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Improving the efficiency of the log-rank test using auxiliary covariates

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  • Xiaomin Lu
  • Anastasios A. Tsiatis

Abstract

Under the assumption of proportional hazards, the log-rank test is optimal for testing the null hypothesis , where denotes the logarithm of the hazard ratio. However, if there are additional covariates that correlate with survival times, making use of their information will increase the efficiency of the log-rank test. We apply the theory of semiparametrics to characterize a class of regular and asymptotically linear estimators for when auxiliary covariates are incorporated into the model, and derive estimators that are more efficient. The Wald tests induced by these estimators are shown to be more powerful than the log-rank test. Simulation studies are used to illustrate the gains in efficiency. Copyright 2008, Oxford University Press.

Suggested Citation

  • Xiaomin Lu & Anastasios A. Tsiatis, 2008. "Improving the efficiency of the log-rank test using auxiliary covariates," Biometrika, Biometrika Trust, vol. 95(3), pages 679-694.
    • Handle: RePEc:oup:biomet:v:95:y:2008:i:3:p:679-694
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    File URL: http://hdl.handle.net/10.1093/biomet/asn003
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    Cited by:

    1. Layla Parast & Beth Ann Griffin, 2017. "Landmark estimation of survival and treatment effects in observational studies," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 23(2), pages 161-182, April.
    2. Ritesh Ramchandani & Dianne M. Finkelstein & David A. Schoenfeld, 2020. "Estimation for an accelerated failure time model with intermediate states as auxiliary information," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 26(1), pages 1-20, January.
    3. Michal Juraska & Peter B. Gilbert, 2016. "Mark-specific hazard ratio model with missing multivariate marks," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 22(4), pages 606-625, October.
    4. Paul Frédéric Blanche & Anders Holt & Thomas Scheike, 2023. "On logistic regression with right censored data, with or without competing risks, and its use for estimating treatment effects," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 29(2), pages 441-482, April.
    5. Yuan, Ao & Zheng, Yanxun & Huang, Peng & Tan, Ming T., 2016. "A nonparametric test for the evaluation of group sequential clinical trials with covariate information," Journal of Multivariate Analysis, Elsevier, vol. 152(C), pages 82-99.

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