric setting. Simple goodness-of-fit tests are discussed for evaluating a fixed odds rate assumption. The parametric regression methods are compared with an existing semiparametric regression analysis on a breast cancer dataset where the cumulative incidence of recurrence is of interest. The results demonstrate that the likelihood based parametric analyses for the cumulative incidence function are a practically useful alternative to the semiparametric analyses.

Keywords: Breast cancer; Clinical trial; Competing risks; Cumulative incidence; Cure model; Improper distribution; Regression; Transformation model.
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