基于病例队列数据的比例风险模型的诊断

余吉昌, 曹永秀

数学学报 ›› 2020, Vol. 63 ›› Issue (2) : 137-148.

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数学学报 ›› 2020, Vol. 63 ›› Issue (2) : 137-148. DOI: 10.12386/A2020sxxb0011
论文

基于病例队列数据的比例风险模型的诊断

    余吉昌, 曹永秀
作者信息 +

Model Diagnostics for the Proportional Hazards Model with Case-Cohort Data

    Ji Chang YU, Yong Xiu CAO
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文章历史 +

摘要

病例队列设计是一种在生存分析中广泛应用的可以降低成本又能提高效率的抽样方法.对于病例队列数据,已经有很多统计方法基于比例风险模型来估计协变量对生存时间的影响.然而,很少有工作基于病例队列数据来检验模型的假设是否成立.在这篇文章中,我们基于渐近的零均的值随机过程提出了一类检验统计量,这类检验统计量可以基于病例队列数据来检验比例风险模型的假设是否成立.我们通过重抽样的方法来逼近上述检验统计量的渐近分布,通过数值模拟来研究所提方法在有限样本下的表现,最后将所提出的方法应用于一个国家肾母细胞瘤研究的真实数据集上.

Abstract

Case-cohort design is a well-known cost-effective design and has been widely used in survival analysis. Many statistical methods have been developed to estimate the covariates effects on the survival time based on case-cohort data. However, little work has focused on checking the proportional hazards model assumptions with case-cohort data. In this article, we propose a class of test statistics through the asymptotically mean-zero processes for testing the proportional hazards assumption with case-cohort data. Re-sampling scheme is proposed to approximate the asymptotic distribution of the test statistics. Simulation studies are conducted to evaluate the finite sample performances of the proposed method and a data set from the National Wilm's Tumor Study Group is analyzed to illustrate the proposed method.

关键词

病例队列设计 / 模型诊断 / 比例风险模型 / 重抽样 / 生存分析

Key words

case-cohort design / model diagnostics / proportional hazards model / resampling / survival analysis

引用本文

导出引用
余吉昌, 曹永秀. 基于病例队列数据的比例风险模型的诊断. 数学学报, 2020, 63(2): 137-148 https://doi.org/10.12386/A2020sxxb0011
Ji Chang YU, Yong Xiu CAO. Model Diagnostics for the Proportional Hazards Model with Case-Cohort Data. Acta Mathematica Sinica, Chinese Series, 2020, 63(2): 137-148 https://doi.org/10.12386/A2020sxxb0011

参考文献

[1] Borgan O., Langholz B., Samuelsen S., et al., Exposure stratified case-cohort designs, Lifetime Data Analysis, 2000, 6:39-58.
[2] Breslow N., Cain K., Logistic regression for two-stage case-control data, Biometrika, 1988, 75:11-20.
[3] Breslow N, Holubkov R., Maximum likelihood estimation of logistic regression parameters under two-phase, outcome-dependent sampling, Journal of the Royal Statistical Society, Series B, 1997, 59:447-461.
[4] Cao Y., Yu J., Liu Y., Optimal generalized case-cohort analysis with Cox's proportional hazards model, Acta Mathematicae Applicatae Sinica, English Series, 2015, 31:841-854.
[5] Chen K., Lo S., Case-cohort and case-control analysis with Cox's model, Biometrika, 1999, 86:755-764.
[6] Chen H. Y., Fitting semiparametric transformation regression models to data from a modified case-cohort design, Biometrika, 2001, 88:255-268.
[7] Deng L., Ding J., Liu Y., et al., Regression analysis for the proportional hazards model with parameter constraints under case-cohort design, Computational Statistics and Data Analysis, 2018, 117:194-206.
[8] Ding J., Chen X., Fang H., et al., Case-cohort design for accelerated hazards model, Statistics and Its Interface, 2018, 11:657-668.
[9] Ding J., Lu T., Cai J., et al., Recent progresses in outcome-dependent sampling with failure time data, Lifetime Data Analysis, 2017, 23:57-82.
[10] Ding J., Zhou H., Liu Y., et al., Estimating effect of environmental contaminants on women's subfecundity for the MoBa study data with an outcome-dependent sampling scheme, Biostatistics, 2014, 15:636-650.
[11] Fleming T., Harrington D., Counting Processes and Survival Analysis, Wiley, New York, 1991.
[12] Kang S., Lu W., Liu M., Efficient estimation for accelerated failure time model under case-cohort and nested casecontrol sampling, Biometrics, 2017, 73:114-123.
[13] Kim S., Cai J., Lu W., More efficient estimators for case-cohort studies, Biometrika, 2013, 100:695-708.
[14] Kong L., Cai J., Case-cohort analysis with accelerated failure time model, Biometrics, 2009, 65, 135-142.
[15] Kong L., Cai J., Sen P., Weighted estimating equations for semiparametric transformation models with censored data from a case-cohort design, Biometrika, 2004, 91:305-319.
[16] Kosorok M., Introduction to Empirical Processes and Semiparametric Inference, Springer, New York, 2008.
[17] Kulich M., Lin D., Additive hazards regression for case-cohort studies, Biometrika, 2000, 87:73-87.
[18] Lee C., Ning J., Shen Y., Model diagnostics for the proportional hazards model with length-biased data, Lifetime Data Analysis, 2019, 1:79-96.
[19] Lin D., Wei L., Ying Z., Checking the Cox model with cumulative sums of martingale-based residuals, Biometrika, 1993, 80:557-572.
[20] Lu W., Liu M., Chen Y., Testing goodness-of-fit for the proportional hazards model based on nested case-control data, Biometrics, 2014, 70:845-851.
[21] Lu W., Tsiatis A., Semiparametric transformation models for the case-cohort study, Biometrika, 2006, 93:207-214.
[22] Prentice R., A case-cohort design for epidemiologic cohort studies and disease prevention trials, Biometrika, 1986, 73:1-11.
[23] Prentice R., Pyke R., Logistic disease incidence models and case-control studies, Biometrika, 1979, 66:403-412.
[24] Qi L., Wang C., Prentice R., Weighted estimators for proportional hazards regression with missing covariates, Journal of the American Statistical Association, 2005, 100:1250-1263.
[25] Self S., Prentice R., Asymptotic distribution theory and efficiency results for case-cohort studies, Annals of Statistics, 1988, 16:64-81.
[26] Spiekerman C., Lin D., Checking the marginal Cox model for correlated failure time data, Biometrika, 1996, 83:143-156.
[27] Wang X., Zhou H., Design and inference for cancer biomarker study with an outcome and auxiliary-dependent subsampling, Biometrics, 2010, 66:502-511.
[28] Weaver M., Zhou H., An estimated likelihood method for continuous outcome regression models with outcome-dependent sampling, Journal of The American Statistical Association, 2005, 100:459-469.
[29] Xue X., Xie X., Gunter M., et al., Testing the proportional hazards assumption in case-cohort analysis, BMC Medical Research Methodology, 2013, 13:88.
[30] Yu J., Liu Y., Cai J., et al., Outcome-dependent sampling design and inference for Cox's proportional hazards Model, Journal of Statistical Planning and Inference, 2016, 178:24-36.
[31] Yu J., Liu Y., Sandler D., et al., Statistical inference for the additive hazards model under outcome-dependent sampling, Canadian Journal of Statistics, 2015, 43:436-453.
[32] Zhou H., Weaver M., Qin J., et al., A semiparametric empirical likelihood method for data from an outcomedependent sampling scheme with a continuous outcome, Biometrics, 2002, 58:413-421.

基金

国家自然科学基金(11501578,11701571);中央高校基本科研业务费团队项目(31511911201)

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