For the analysis of time-to-event data well established methods are available given the assumption of proportional hazards (PH) holds, e.g. log-rank test or Cox PH model. Although a wide range of parametric and non-parametric methods for non-proportional hazards (NPH) is available, no consensus on the best approach exists. We conducted a systematic literature search to identify available statistical methods and software appropriate under NPH.

Our literature search identified 907 abstracts. In our systematic review, we included 211 articles, mostly methodological ones.

The articles include effect measures, effect estimation and regression approaches, hypothesis tests, and sample size calculation approaches which are often tailored to specific NPH situations.

This study presents the results of a comprehensive simulation study that evaluates the performance of statistical methods for time-to-event analysis under non-proportional hazards (NPH). The study covers a wide range of plausible distributional assumptions and typical design options, and compares the operating characteristics of selected statistical methods for testing and estimation in clinical trials with time-to-event endpoints under NPH. The selection of methods and simulation scenarios is based on a systematic review of the scientific literature to identify available options for methods for testing and estimation under NPH and a review of past marketing authorization procedures reporting results from 18 distinct trials. The study covers four broad scenario classes - crossing hazards, delayed onset of treatment effect, progression, and differential treatment effects in subgroups. The findings have important regulatory implications for clinical trials that are pivotal for drug development and benefit-risk assessment under NPH. Additionally, an open-source software package was developed to facilitate simulation of time-to-event data.