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A permutation test for the two-sample right-censored model

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  • Grzegorz Wyłupek

    (University of Wrocław)

Abstract

The paper presents a novel approach to solve a classical two-sample problem with right-censored data. As a result, an efficient procedure for verifying equality of the two survival curves is developed. It generalizes, in a natural manner, a well-known standard, that is, the log-rank test. Under the null hypothesis, the new test statistic has an asymptotic Chi-square distribution with one degree of freedom, while the corresponding test is consistent for a wide range of the alternatives. On the other hand, to control the actual Type I error rate when sample sizes are finite, permutation approach is employed for the inference. An extensive simulation study shows that the new test procedure improves upon classical solutions and popular recent developments in the field. An analysis of the real datasets is included. A routine, written in R, is attached as Supplementary Material.

Suggested Citation

  • Grzegorz Wyłupek, 2021. "A permutation test for the two-sample right-censored model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(5), pages 1037-1061, October.
    • Handle: RePEc:spr:aistmt:v:73:y:2021:i:5:d:10.1007_s10463-020-00777-w
    DOI: 10.1007/s10463-020-00777-w
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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. Lee, Seung-Hwan & Lee, Eun-Joo & Omolo, Bernard Oguna, 2008. "Using integrated weighted survival difference for the two-sample censored data problem," Computational Statistics & Data Analysis, Elsevier, vol. 52(9), pages 4410-4416, May.
    3. Lang Wu & Peter B. Gilbert, 2002. "Flexible Weighted Log-Rank Tests Optimal for Detecting Early and/or Late Survival Differences," Biometrics, The International Biometric Society, vol. 58(4), pages 997-1004, December.
    4. 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.
    5. Yu-Mei Chang & Chun-Shu Chen & Pao-Sheng Shen, 2012. "A jackknife-based versatile test for two-sample problems with right-censored data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(2), pages 267-277, April.
    6. 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.
    7. R.D. Gill, 1980. "Censoring and Stochastic Integrals," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 34(2), pages 124-124, June.
    8. Michael Brendel & Arnold Janssen & Claus-Dieter Mayer & Markus Pauly, 2014. "Weighted Logrank Permutation Tests for Randomly Right Censored Life Science Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(3), pages 742-761, September.
    9. 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.
    10. Zhang, Jin & Wu, Yuehua, 2007. "k-Sample tests based on the likelihood ratio," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4682-4691, May.
    11. C. Chauvel & J. O'Quigley, 2014. "Tests for comparing estimated survival functions," Biometrika, Biometrika Trust, vol. 101(3), pages 535-552.
    12. Darilay, Annie Tordilla & Naranjo, Joshua D., 2011. "A pretest for using logrank or Wilcoxon in the two-sample problem," Computational Statistics & Data Analysis, Elsevier, vol. 55(7), pages 2400-2409, July.
    13. 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.
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