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Restricted Mean Survival Time for a Randomized Study with Survival Outcome
Guogen Shan  

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https://doi.org/10.6339/25-JDS1177
Pub. online: 31 March 2025      Type: Statistical Data Science      Open accessOpen Access

Received
21 June 2024
Accepted
17 March 2025
Published
31 March 2025

Abstract

When comparing two survival curves, three tests are widely used: the Cox proportional hazards test, the logrank test, and the Wilcoxon test. Despite their popularity in survival data analysis, there is no clear clinical interpretation especially when the proportional hazard assumption is not valid. Meanwhile, the restricted mean survival time (RMST) offers an intuitive and clinically meaningful interpretation. We compare these four tests with regards to statistical power under many configurations (e.g., proportional hazard, early benefit, delayed benefit, and crossing survivals) with data simulated from the Weibull distributions. We then use an example from a lung cancer trial to compare their required sample sizes. As expected, the CoxPH test is more powerful than others when the PH assumption is valid. The Wilcoxon test is often preferable when there is a decreasing trajectory in the event rate as time goes. The RMST test is much more powerful than others when a new treatment has early benefit. The recommended test(s) under each configuration are suggested in this article.

Supplementary material

 Supplementary Material
The R function to compute simulated TIE and statistical power.

References

 
Cox DR (1972). Regression models and life-tables. Journal of the Royal Statistical Society, Series B, Methodological, 34(2): 187–202. https://doi.org/10.1111/j.2517-6161.1972.tb00899.x
 
Harrington DP, Fleming TR (1982). A class of rank test procedures for censored survival data. Biometrika, 69(3): 553–566. https://doi.org/10.1093/biomet/69.3.553
 
Jiang T, Cao B, Shan G (2020). Accurate confidence intervals for risk difference in meta-analysis with rare events. BMC Medical Research Methodology, 20(1): 98. https://doi.org/10.1186/s12874-020-00954-8
 
Liao JJ, Liu GF, Wu WC (2020). Dynamic RMST curves for survival analysis in clinical trials. BMC Medical Research Methodology, 20(1): 218. https://doi.org/10.1186/s12874-020-01098-5
 
Lu X, Zhang Y, Tang Y, Bernick C, Shan G (2025). Conversion to Alzheimer’s disease dementia from normal cognition directly or with the intermediate mild cognitive impairment stage. Alzheimer’s & Dementia, 21(1): e14393. https://doi.org/10.1002/alz.14393
 
Lu Y, Tian L (2021). Statistical considerations for sequential analysis of the restricted mean survival time for randomized clinical trials. Statistics in Biopharmaceutical Research, 13(2): 210–218. https://doi.org/10.1080/19466315.2020.1816491
 
Mantel N (1966). Evaluation of survival data and two new rank order statistics arising in its consideration. Cancer Chemotherapy Reports, Part 1, 50(3): 163–170.
 
Peto R, Peto J (1972). Asymptotically efficient rank invariant test procedures. Journal of the Royal Statistical Society. Series A. General, 135(2): 185. https://doi.org/10.2307/2344317
 
Royston P, Parmar MK (2013). Restricted mean survival time: an alternative to the hazard ratio for the design and analysis of randomized trials with a time-to-event outcome. BMC Medical Research Methodology, 13: 152. https://doi.org/10.1186/1471-2288-13-152
 
Shan G (2020). Two-stage optimal designs based on exact variance for a single-arm trial with survival endpoints. Journal of Biopharmaceutical Statistics, 30(5): 797–805. https://doi.org/10.1080/10543406.2020.1730869
 
Shan G (2021). Optimal two-stage designs based on restricted mean survival time for a single-arm study. Contemporary Clinical Trials Communications, 21: 100732. https://doi.org/10.1016/j.conctc.2021.100732
 
Shan G (2022). Randomized two-stage optimal design for interval-censored data. Journal of Biopharmaceutical Statistics, 32(2): 298–307. https://doi.org/10.1080/10543406.2021.2009499
 
Shan G (2023). Response adaptive randomization design for a two-stage study with binary response. Journal of Biopharmaceutical Statistics, 33(5): 575–585.
 
Shan G, Dodge Francis C, Liu J, Hong X, Bernick C (2024). Application of adaptive designs in clinical research. In: Modern Inference Based on Health-Related Markers: Biomarkers and Statistical Decision Making, 229–243. Academic Press.
 
Shan G, Wilding GE, Hutson AD, Gerstenberger S (2016). Optimal adaptive two-stage designs for early phase II clinical trials. Statistics in Medicine, 35(8): 1257–1266.
 
Shan G, Zhang H (2019). Two-stage optimal designs with survival endpoint when the follow-up time is restricted. BMC Medical Research Methodology, 19: 74. https://doi.org/10.1186/s12874-019-0696-x
 
Shan G, Zhang Y, Tang Z, Ding A, Wu S (2025). Disease progression trajectory curves to estimate saved time in Alzheimer’s disease trialsitle. Contemporary Clinical Trials, 151: 107814. https://doi.org/10.1016/j.cct.2025.107814
 
Takiguchi Y, Moriya T, Asaka-Amano Y, Kawashima T, Kurosu K, Tada Y, et al. (2007). Phase II study of weekly irinotecan and cisplatin for refractory or recurrent non-small cell lung cancer. Lung Cancer, 58(2): 253–259. https://doi.org/10.1016/j.lungcan.2007.06.004
 
Tian L, Fu H, Ruberg SJ, Uno H, Wei LJ (2018). Efficiency of two sample tests via the restricted mean survival time for analyzing event time observations. Biometrics, 74(2): 694–702. https://doi.org/10.1111/biom.12770
 
Uno H (2017). Vignette for survRM2 package: Comparing two survival curves using the restricted mean survival time. Technical report.
 
Uno H, Wittes J, Fu H, Solomon SD, Claggett B, Tian L, et al. (2015). Alternatives to hazard ratios for comparing the efficacy or safety of therapies in noninferiority studies. Annals of Internal Medicine, 163(2): 127–134. https://doi.org/10.7326/M14-1741
 
Zhang Y, Li Y, Song S, Li Z, Lu M, Shan G (2024). Predicting conversion time from mild cognitive impairment to dementia with interval-censored models. Journal of Alzheimer’s Disease, 101(1): 147–157. https://doi.org/10.3233/JAD-240285

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Copyright
2025 The Author(s). Published by the School of Statistics and the Center for Applied Statistics, Renmin University of China.
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Open access article under the CC BY license.

Keywords
Cox proportional hazards model logrank test randomized trial restricted mean survival time Wilcoxon test

Funding
Research reported in this publication was supported by the National Institutes of Health under Award Number R01AG070849 and R03AG083207.

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