August 15, 2024
In clinicaltrials that use time to event endpoints, a traditional measure has been using
the hazard ratio derived from a Cox proportional hazard regression, but one
must satisfy this assumption. Over time, measures that have relaxed this
assumption have been developed. One ofthem is the average hazard ratio (AHR) where its core idea is to utilize a time-dependent weighting function that accounts for time variation. However, though it has been published inmethodological research papers, the AHR has been rarely used in practice. To facilitate its application, the authors have published their approaches for
sample size calculation of an AHR test.
One of the alternate measures is the restricted mean survival time (RMST) which describes the average event-free survivalup to a specific time point (Royston and Parmar, 2013). The AHR has shown to stay interpretable under non-proportional hazard ratios. The RMST has had a sample size calculationpackage made in R, SSRMST (Horiguchi and Uno, 2017; Uno et al, 2015). The R package, coxphw, does have an implementation of AHR and doeshave a sample size calculation based on Schoenfeld’s formula for proportional hazards. The authors have instead provided guidance where AHR is the primary endpoint in a clinical trial. Theydesigned a very simplistic sample size calculation based on assuming asymptotic normality of the AHR and a variance which they say was based on medical knowledge and the literature. It was obviously motivated as well by the Schoenfeld calculation.
In simulations, they compared their test to the log-rank test, Schoenfeld test, asymptotic AHR,
and simulation based AHR and found their new estimation for AHR appeared to be
more robust to misspecifications and they also tested this in a real dataset
analysis. They did admit in their discussion that they focused on one type of
weight which could have had limitations. Their method still has seemed to work
better under the assumption of non-proportional hazards than the usual log-rank
test or Schoenfeld test.
Written by,
Usha Govindarajulu, PhD
Keywords: survival analysis, RMST, average hazard, Cox model, hazard ratio, sample size
References
Dormuth I, Pauly M, Rauch G, andHerrmann C (2024) Sample Size Calculation under Nonproportional Hazards Using
Average Hazard Ratios. BiometricalJournal. https://doi.org/10.1002/bimj.202300271
Horiguchi, M., and H. Uno. 2017. SSRMST: Sample SizeCalculation Using Restricted Mean Survival Time. R package version 0.1.1.
Royston, P., and M. K. Parmar. 2013. “Restricted MeanSurvival Time: An Alternative to the Hazard Ratio for the Design and Analysis of Randomized Trials With a Time-to-Event Outcome.” BMC Medical ResearchMethodology 13, no. 1: 1–15.
Uno, H., J. Wittes, H. Fu, et al. 2015. “Alternatives toHazard Ratios for Comparing the Efficacy or Safety of Therapies in Noninferiority Studies.” Annals of Internal Medicine 163, no. 2:127–134.
