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A nonparametric test for comparing survival functions based on restricted distance correlation

Author

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  • Zhang Qingyang

    (Department of Mathematical Sciences, University of Arkansas, AR 72701, Fayetteville, United States)

Abstract

In this article, we propose an omnibus test for comparing two survival functions under non-proportional hazards. The test statistic is based on a product-limit estimate of the restricted distance correlation, which is closely related to the L 2 {L}_{2} distance between survival curves. The strong consistency is established under mild regularity conditions. Our simulation studies show that the new test has satisfactory power under proportional hazard and various non-proportional hazards settings including delayed treatment effect, diminishing effect, and crossing survival curves; therefore, it can be a competitive alternative to the existing omnibus tests such as Kolmogorov-Smirnov test, Cramer-von Mises test, two-stage test, and the maxCombo test based on weighted log-rank statistics. Two extensions of the new test to one-sided alternatives and a Gaussian kernel are also discussed.

Suggested Citation

  • Zhang Qingyang, 2023. "A nonparametric test for comparing survival functions based on restricted distance correlation," Dependence Modeling, De Gruyter, vol. 11(1), pages 1-15.
    • Handle: RePEc:vrs:demode:v:11:y:2023:i:1:p:15:n:1013
    DOI: 10.1515/demo-2023-0108
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    References listed on IDEAS

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    1. Tamara Fernández & Arthur Gretton & David Rindt & Dino Sejdinovic, 2023. "A Kernel Log-Rank Test of Independence for Right-Censored Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 118(542), pages 925-936, April.
    2. 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.
    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. Lee, Seung-Hwan, 2007. "On the versatility of the combination of the weighted log-rank statistics," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 6557-6564, August.
    5. Jing Zhang & Yanyan Liu & Hengjian Cui, 2021. "Model-free feature screening via distance correlation for ultrahigh dimensional survival data," Statistical Papers, Springer, vol. 62(6), pages 2711-2738, December.
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