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On the win-ratio statistic in clinical trials with multiple types of event

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  • D. Oakes

Abstract

Pocock et al. (2012), following Finkelstein & Schoenfeld (1999), has popularized the win ratio for analysis of controlled clinical trials with multiple types of outcome event. The approach uses pairwise comparisons between patients in the treatment and control groups using a primary outcome, say the time to death, with ties broken using a secondary outcome, say the time to hospitalization. In general the observed pairwise preferences and the weight they attach to the component rankings will depend on the distribution of potential follow-up time. We present expressions for the win and loss probabilities for general bivariate survival models when follow-up of all patients is limited to a specified time horizon. In the special case of a bivariate Lehmann model we show that the win ratio does not depend on this horizon. We show how the win ratio may be estimated nonparametrically or from a parametric model. Extensions to events of three or more types are described. Application of the method of marginal estimation due to Wei et al. (1989) to this problem is described.

Suggested Citation

  • 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.
    • Handle: RePEc:oup:biomet:v:103:y:2016:i:3:p:742-745.
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    File URL: http://hdl.handle.net/10.1093/biomet/asw026
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    Citations

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    Cited by:

    1. Xiaodong Luo & Hui Quan, 2020. "Some Meaningful Weighted Log-Rank and Weighted Win Loss Statistics," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 12(2), pages 216-224, July.
    2. Lu Mao & Tuo Wang, 2021. "A class of proportional win‐fractions regression models for composite outcomes," Biometrics, The International Biometric Society, vol. 77(4), pages 1265-1275, December.
    3. Lu Mao & KyungMann Kim & Xinran Miao, 2022. "Sample size formula for general win ratio analysis," Biometrics, The International Biometric Society, vol. 78(3), pages 1257-1268, 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. David Oakes, 2018. "Survival models and health sequences: discussion," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 24(4), pages 592-594, October.
    6. Xiaodong Luo & Hong Tian & Surya Mohanty & Wei Yann Tsai, 2019. "Rejoinder to “on the alternative hypotheses for the win ratio”," Biometrics, The International Biometric Society, vol. 75(1), pages 352-354, March.
    7. 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.
    8. Lu Mao, 2019. "On the alternative hypotheses for the win ratio," Biometrics, The International Biometric Society, vol. 75(1), pages 347-351, March.
    9. 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.

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