Analysing clinical time-to-event data under non-proportional hazards

• Applicant: Professorin Dr. Kathrin Möllenhoff
• Subject Area: Epidemiology and Medical Biometry/Statistics ; Mathematics
• Term: since 2025
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 557597093

Key tools in survival analysis include the Kaplan-Meier estimator to estimate survival probabilities and the log-rank test to compare survival between groups. In addition, the Cox model is often used to account for the effect of covariates on survival, assuming that the hazard rates of the two groups are proportional to each other. This assumption is crucial not only for the Cox model, but also for the log-rank test, which may be less powerful if it is violated. However, in many cases the proportional hazards assumption is not tested, or even obviously violated, and statistical methods are chosen anyway, leading to potentially inaccurate results. Alternative measures such as the average hazard ratio, the Mann-Whitney effect and the median survival time have recently been investigated. The restricted mean survival time (RMST) is another promising measure that offers straightforward clinical interpretation. Further, alternative tests such as weighted log-rank tests, combination tests and RMST-based tests have been proposed. The RMST can be obtained by non-parametric and parametric approaches. However, the latter are still underexplored and proper implementation is limited, although they offer advantages such as extrapolation and prediction. Therefore, one part of this project is to combine the advantages of parametric models and the use of meaningful estimands of treatment effect by parametrically deriving the RMST, as well as corresponding confidence intervals and statistical tests. Similar problems to the violation of the proportional hazards assumption can occur when competing risks are present. Traditional methods such as the Kaplan Meier estimator and the log rank test can be biased in those situations. Non-parametric and semi-parametric methods are often used to analyse competing risks, assuming that cause-specific and sub-distribution hazards are proportional, which leads to similar problems to those mentioned above. Parametric modeling and the restricted mean time lost (RMTL) as a measure of treatment effect are alternative approaches that can address these challenges and are thus in the focus of the second part of this project. Parametric competing risk models will be applied to obtain RMTL estimates, confidence intervals, and simultaneous confidence bands. A statistical test will be developed to assess the significance of the treatment effect, considering both difference and equivalence/non-inferiority hypotheses. All methods will be implemented and made publicly available in R packages, appropriate repositories and, in part, R shiny apps. A large simulation study will be carried out to compare the newly derived methods with existing non-parametric methods in order to provide guidance to clinicians on the most appropriate test for different situations. Finally, as a key aspect of this project, data sets provided by clinicians from various medical fields will be analysed by the newly derived methods.

• DFG Programme: Research Grants