Weighted composite time to event endpoints with recurrent events: comparison of three analytical approaches

In clinical trials the study interest often lies in the comparison of a treatment to a control regarding a time to event endpoint. A composite endpoint allows to consider several time to event endpoints at once. Usually, only the time to the first occurring event for a patient is thereby analyzed. However, an individual may experience more than one non-fatal event. Including all observed events in the analysis can increase the power and provides a more complete picture of the disease. Thus, analytical methods for recurrent events are required. A challenge is that the different event types belonging to the composite often are of different clinical relevance. In this case, weighting the event types according to their clinical relevance is an option. Different weight-based methods for composite time to event endpoints were proposed. So far, there exists no systematic comparison of these methods.

Within this work we provide a systematic comparison of three methods proposed for weighted composite endpoints in a recurrent event setting combining non-fatal and fatal events of different clinical relevance. We consider an extension of an approach proposed by Wei and Lachin, an approach by Rauch et al., and an approach by Bakal et al.. Comparison is done based on a simulation study and based on a clinical study example.

For all three approaches closed formula test statistics are available. The Wei-Lachin approach and the approach by Rauch et al. show similar results in mean squared error. For the approach by Wei and Lachin confidence intervals are provided. The approach by Bakal et al. is not related to a quantifiable estimand. The relevance weights of the different approaches work on different level, i.e. either on cause-specific hazard ratios or on event count.

The provided comparison and simulations can help to guide applied researchers to choose an adequate method for the analysis of composite endpoints combining (recurrent) events of different clinical relevance. The approach by Wei and Lachin and Rauch et al. can be recommended in scenarios where the composite effect is time-independent. The approach by Bakal et al. should be applied carefully.