Quantifying treatment differences in confirmatory trials under non-proportional hazards

Abstract

Proportional hazards are a common assumption when designing confirmatory clinical trials in oncology. With the emergence of immunotherapy and novel targeted therapies, departure from the proportional hazard assumption is not rare in nowadays clinical research. Under non-proportional hazards, the hazard ratio does not have a straightforward clinical interpretation, and the log-rank test is no longer the most powerful statistical test even though it is still valid. Nevertheless, the log-rank test and the hazard ratio are still the primary analysis tools, and traditional approaches such as sample size increase are still proposed to account for the impact of non-proportional hazards. The weighed log-rank test and the test based on the restricted mean survival time (RMST) are receiving a lot of attention as a potential alternative to the log-rank test. We conduct a simulation study comparing the performance and operating characteristics of the log-rank test, the weighted log-rank test and the test based on the RMST, including a treatment effect estimation, under different non-proportional hazards patterns. Results show that, under non-proportional hazards, the hazard ratio and weighted hazard ratio have no straightforward clinical interpretation whereas the RMST ratio can be interpreted regardless of the proportional hazards assumption. In terms of power, the RMST achieves a similar performance when compared to the log-rank test.

Keywords:

• Log-rank
• non-proportional hazards
• restricted mean survival time
• weighted log-rank

Data availability

The R code used in this article is available at https://github.com/jjimenezm1989.

Disclaimer

The views and opinions expressed in this article are those of the author and do not necessarily reflect the official policy or position of Novartis Pharma A.G.

I am grateful to the Associate Editor and one anonymous referee for their constructive comments on earlier versions of this manuscript.

Disclosure statement

No potential conflict of interest was reported by the author(s).