A new measure of treatment effect in clinical trials involving competing risks based on generalized pairwise comparisons

In survival analysis with competing risks, the treatment effect is typically expressed using cause-specific or subdistribution hazard ratios, both relying on proportional hazards assumptions. This paper proposes a nonparametric approach to analyze competing risks data based on generalized pairwise comparisons (GPC). GPC estimate the net benefit, defined as the probability that a patient from the treatment group has a better outcome than a patient from the control group minus the probability of the opposite situation, by comparing all pairs of patients taking one patient from each group. GPC allow using clinically relevant thresholds and simultaneously analyzing multiple prioritized endpoints. We show that under proportional subdistribution hazards, the net benefit for competing risks settings can be expressed as a decreasing function of the subdistribution hazard ratio, taking a value 0 when the latter equals 1. We propose four net benefit estimators dealing differently with censoring. Among them, the Peron estimator uses the Aalen-Johansen estimator of the cumulative incidence functions to classify the pairs for which the patient with the best outcome could not be determined due to censoring. We use simulations to study the bias of these estimators and the size and power of the tests based on the net benefit. The Peron estimator was approximately unbiased when the sample size was large and the censoring distribution's support sufficiently wide. With one endpoint, our approach showed a comparable power to a proportional subdistribution hazards model even under proportional subdistribution hazards. An application of the methodology in oncology is provided.