A very classic problem in statistics is testing whether one distribution is probabilistically better than another. However, existing approaches are mainly developed for independent samples and additionally do not consider censored data. In the context of right-censored survival data with matched pairs he develops a new measure to compare the efficacy of two treatments. With the help of the competing risks technique, so-called relative therapeutic effects are estimated. It quantifies the probability that individuals who received the first treatment will survive better than matched individuals who received the second treatment. Hypothesis tests and confidence intervals are based on the studentized versions of the estimators, and resampling-based inferences are established by randomization methods. In our simulation study, we found that the developed test showed superior power compared to our competitors, which actually tested the simple null hypothesis that both marginal survival functions are equal. Finally, we apply this methodology to a well-known benchmark data set from trials involving patients suffering from diabetic retinopathy.
