A Predictive Time-to-Event Modeling Approach with Longitudinal Measurements and Missing Data

Abstract

An important practical problem in the survival analysis is predicting the time to a future event such as the death or failure of a subject. It is of great importance for the medical decision making to investigate how the predictor variables including repeated measurements of the same subjects are affecting the future time-to-event. Such a prediction problem is particularly more challenging due to the fact that the future values of predictor variables are unknown, and they may vary dynamically over time. In this dissertation, we consider a predictive approach based on modeling the forward intensity function. To handle the practical difficulty due to missing data in longitudinal measurements, and to accommodate observations at irregularly spaced time points, we propose a smoothed composite likelihood approach for estimations. The forward intensity function approach intrinsically incorporates the future dynamics in the predictor variables that affect the stochastic occurrence of the future event. Thus the proposed framework is advantageous and parsimonious from requiring no separated modeling step for the stochastic mechanism of the predictor variables. Our theoretical analysis establishes the validity of the forward intensity modeling approach and the smoothed composite likelihood method. To model the parameters as continuous functions of time, we introduce the penalized B-spline method into the proposed approach. Extensive simulations and real-data analyses demonstrate the promising performance of the proposed predictive approach.