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Partitioned log-rank tests for the overall homogeneity of hazard rate functions

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  • Yukun Liu

    (East China Normal University)

  • Guosheng Yin

    (The University of Hong Kong)

Abstract

In survival analysis, it is routine to test equality of two survival curves, which is often conducted by using the log-rank test. Although it is optimal under the proportional hazards assumption, the log-rank test is known to have little power when the survival or hazard functions cross. To test the overall homogeneity of hazard rate functions, we propose a group of partitioned log-rank tests. By partitioning the time axis and taking the supremum of the sum of two partitioned log-rank statistics over different partitioning points, the proposed test gains enormous power for cases with crossing hazards. On the other hand, when the hazards are indeed proportional, our test still maintains high power close to that of the optimal log-rank test. Extensive simulation studies are conducted to compare the proposed test with existing methods, and three real data examples are used to illustrate the commonality of crossing hazards and the advantages of the partitioned log-rank tests.

Suggested Citation

  • Yukun Liu & Guosheng Yin, 2017. "Partitioned log-rank tests for the overall homogeneity of hazard rate functions," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 23(3), pages 400-425, July.
    • Handle: RePEc:spr:lifeda:v:23:y:2017:i:3:d:10.1007_s10985-016-9365-0
    DOI: 10.1007/s10985-016-9365-0
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    References listed on IDEAS

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    1. Peihua Qiu & Jun Sheng, 2008. "A two‐stage procedure for comparing hazard rate functions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(1), pages 191-208, February.
    2. Song Yang & Ross Prentice, 2005. "Semiparametric analysis of short-term and long-term hazard ratios with two-sample survival data," Biometrika, Biometrika Trust, vol. 92(1), pages 1-17, March.
    3. Song Yang & Ross Prentice, 2010. "Improved Logrank-Type Tests for Survival Data Using Adaptive Weights," Biometrics, The International Biometric Society, vol. 66(1), pages 30-38, March.
    4. R.D. Gill, 1980. "Censoring and Stochastic Integrals," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 34(2), pages 124-124, June.
    5. Kevin Hasegawa Eng & Michael R. Kosorok, 2005. "A Sample Size Formula for the Supremum Log-Rank Statistic," Biometrics, The International Biometric Society, vol. 61(1), pages 86-91, March.
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