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On the restricted mean survival time curve in survival analysis

Author

Listed:
  • Lihui Zhao
  • Brian Claggett
  • Lu Tian
  • Hajime Uno
  • Marc A. Pfeffer
  • Scott D. Solomon
  • Lorenzo Trippa
  • L. J. Wei

Abstract

type="main" xml:lang="en"> For a study with an event time as the endpoint, its survival function contains all the information regarding the temporal, stochastic profile of this outcome variable. The survival probability at a specific time point, say t, however, does not transparently capture the temporal profile of this endpoint up to t. An alternative is to use the restricted mean survival time (RMST) at time t to summarize the profile. The RMST is the mean survival time of all subjects in the study population followed up to t, and is simply the area under the survival curve up to t. The advantages of using such a quantification over the survival rate have been discussed in the setting of a fixed-time analysis. In this article, we generalize this approach by considering a curve based on the RMST over time as an alternative summary to the survival function. Inference, for instance, based on simultaneous confidence bands for a single RMST curve and also the difference between two RMST curves are proposed. The latter is informative for evaluating two groups under an equivalence or noninferiority setting, and quantifies the difference of two groups in a time scale. The proposal is illustrated with the data from two clinical trials, one from oncology and the other from cardiology.

Suggested Citation

  • Lihui Zhao & Brian Claggett & Lu Tian & Hajime Uno & Marc A. Pfeffer & Scott D. Solomon & Lorenzo Trippa & L. J. Wei, 2016. "On the restricted mean survival time curve in survival analysis," Biometrics, The International Biometric Society, vol. 72(1), pages 215-221, March.
    • Handle: RePEc:bla:biomet:v:72:y:2016:i:1:p:215-221
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    Citations

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    Cited by:

    1. Chenyang Zhang & Guosheng Yin, 2023. "Bayesian nonparametric analysis of restricted mean survival time," Biometrics, The International Biometric Society, vol. 79(2), pages 1383-1396, June.
    2. Iván Díaz & Elizabeth Colantuoni & Daniel F. Hanley & Michael Rosenblum, 2019. "Improved precision in the analysis of randomized trials with survival outcomes, without assuming proportional hazards," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 25(3), pages 439-468, July.
    3. Yasuhiro Hagiwara & Tomohiro Shinozaki & Yutaka Matsuyama, 2020. "G‐estimation of structural nested restricted mean time lost models to estimate effects of time‐varying treatments on a failure time outcome," Biometrics, The International Biometric Society, vol. 76(3), pages 799-810, September.
    4. Lu Mao, 2023. "On restricted mean time in favor of treatment," Biometrics, The International Biometric Society, vol. 79(1), pages 61-72, March.
    5. Julie K. Furberg & Christian B. Pipper & Thomas Scheike, 2021. "Testing equivalence of survival before but not after end of follow-up," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 27(2), pages 216-243, April.
    6. Lu Mao, 2023. "Nonparametric inference of general while‐alive estimands for recurrent events," Biometrics, The International Biometric Society, vol. 79(3), pages 1749-1760, September.
    7. Yingchao Zhong & Douglas E. Schaubel, 2022. "Restricted mean survival time as a function of restriction time," Biometrics, The International Biometric Society, vol. 78(1), pages 192-201, March.
    8. Chi Hyun Lee & Jing Ning & Yu Shen, 2018. "Analysis of restricted mean survival time for length†biased data," Biometrics, The International Biometric Society, vol. 74(2), pages 575-583, June.
    9. Lu Tian & Hua Jin & Hajime Uno & Ying Lu & Bo Huang & Keaven M. Anderson & LJ Wei, 2020. "On the empirical choice of the time window for restricted mean survival time," Biometrics, The International Biometric Society, vol. 76(4), pages 1157-1166, December.
    10. Larry F. León & Ray Lin & Keaven M. Anderson, 2020. "On Weighted Log-Rank Combination Tests and Companion Cox Model Estimators," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 12(2), pages 225-245, July.
    11. Zijing Yang & Chengfeng Zhang & Yawen Hou & Zheng Chen, 2023. "Analysis of dynamic restricted mean survival time based on pseudo‐observations," Biometrics, The International Biometric Society, vol. 79(4), pages 3690-3700, December.
    12. Anne Eaton & Yifei Sun & James Neaton & Xianghua Luo, 2022. "Nonparametric estimation in an illness‐death model with component‐wise censoring," Biometrics, The International Biometric Society, vol. 78(3), pages 1168-1180, September.
    13. Xin Wang & Douglas E. Schaubel, 2018. "Modeling restricted mean survival time under general censoring mechanisms," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 24(1), pages 176-199, January.
    14. Godwin Yung & Yi Liu, 2020. "Sample size and power for the weighted log‐rank test and Kaplan‐Meier based tests with allowance for nonproportional hazards," Biometrics, The International Biometric Society, vol. 76(3), pages 939-950, September.
    15. Mihai C. Giurcanu & Theodore G. Karrison, 2022. "Nonparametric inference in the accelerated failure time model using restricted means," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 28(1), pages 23-39, January.
    16. Ross L. Prentice, 2022. "On the targets of inference with multivariate failure time data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 28(4), pages 546-559, October.
    17. Torben Martinussen & Stijn Vansteelandt & Per Kragh Andersen, 2020. "Subtleties in the interpretation of hazard contrasts," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 26(4), pages 833-855, October.

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