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A two‐stage procedure for comparing hazard rate functions

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  • Peihua Qiu
  • Jun Sheng

Abstract

Summary. Comparison of two hazard rates is important in applications that are related to times to occurrence of a specific event. Conventional comparison procedures, such as the log‐rank, Gehan–Wilcoxon and Peto–Peto tests, are powerful only when the two hazard rates do not cross each other. Because crossing hazard rates are common in practice, several procedures have been proposed in the literature for comparing such rates. However, most of these procedures consider only the alternative hypothesis with crossing hazard rates; many other realistic cases, including those when the two hazard rates run parallel to each other, are excluded from consideration. We propose a two‐stage procedure that considers all possible alternatives, including ones with crossing or running parallel hazard rates. To define its significance level and p‐value properly, a new procedure for handling the crossing hazard rates problem is suggested, which has the property that its test statistic is asymptotically independent of the test statistic of the log‐rank test. We show that the two‐stage procedure, with the log‐rank test and the suggested procedure for handling the crossing hazard rates problem used in its two stages, performs well in applications in comparing two hazard rates.

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  • 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.
    • Handle: RePEc:bla:jorssb:v:70:y:2008:i:1:p:191-208
    DOI: 10.1111/j.1467-9868.2007.00622.x
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    Cited by:

    1. Mathew, Litty & P., Anisha & Kattumannil, Sudheesh K., 2022. "A jackknife empirical likelihood ratio test for strong mean inactivity time order," Statistics & Probability Letters, Elsevier, vol. 190(C).
    2. Huimin Li & Dong Han & Yawen Hou & Huilin Chen & Zheng Chen, 2015. "Statistical Inference Methods for Two Crossing Survival Curves: A Comparison of Methods," PLOS ONE, Public Library of Science, vol. 10(1), pages 1-18, January.
    3. Kayoung Park & Peihua Qiu, 2018. "Evaluation of the treatment time-lag effect for survival data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 24(2), pages 310-327, April.
    4. 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.
    5. Kristin McCullough & Tatiana Dmitrieva & Nader Ebrahimi, 2022. "New approximate Bayesian computation algorithm for censored data," Computational Statistics, Springer, vol. 37(3), pages 1369-1397, July.
    6. 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.
    7. 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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