Use of the Wei-Lin-Weissfeld method for the analysis of a recurring and a terminating event

We consider application of the Wei-Lin-Weissfeld (WLW) method for multiple failure time data when analysing a disease process consisting of a recurring outcome, such as clinical progression, and a terminating outcome, such as death. In order to adapt WLW for this situation, 'events' must be specified that define multiple failure times and whether these are censored. Various choices of events are possible, and each corresponds to inferences about a different aspect of the underlying disease process. Definitions which regard the terminating outcome as a censor of the recurring outcome focus on specific cause-specific hazard functions, while event definitions which make no distinction between a recurring and terminating outcome focus on hazard functions of the induced failure times. Some event definitions require strong statistical assumptions to yield valid inferences and are not recommended. The application of WLW for recurring/terminating processes is illustrated with the results of two recently conducted clinical trials in persons with HIV.