Analyzing semi-competing risks data with missing cause of informative terminal event.

Cancer studies frequently yield multiple event times that correspond to landmarks in disease progression, including non-terminal events (i.e., cancer recurrence) and an informative terminal event (i.e., cancer-related death). Hence, we often observe semi-competing risks data. Work on such data has focused on scenarios in which the cause of the terminal event is known. However, in some circumstances, the information on cause for patients who experience the terminal event is missing; consequently, we are not able to differentiate an informative terminal event from a non-informative terminal event. In this article, we propose a method to handle missing data regarding the cause of an informative terminal event when analyzing the semi-competing risks data. We first consider the nonparametric estimation of the survival function for the terminal event time given missing cause-of-failure data via the expectation-maximization algorithm. We then develop an estimation method for semi-competing risks data with missing cause of the terminal event, under a pre-specified semiparametric copula model. We conduct simulation studies to investigate the performance of the proposed method. We illustrate our methodology using data from a study of early-stage breast cancer.