A proportional hazards model for the subdistribution of a competing risk

FINE, JP and RJ GRAY. A proportional hazards model for the subdistribution of a competing risk. Journal of the American Statistical Association. Alexandria: Amer Statistical Assoc, 1999, vol. 94, No 446, p. 496-509. ISSN 0162-1459. Available from: https://dx.doi.org/10.2307/2670170.

Basic information

• Original name: A proportional hazards model for the subdistribution of a competing risk
• Authors: FINE, JP and RJ GRAY.
• Edition: Journal of the American Statistical Association, Alexandria, Amer Statistical Assoc, 1999, 0162-1459.

Other information

• Original language: English
• Type of outcome: Article in a journal
• Confidentiality degree: is not subject to a state or trade secret
• Impact factor: Impact factor: 1.754
• Doi: http://dx.doi.org/10.2307/2670170
• UT WoS: 000081058500019
• Keywords in English: hazard of subdistribution; martingale; partial likelihood; transformation model

Abstract

With explanatory covariates, the standard analysis for competing risks data involves modeling the cause-specific hazard functions via a proportional hazards assumption. Unfortunately, the cause-specific hazard function does not have a direct interpretation in terms of survival probabilities for the particular failure type. In recent years many clinicians have begun using the cumulative incidence function, the marginal failure probabilities for a particular cause, which is intuitively appealing and more easily explained to the nonstatistician. The cumulative incidence is especially relevant in cost-effectiveness analyses in which the survival probabilities are needed to determine treatment utility. Previously, authors have considered methods for combining estimates of the cause-specific hazard functions under the proportional hazards formulation. However, these methods do not allow the analyst to directly assess the effect of a covariate on the marginal probability function. In this article we propose a novel semiparametric proportional hazards model for the subdistribution. Using the partial likelihood principle and weighting techniques, we derive estimation and inference procedures for the finite-dimensional regression parameter under a variety of censoring scenarios. We give a uniformly consistent estimator for the predicted cumulative incidence for an individual with certain covariates; confidence intervals and bands can be obtained analytically or with an easy-to-implement simulation technique. To contrast the two approaches, we analyze a dataset from a breast cancer clinical trial under both models.