gms | German Medical Science

Comparing survival distributions based on censored data is in general challenging since conclusions are sought about distributions which are observed incompletely. In medical statistics, and in particular in oncology, the logrank test and the Cox model have been established as key tools, which do not require specific distributional assumptions. Under the relatively weak assumption of proportional hazards, they are efficient and their results can be interpreted unambiguously. However, delayed treatment effects, disease progression, treatment switchers or the presence of subgroups with differential treatment effects may challenge the assumption of proportional hazards. In practice, weighted logrank tests emphasizing either early, intermediate or late event times via an appropriate weighting function may be used to accommodate for an expected pattern of non-proportionality.

We model these sources of non-proportional hazards via a mixture of survival functions with piecewise constant hazard. The model is then applied to study the power of unweighted and weighted log-rank tests, as well as maximum tests allowing different time dependent weights. Simulation results suggest a robust performance of maximum tests across different scenarios, with little loss in power compared to the most powerful among the considered weighting schemes and huge power gain compared to unfavourable weights.

We further propose a framework to perform an interim analysis and calculate the conditional power under the non-proportional hazards model to allow futility stopping decision making, sample size reassessment or modification of the testing procedure.

R.R. and N.B. received funding from Merck connected to this work.

The authors declare that an ethics committee vote is not required.