Statistica Sinica 27 (2017), 1059-1077
Abstract: When a disease progression goes through several stages marked by a nonterminal, recurrent event such as relapse, or a terminal event such as death, which terminates the progression, researchers can be concerned with the duration or gap times between successive events (stages) and wish to study the covariates effects on the gap times. How previous events or gap times affect the current gap time can be also of interest. We propose a unifying framework for joint regression analysis of gap times between successive events. The proposed mixture modeling framework consists of a logistic regression for predicting the path of transition (to a nonterminal or terminal event) at each stage, and a proportional hazards model for predicting the gap times for transition to the nonterminal and terminal events at each stage; these components of the model are conditional on the past event history and stage-specific covariates. In particular, when the number of stages is fixed at one or two, the proposed framework can be applied to the analysis of conventional competing risks or semicompeting risks data. We develop a semiparametric maximum likelihood inference procedure for the proposed models. For which the large sample theory follows directly from martingale theory. Explicit expressions for the information matrix are derived, which facilitate direct variance estimation and convenient computation. Simulation results reveal the proposal's worth, and applications to two clinical studies illustrate its utility.
Key words and phrases: Competing risks, martingale processes, mixture model, multiple events, recurrent data.