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On the empirical choice of the time window for restricted mean survival time

Author

Listed:
  • Lu Tian
  • Hua Jin
  • Hajime Uno
  • Ying Lu
  • Bo Huang
  • Keaven M. Anderson
  • LJ Wei

Abstract

The t‐year mean survival or restricted mean survival time (RMST) has been used as an appealing summary of the survival distribution within a time window [0, t]. RMST is the patient's life expectancy until time t and can be estimated nonparametrically by the area under the Kaplan‐Meier curve up to t. In a comparative study, the difference or ratio of two RMSTs has been utilized to quantify the between‐group‐difference as a clinically interpretable alternative summary to the hazard ratio. The choice of the time window [0, t] may be prespecified at the design stage of the study based on clinical considerations. On the other hand, after the survival data have been collected, the choice of time point t could be data‐dependent. The standard inferential procedures for the corresponding RMST, which is also data‐dependent, ignore this subtle yet important issue. In this paper, we clarify how to make inference about a random “parameter.” Moreover, we demonstrate that under a rather mild condition on the censoring distribution, one can make inference about the RMST up to t, where t is less than or even equal to the largest follow‐up time (either observed or censored) in the study. This finding reduces the subjectivity of the choice of t empirically. The proposal is illustrated with the survival data from a primary biliary cirrhosis study, and its finite sample properties are investigated via an extensive simulation study.

Suggested Citation

  • 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.
  • Handle: RePEc:bla:biomet:v:76:y:2020:i:4:p:1157-1166
    DOI: 10.1111/biom.13237
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    References listed on IDEAS

    as
    1. Lu Tian & Haoda Fu & Stephen J. Ruberg & Hajime Uno & Lee†Jen Wei, 2018. "Efficiency of two sample tests via the restricted mean survival time for analyzing event time observations," Biometrics, The International Biometric Society, vol. 74(2), pages 694-702, June.
    2. 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.
    3. Ying, Zhiliang, 1989. "A note on the asymptotic properties of the product-limit estimator on the whole line," Statistics & Probability Letters, Elsevier, vol. 7(4), pages 311-314, February.
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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. Lu Mao, 2023. "On restricted mean time in favor of treatment," Biometrics, The International Biometric Society, vol. 79(1), pages 61-72, March.
    3. Szilárd Nemes & Erik Bülow & Andreas Gustavsson, 2020. "A Brief Overview of Restricted Mean Survival Time Estimators and Associated Variances," Stats, MDPI, vol. 3(2), pages 1-13, May.
    4. 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.
    5. Mei-Ling Ting Lee & John Lawrence & Yiming Chen & G. A. Whitmore, 2022. "Accounting for delayed entry into observational studies and clinical trials: length-biased sampling and restricted mean survival time," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 28(4), pages 637-658, October.
    6. 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.
    7. Lu Mao, 2023. "Study design for restricted mean time analysis of recurrent events and death," Biometrics, The International Biometric Society, vol. 79(4), pages 3701-3714, December.

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