The continual problem of crossing survival curves in clinical trial analysis and methods for effectively addressing it: A narrative review

ABSTRACT The fundamental purpose of survival analysis is to compare the survival curves of two or more groups representing different interventions, thereby determining which treatment is more effective for informed decision-making. A classic statistical tool is the log-rank test, based on the proportional hazards (PH) assumption. However, in clinical studies, crossover of survival curves has often been noted. In such cases, more refined statistical methods are required, as the log-rank test may not yield significant results. In this article, we investigated the effect of the absence of the PH hypothesis. In addition, we evaluated modern tests, such as weighted log-rank tests and their variants, the supremum and modified log-rank tests, as well as Kaplan-Meier-based tests. These approaches offer improved statistical power and better control of type I errors. For the present study, a literature search was conducted to identify studies involving survival analysis with simultaneous deviation from the PH hypothesis. Articles published between January 2018 and April 2025 were retrieved from PubMed and ResearchGate. Of 263 initial articles, 46 were duplicates, 21 did not involve human studies, and 118 were excluded based on further screening. The final selection included 78 studies, with an additional 17 studies included for detailed analysis of alternative tests addressing violation of the PH assumption.