The ICH E9(R1) addendum stresses the importance of clearly pre-specifying clinically interpretable treatment effect measures (estimands) and proposes different strategies to deal with intercurrent events. In this paper, we consider different estimands of the vaccine efficacy that are interpretable even when the proportional hazard assumption is not met, including estimands based on the average hazard ratio, the cumulative incidence ratio, and the restricted mean time lost ratio. Under the assumption that different estimands target relevant clinical questions, power becomes a crucial factor in choosing the preferred estimand. We focus on the power of these different estimands in vaccine efficacy trials, and we illustrate them in a human papillomavirus phase III vaccine trial. In classical settings of prophylactic vaccine efficacy trials, our results show that the average hazard ratio and cumulative incidence ratio give similar results, while the restricted mean time lost ratio is expected to be less powerful.
HalloranMEStruchinerCJLonginiIM. Study designs for evaluating different efficacy and effectiveness aspects of vaccines. Am J Epidemiol1997; 146: 789–803.
2.
KalbfleischJDPrenticeRL. Estimation of the average hazard ratio. Biometrika1981; 68: 105–112.
3.
XuRO’QuigleyJ. Estimating average regression effect under non-proportional hazards. Biostatistics2000; 1: 423–439.
4.
van HouwelingenHCvan de VeldeCJStijnenT. Interim analysis on survival data: its potential bias and how to repair it. Stat Med2005; 24: 2823–2835.
5.
SchemperMWakounigSHeinzeG. The estimation of average hazard ratios by weighted Cox regression. Stat Med2009; 28: 2473–2489.
6.
CallegaroASpiessensB. Testing treatment effect in randomized clinical trials with possible nonproportional hazards. Stat Biopharm Res2017; 9: 204–211.
7.
HernánM. The hazards of hazard ratios. Epidemiology2010; 21: 13–15.
8.
RoystonPParmarMKB. The use of restricted mean survival time to estimate the treatment effect in randomized clinical trials when the proportional hazards assumption is in doubt. Stat Med2011; 30: 2409–2421.
9.
UnoHClaggettBTianL, et al.Moving beyond the hazard ratio in quantifying the between-group difference in survival analysis. J Clin Oncol2014; 32: 2380–2385.
10.
UnoHHoriguchiM. Ratio and difference of average hazard with survival weight: new measures to quantify survival benefit of new therapy. Stat Med2023; 42: 936–952.
11.
PrenticeRLAragakiAK. Intention-to-treat comparisons in randomized trials. Stat Sci2022; 37: 380–393.
12.
TianLFuHRubergSJ, et al.Efficiency of two sample tests via the restricted mean survival time for analyzing event time observations. Biometrics2018; 74: 694–702.
13.
FreidlinBHuCKornEL. Are restricted mean survival time methods especially useful for noninferiority trials?Clin Trials2021; 18: 188–196.
14.
MichielsHVandeboschAVansteelandtS. Estimation and interpretation of vaccine efficacy in COVID-19 randomized clinical trials. Stat Commun Infect Dis2022; 14: 20220003.
15.
PaavonenJNaudPSalmerónJ, et al.Efficacy of human papillomavirus (HPV)-16/18 AS04-adjuvanted vaccine against cervical infection and precancer caused by oncogenic HPV types (PATRICIA): final analysis of a double-blind, randomised study in young women. Lancet2009; 374: 301–314.
16.
MartinussenTVansteelandtSAndersenPK. Subtleties in the interpretation of hazard contrasts. Lifetime Data Anal2020; 26: 833–855.
17.
WeiGSchaubelDE. Estimating cumulative treatment effects in the presence of nonproportional hazards. Biometrics2008; 64: 724–732.
18.
US Food and Drug Administration (FDA). Adjusting for covariates in randomized clinical trials for drugs and biological products. Guidance for industry, https://www.fda.gov/media/148910/download (2023, accessed 3 December 2025).
19.
LuXTsiatisAA. Improving the efficiency of the log-rank test using auxiliary covariates. Biometrika2008; 95: 679–694.
20.
YeTShaoJYiY. Covariate-adjusted log-rank test: guaranteed efficiency gain and universal applicability. Biometrika2024; 111: 691–705.
21.
CaiWvan der LaanMJ. One-step targeted maximum likelihood estimation for time-to-event outcomes. Biometrics2020; 76: 722–733.
22.
US Food and Drug Administration (FDA). Approaches to assessment of overall survival in oncology clinical trials. Guidance for Industry, https://www.fda.gov/media/188274/download (2025, accessed 3 December 2025).
23.
FuRLiHWangX, et al.Application of estimand framework in ICH E9 (R1) to vaccine trials. J Biopharm Stat2023; 33: 502–513.
24.
NoirjeanSBottigliengoDCinconzeE, et al.Implementation of the ICH E9 (R1) addendum in vaccine efficacy studies: the hypothetical and principal stratum strategies. J Biopharm Stat2025; 1–18. doi: 10.1080/10543406.2025.2547588
25.
BeckersFKarkadaNYangY, et al.Adopting the estimand framework in prophylactic vaccine trials. Vaccine2025; 64: 1–7.
26.
MorganKEWhiteIRLeyratC, et al.Applying the estimands framework to non-inferiority trials: Guidance on choice of hypothetical estimands for non-adherence and comparison of estimation methods. Stat Med2025; 44: e10348.
27.
HernánMAHernández-DíazS. Beyond the intention-to-treat in comparative effectiveness research. Clin Trials2012; 9: 48–55.
28.
HernánMAHernández-DíazSRobinsJM. Randomized trials analyzed as observational studies. Ann Intern Med2013; 159: 560–563.
29.
HalloranME. Design and analysis of vaccine studies. Statistics for Biology and Health. , New York, NY: Springer, 2009.
30.
LinDYWeiLJ. The robust inference for the Cox proportional hazards model. J Am Stat Assoc1989; 84: 1074–1078.
31.
HattoriSUnoH. On sample size determination for restricted mean survival time-based tests in randomized clinical trials. arXiv preprint arXiv:221208259, 2022.
