Modeling the subdistribution of a competing risk

Competing risk failure time data occur frequently in medical studies, and a number of methods have been proposed for the analysis of these data. To assess covariate effects, a standard approach is to model the cause-specific hazard functions of different failure types. Recently, Fine and Gray (1999) proposed directly modeling the subdistribution of a competing risk with a Cox type model. In this paper, we consider a more flexible and general hazard model for the subdistribution. It is a combination of the additive model and the Cox model and allows one to perform a more detailed study of covariate effects. Inference procedures are developed for estimation of both parametric and nonparametric components of the model, and the asymptotic properties of the proposed estimators are established. Robust variance estimates along with some goodness-of-fit test procedures are also presented, and the prediction of the cumulative incidence function is discussed. The proposed methodology is applied to a set of competing risk data from a bone marrow transplant study.