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Weighted Log-Rank Test for Clinical Trials with Delayed Treatment Effect Based on a Novel Hazard Function Family

Author

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  • Kaihuan Qian

    (Department of Biostatistics, School of Public Health, Peking University, Beijing 100191, China)

  • Xiaohua Zhou

    (Department of Biostatistics, School of Public Health, Peking University, Beijing 100191, China
    Beijing International Center for Mathematical Research, Peking University, Beijing 100871, China
    Pazhou Lab, No. 70 Yuean Road, Haizhu District, Guangzhou 510335, China)

Abstract

In clinical trials with delayed treatment effect, the standard log-rank method in testing the difference between survival functions may have problems, including low power and poor robustness, so the method of weighted log-rank test (WLRT) is developed to improve the test performance. In this paper, a hyperbolic-cosine-shaped ( C H ) hazard function family model is proposed to simulate delayed treatment effect scenarios. Then, based on Fleming and Harrington’s method, this paper derives the corresponding weight function and its regular corrections, which are powerful in test, theoretically. Alternative methods of parameters selection based on potential information are also developed. Further, the simulation study is conducted to compare the power performance between C H WLRT, classical WLRT, modest weighted log-rank test and WLRT with logistic-type weight function under different hazard scenarios and simulation settings. The results indicate that the C H statistics are powerful and robust in testing the late difference, so the C H test is useful and meaningful in practice.

Suggested Citation

  • Kaihuan Qian & Xiaohua Zhou, 2022. "Weighted Log-Rank Test for Clinical Trials with Delayed Treatment Effect Based on a Novel Hazard Function Family," Mathematics, MDPI, vol. 10(15), pages 1-22, July.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:15:p:2573-:d:870767
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    References listed on IDEAS

    as
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    3. 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.
    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. Theodore G. Karrison, 2016. "Versatile tests for comparing survival curves based on weighted log-rank statistics," Stata Journal, StataCorp LP, vol. 16(3), pages 678-690, September.
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