Semiparametric regression methods for temporal processes subject to multiple sources of censoring

Process regression methodology is underdeveloped relative to the frequency with which pertinent data arise. In this article, the response is a binary indicator process representing the joint event of being alive and remaining in a specific state. The process is indexed by time (e.g., time since diagnosis) and observed continuously. Data of this sort occur frequently in the study of chronic disease. A general area of application involves a recurrent event with non-negligible duration (e.g., hospitalization and associated length of hospital stay) and subject to a terminating event (e.g., death). We propose a semiparametric multiplicative model for the process version of the probability of being alive and in the (transient) state of interest. Under the proposed methods, the regression parameter is estimated through a procedure that does not require estimating the baseline probability. Unlike the majority of process regression methods, the proposed methods accommodate multiple sources of censoring. In particular, we derive a computationally convenient variant of inverse probability of censoring weighting based on the additive hazards model. We show that the regression parameter estimator is asymptotically normal, and that the baseline probability function estimator converges to a Gaussian process. Simulations demonstrate that our estimators have good finite sample performance. We apply our method to national end-stage liver disease data.