Semiparametric Regression Analysis of Recurrent Gap Times in the Presence of Competing Risks

Abstract

When a disease progression is assumed to go through several stages marked by a nonterminal, recurrent event such as relapse, or a terminal event such as death, whose occurrence terminates the progression, researchers might be concerned with the duration or gap times between successive events (stages) and would like to study the covariates effects on the gap times. In addition, how the previous event or gap times affect the current gap time may be also of interest. We propose a unifying framework for joint regression analysis of gap times between successive events. The proposed mixture modelling framework consists of a logistic regression for predicting the path of transition (to a nonterminal or terminal event) at each stage, and proportional hazards models for predicting the gap times for transition to the nonterminal and terminal events at each stage, and both the two components of models are conditional on the past event history and stage-specific covariates. As special cases, when the number of stages is fixed at one or two, the proposed framework can be applied to analysis of conventional competing risks or semicompeting risks data. We develop semiparametric maximum likelihood inference procedure for the proposed models, where the score functions are explicitly expressed as martingales, and hence the large sample theory follows directly from martingale theory. Explicit expressions for the information matrix are also derived, which facilitate direct variance estimation and convenient computation. Simulation results reveal the nice performance, and applications to two clinical studies illustrate the real utilities of the proposed model. This is the joint work with Yi-Hau Chen and Ya-Wen Chuang. Key words: Competing risks, Martingale processes, Mixture model, Multiple events, Recurrent data.