Recurrent Marker Processes in the Presence of Competing Terminal Events
Yifei Sun, Johns Hopkins University
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 talk, 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 medical 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 analyzing recurrent marker process. 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 ignoring the failure type. The large sample properties and optimality of the second estimator is established. An application to the SEER-Medicare linked data is presented to illustrate the proposed methods.