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OptBand: optimization-based confidence bands for functions to characterize time-to-event distributions

Author

Listed:
  • T. Chen

    (Harvard Medical School and Harvard Pilgrim Health Care)

  • S. Tracy

    (Harvard T.H. Chan School of Public Health
    Dana-Faber Cancer Institute)

  • H. Uno

    (Dana-Faber Cancer Institute)

Abstract

Classical simultaneous confidence bands for survival functions (i.e., Hall–Wellner, equal precision, and empirical likelihood bands) are derived from transformations of the asymptotic Brownian nature of the Nelson–Aalen or Kaplan–Meier estimators. Due to the properties of Brownian motion, a theoretical derivation of the highest confidence density region cannot be obtained in closed form. Instead, we provide confidence bands derived from a related optimization problem with local time processes. These bands can be applied to the one-sample problem regarding both cumulative hazard and survival functions. In addition, we present a solution to the two-sample problem for testing differences in cumulative hazard functions. The finite sample performance of the proposed method is assessed by Monte Carlo simulation studies. The proposed bands are applied to clinical trial data to assess survival times for primary biliary cirrhosis patients treated with D-penicillamine.

Suggested Citation

  • T. Chen & S. Tracy & H. Uno, 2021. "OptBand: optimization-based confidence bands for functions to characterize time-to-event distributions," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 27(3), pages 481-498, July.
    • Handle: RePEc:spr:lifeda:v:27:y:2021:i:3:d:10.1007_s10985-021-09522-8
    DOI: 10.1007/s10985-021-09522-8
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    References listed on IDEAS

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    1. Lu Tian & Rui Wang & Tianxi Cai & Lee-Jen Wei, 2011. "The Highest Confidence Density Region and Its Usage for Joint Inferences about Constrained Parameters," Biometrics, The International Biometric Society, vol. 67(2), pages 604-610, June.
    2. McKeague, Ian W. & Zhao, Yichuan, 2002. "Simultaneous confidence bands for ratios of survival functions via empirical likelihood," Statistics & Probability Letters, Elsevier, vol. 60(4), pages 405-415, December.
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