基于两条生存曲线间面积的非参数统计推断方法研究
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摘要
目的在生存数据组间比较研究中,当风险率成比例假设失效,特别是生存曲线交叉时,Log-rank检验的检验效能很低,本文介绍和研究一类无上述假设条件的检验法。方法首先介绍一种基于两条生存曲线间面积值的检验法,其次基于置换检验思想提出校正的置换面积检验法,并通过Monte Carlo模拟将上述两种方法与常用的Log-rank和加权Kaplan-Meier检验进行性能比较和评价。结果模拟结果显示,在I类错误上除面积检验法偏离较大外,其余检验法仅有轻微波动。在检验效能方面,风险率成比例假设满足时,Log-rank的检验效能最高;生存曲线交叉于早期时,面积检验和置换面积检验的检验效能最高;除此之外,置换面积检验法效能最高。结论当生存数据风险率成比例假设成立时,推荐Log-rank检验;但当该假设失效,特别是生存曲线出现交叉时,推荐使用置换面积检验法。
Objective In the comparative study of two groups for time-to-event data,when the proportional hazards assumption is violated,especially two survival curves cross,the power of Log-rank test is low to lose reliability,this paper introduced and proposed a kind of methods without proportional hazards assumption.Methods First,we introduced a method based on the area between survival curves(i.e.the area test).Second,a permutation test to adjust the area value test(i.e.the permutation area test)was proposed.Last,the performance of Log-rank test、weighted Kaplan-Meier test,the area test and the proposed permutation area test were compared by Monte Carlo simulation.Results The simulations showed that the type I error of the permutation area test and other methods were slightly fluctuated while the area test deviated from significant level.Log-rank test had the highest power under the assumption of proportional hazards.The area test and the permutation area test were better than other methods when survival curves crossed early; in addition,the permutation area test outperformed other methods.Conclusion Log-rank test is recommended under the assumption of proportional hazards;the permutation area test is robust and recommended when the proportional hazard assumption is violated,especially when two survival curves cross.
Objective In the comparative study of two groups for time-to-event data,when the proportional hazards assumption is violated,especially two survival curves cross,the power of Log-rank test is low to lose reliability,this paper introduced and proposed a kind of methods without proportional hazards assumption.Methods First,we introduced a method based on the area between survival curves(i.e.the area test).Second,a permutation test to adjust the area value test(i.e.the permutation area test)was proposed.Last,the performance of Log-rank test、weighted Kaplan-Meier test,the area test and the proposed permutation area test were compared by Monte Carlo simulation.Results The simulations showed that the type I error of the permutation area test and other methods were slightly fluctuated while the area test deviated from significant level.Log-rank test had the highest power under the assumption of proportional hazards.The area test and the permutation area test were better than other methods when survival curves crossed early; in addition,the permutation area test outperformed other methods.Conclusion Log-rank test is recommended under the assumption of proportional hazards;the permutation area test is robust and recommended when the proportional hazard assumption is violated,especially when two survival curves cross.
引文
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[2] Pepe MS,Fleming TR.Weighted Kaplan-Meier statistics:a class of distance tests for censored survival data.Biometrics,1989,45(2):497-507.
[3] Li H,Han D,Hou Y,et al.Statistical Inference Methods for Two Crossing Survival Curves:A Comparison of Methods.PloS One,2015,10(1):e0116774.
[4] Lin X,Xu Q.A new method for the comparison of survival distributions.Pharmaceutical Statistics,2010,9(1):67-76.
[5] Galimberti S,Valsecchi MG.Multivariate permutation test to compare survival curves for matched data.BMC Medical Research Methodology,2013,13(1):16.
[6] 马兴华,张晋昕.数值变量正态性检验常用方法的对比.循证医学,2014,14(2):123-123.
[7] 李慧敏,韩栋,陈征,等.生存曲线交叉时统计推断方法的比较和选择.中国卫生统计,2013,30(5):668-672.
[8] Chang YM,Chen CS,Shen PS.A jackknife-based versatile test for two-sample problems with right-censored data.Journal of Applied Statistics,2012,39(2):267-277.
[9] Kraus D.Adaptive Neyman′s smooth tests of homogeneity of two samples of survival data.Journal of Statistical Planning & Inference,2009,139(10):3559-3569.
[10] 陈金宝,侯雅文,陈征.竞争风险数据中累积发生率置信区间的估计研究.中国卫生统计,2018,35(1):22-25.
[11] Andrews DF,Hertzberg AM(1985),DATA:A Collection of Problems from Many Fields for the Student and Research Worker,New York:Springer-Verlag.
[12] Mok TS,Wu YL,Thongprasert S,et al.Gefitinib or carboplatin-paclitaxel in pulmonary adenocarcinoma.New England Journal of Medicine,2009,361(10):947-957.
[13] Royston P,Parmar MKB.The use of restricted mean survival time to estimate the treatment effect in randomized clinical trials when the proportional hazards assumption is in doubt.Statistics in Medicine,2011,30(19):2409.
[14] 陈金宝,邱李斌,王北琪,等.长期生存率比较的统计检验法.中国卫生统计,2016,33(3):534-536.