For the analysis of time-to-event data, frequently used methods such as the log-rank test or the Cox proportional hazards model are based on the proportional hazards assumption, which is often debatable. Although a wide range of parametric and non-parametric methods for non-proportional hazards (NPH) has been proposed, there is no consensus on the best approaches. To close this gap, we conducted a systematic literature search to identify statistical methods and software appropriate under NPH. Our literature search identified 907 abstracts, out of which we included 211 articles, mostly methodological ones. Review articles and applications were less frequently identified. The articles discuss effect measures, effect estimation and regression approaches, hypothesis tests, and sample size calculation approaches, which are often tailored to specific NPH situations. Using a unified notation, we provide an overview of methods available. Furthermore, we derive some guidance from the identified articles. We summarized the contents from the literature review in a concise way in the main text and provide more detailed explanations in the supplement (page 29).

翻译：对于生存时间数据的分析，常用的方法如对数秩检验或Cox比例风险模型均基于比例风险假设，而这一假设常常存在争议。尽管针对非比例风险已提出了多种参数与非参数方法，但至今尚未就最佳方法达成共识。为填补这一空白，我们开展了系统性文献检索，以识别适用于非比例风险的统计方法及软件。文献检索共获得907篇摘要，其中纳入211篇文章，主要为方法学研究。综述类文章与应用研究较少。这些文献讨论了针对特定非比例风险情境的效果度量、效应估计与回归方法、假设检验以及样本量计算方法。我们采用统一的符号体系，对现有方法进行了概述，并基于所识别文献提出了一些指导建议。我们将文献综述内容在正文中进行了简洁总结，并在附录（第29页）中提供了更详细的解释。