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Accounting for delayed entry into observational studies and clinical trials: length-biased sampling and restricted mean survival time

Author

Listed:
  • Mei-Ling Ting Lee

    (University of Maryland)

  • John Lawrence

    (U.S. Food and Drug Administration)

  • Yiming Chen

    (University of Maryland)

  • G. A. Whitmore

    (McGill University
    Ottawa Hospital Research Institute)

Abstract

Individuals in many observational studies and clinical trials for chronic diseases are enrolled well after onset or diagnosis of their disease. Times to events of interest after enrollment are therefore residual or left-truncated event times. Individuals entering the studies have disease that has advanced to varying extents. Moreover, enrollment usually entails probability sampling of the study population. Finally, event times over a short to moderate time horizon are often of interest in these investigations, rather than more speculative and remote happenings that lie beyond the study period. This research report looks at the issue of delayed entry into these kinds of studies and trials. Time to event for an individual is modelled as a first hitting time of an event threshold by a latent disease process, which is taken to be a Wiener process. It is emphasized that recruitment into these studies often involves length-biased sampling. The requisite mathematics for this kind of sampling and delayed entry are presented, including explicit formulas needed for estimation and inference. Restricted mean survival time (RMST) is taken as the clinically relevant outcome measure. Exact parametric formulas for this measure are derived and presented. The results are extended to settings that involve study covariates using threshold regression methods. Methods adapted for clinical trials are presented. An extensive case illustration for a clinical trial setting is then presented to demonstrate the methods, the interpretation of results, and the harvesting of useful insights. The closing discussion covers a number of important issues and concepts.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:lifeda:v:28:y:2022:i:4:d:10.1007_s10985-022-09562-8
    DOI: 10.1007/s10985-022-09562-8
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    References listed on IDEAS

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    1. 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.
    2. D. Oakes, 2016. "On the win-ratio statistic in clinical trials with multiple types of event," Biometrika, Biometrika Trust, vol. 103(3), pages 742-745.
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    Cited by:

    1. Yiming Chen & Paul J. Smith & Mei-Ling Ting Lee, 2023. "Causal Inference in Threshold Regression and the Neural Network Extension (TRNN)," Stats, MDPI, vol. 6(2), pages 1-24, April.
    2. Chrys Caroni, 2022. "Regression Models for Lifetime Data: An Overview," Stats, MDPI, vol. 5(4), pages 1-11, December.

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