Joint modeling of longitudinal, recurrent events and failure time data for survivor's population

Recurrent events together with longitudinal measurements are commonly observed in follow‐up studies where the observation is terminated by censoring or a primary failure event. In this article, we developed a joint model where the dependence of longitudinal measurements, recurrent event process and time to failure event is modeled through rescaling the time index. The general idea is that the trajectories of all biology processes of subjects in the survivors’ population are elongated or shortened by the rate identified from a model for the failure event. To avoid making disputing assumptions on recurrent events or biomarkers after the failure event (such as death), the model is constructed on the basis of survivors’ population. The model also possesses a specific feature that, by aligning failure events as time origins, the backward‐in‐time model of recurrent events and longitudinal measurements shares the same parameter values with the forward time model. The statistical properties, simulation studies and real data examples are conducted. The proposed method can be generalized to analyze left‐truncated data.