Introducing a new estimator and test for the weighted all-cause hazard ratio

The rationale for the use of composite time-to-event endpoints is to increase the number of expected events and thereby the power by combining several event types of clinical interest. The all-cause hazard ratio is the standard effect measure for composite endpoints where the all-cause hazard function is given as the sum of the event-specific hazards. However, the effect of the individual components might differ, in magnitude or even in direction, which leads to interpretation difficulties. Moreover, the individual event types often are of different clinical relevance which further complicates interpretation. Our working group recently proposed a new weighted effect measure for composite endpoints called the ‘weighted all-cause hazard ratio’. By imposing relevance weights for the components, the interpretation of the composite effect becomes more ‘natural’. Although the weighted all-cause hazard ratio seems an elegant solution to overcome interpretation problems, the originally published approach has several shortcomings: First, the proposed point estimator requires pre-specification of a parametric survival model. Second, no closed formula for a corresponding test statistic was provided. Instead, a permutation test was proposed. Third, no clear guidance for the choice of the relevance weights was provided. In this work, we will overcome these problems.

Within this work a new non-parametric estimator and a related closed formula test statistic are presented. Performance of the new estimator and test is compared to the original ones by a Monte-Carlo simulation study.

The original parametric estimator is sensible to miss-specifications of the survival model. The new non-parametric estimator turns out to be very robust even if the required assumptions are not met. The new test shows considerably better power properties than the permutation test, is computationally much less expensive but might not preserve type one error in all situations. A scheme for choosing the relevance weights in the planning stage is provided.

We recommend to use the non-parametric estimator along with the new test to assess the weighted all-cause hazard ratio. Concrete guidance for the choice of the relevance weights is now available. Thus, applying the weighted all-cause hazard ratio in clinical applications is both - feasible and recommended.