Evaluating Utility Measurement From Recurrent Marker Processes in the Presence of Competing Terminal Events

In follow-up studies, utility marker measurements are usually collected upon the occurrence of recurrent events until a terminal event such as death takes place. In this article, we define the recurrent marker process to characterize utility accumulation over time. For example, with medical cost and repeated hospitalizations being treated as marker and recurrent events, respectively, the recurrent marker process is the trajectory of cumulative cost, which stops to increase after death. In many applications, competing risks arise as subjects are at risk of more than one mutually exclusive terminal event, such as death from different causes, and modeling the recurrent marker process for each failure type is often of interest. However, censoring creates challenges in the methodological development, because for censored subjects, both failure type and recurrent marker process after censoring are unobserved. To circumvent this problem, we propose a nonparametric framework for the recurrent marker process with competing terminal events. In the presence of competing risks, we start with an estimator by using marker information from uncensored subjects. As a result, the estimator can be inefficient under heavy censoring. To improve efficiency, we propose a second estimator by combining the first estimator with auxiliary information from the estimate under noncompeting risks model. The large sample properties and optimality of the second estimator are established. Simulation studies and an application to the SEER-Medicare linked data are presented to illustrate the proposed methods. Supplementary materials for this article are available online.