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Nontransitivity in a class of weighted logrank statistics under nonproportional hazards

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  • Gillen, Daniel L.
  • Emerson, Scott S.

Abstract

Transitivity is an important property of any statistic applied in the setting of multi-arm clinical trials and non-inferiority trials where active-controls are used. The G[rho],[gamma] class of weighted logrank statistics for right-censored survival data as proposed by Fleming and Harrington [1991. Counting Processes and Survival Analysis. Wiley, New York] is often used to improve efficiency in the setting of nonproportional hazards. These statistics utilize a weighting scheme based upon the combined Kaplan-Meier estimate of survival for all comparison groups. Members of this class include the usual logrank statistic as well as the generalized Wilcoxon statistic. It is demonstrated that all useful members of this class exhibit nontransitivity. We propose a general modification of the G[rho],[gamma] statistic which asymptotically achieves transitivity.

Suggested Citation

  • Gillen, Daniel L. & Emerson, Scott S., 2007. "Nontransitivity in a class of weighted logrank statistics under nonproportional hazards," Statistics & Probability Letters, Elsevier, vol. 77(2), pages 123-130, January.
    • Handle: RePEc:eee:stapro:v:77:y:2007:i:2:p:123-130
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    Cited by:

    1. 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.
    2. Gillen, Daniel L., 2009. "A random walk approach for quantifying uncertainty in group sequential survival trials," Computational Statistics & Data Analysis, Elsevier, vol. 53(3), pages 609-620, January.
    3. Olga V. Demler & Ilona A. Demler, 2023. "Non-Transitivity of the Win Ratio and the Area Under the Receiver Operating Characteristics Curve (AUC): a case for evaluating the strength of stochastic comparisons," Papers 2309.01791, arXiv.org, revised Sep 2023.

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