Nonparametric Benefit–Risk Assessment Using Marker Process in the Presence of a Terminal Event

Benefit–risk assessment is a crucial step in medical decision process. In many biomedical studies, both longitudinal marker measurements and time to a terminal event serve as important endpoints for benefit–risk assessment. The effect of an intervention or a treatment on the longitudinal marker process, however, can be in conflict with its effect on the time to the terminal event. Thus, questions arise on how to evaluate treatment effects based on the two endpoints, for the purpose of deciding on which treatment is most likely to benefit the patients. In this article, we present a unified framework for benefit–risk assessment using the observed longitudinal markers and time to event data. We propose a cumulative weighted marker process to synthesize information from the two endpoints, and use its mean function at a prespecified time point as a benefit–risk summary measure. We consider nonparametric estimation of the summary measure under two scenarios: (i) the longitudinal marker is measured intermittently during the study period, and (ii) the value of the longitudinal marker is observed throughout the entire follow-up period. The large-sample properties of the estimators are derived and compared. Simulation studies and data examples exhibit that the proposed methods are easy to implement and reliable for practical use. Supplemental materials for this article are available online.