失效原因缺失的加速失效时间模型下竞争风险数据的半参数估计
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摘要
本文在加速失效时间模型下,研究了竞争风险数据失效原因缺失情况下模型系数的估计问题。在随机缺失的假设下,利用倒概率加权和双重稳健增广技术构建估计方程,用非参数的核光滑方法估计失效原因缺失的概率。通过将估计方程转化成优化问题的方式,给出了求解估计方程的算法,研究了所提出估计量的渐近性质,通过随机模拟来评价估计量的表现,并将提出的估计方法用于研究实际的乳腺癌数据.
This paper considers analyzing competing risks data with missing cause of failure under the accelerated failure time model.The missing mechanism is assumed to be missing at random.None parametric model for the probability of missing cause of failure is assumed.The inverse probability weighted and double robust techniques are used to modify the rank based estimating functions.Kernel smoothing technique is used to estimate the probability of missing cause of failure.The algorithm of the estimating equations is developed through transforming the estimating equations into an optimization problem.The asymptotic properties of the proposed estimators are established.A simulation study is carried out to evaluate the performance of the estimators.The proposed estimating method is illustrated by a breast cancer study data.
This paper considers analyzing competing risks data with missing cause of failure under the accelerated failure time model.The missing mechanism is assumed to be missing at random.None parametric model for the probability of missing cause of failure is assumed.The inverse probability weighted and double robust techniques are used to modify the rank based estimating functions.Kernel smoothing technique is used to estimate the probability of missing cause of failure.The algorithm of the estimating equations is developed through transforming the estimating equations into an optimization problem.The asymptotic properties of the proposed estimators are established.A simulation study is carried out to evaluate the performance of the estimators.The proposed estimating method is illustrated by a breast cancer study data.
引文
[1]Prentice R L,Kalbeisch J D.The analysis of failure times in the presence of competing risks.Biometrics, 19785 34:541-554
[2]Goetghebeur E,Ryan L.Analysis of competing risks survival data when some failure types are missing.Biometrika, 1995,82:821-834
[3]Hyun S,Lee J,Sun Y.Proportional hazards model for competing risks data with missing cause of failure.Journal of Statistical Planning and Inference,2012,142:1767-1779
[4]Lu,K,Tsiatis A A.Multiple imputation methods for estimating regression coefficients in the competing risks model with missing cause of failure.Biometrics,2001,57:1191-1197
[5]Gao G,Tsiatis A A.Semiparametric estimators for the regression coefficients in the linear transformation competing risks model with missing cause of failure.Biometrika, 2005,92:875-891
[6]Lu W,Liang Y.Analysis of competing risks data with missing cause of failure under additive hazards model.Statistica Sinica, 2008,18:219-234
[7]Song X,Sun L,Mu X,Dinse G E.Additive hazards regression with censoring indicators missing at random.The Canadian Journal of Statistics,2010,38:333-351
[8]Lin D Y,Wei L J,Ying Z.Accelerated failure time models for counting processes.Biometrika,1998,85:605-618
[9]Prentice R L.Linear rank tests with right censored data.Biometrika,1978,65:167-179
[10]Tsiatis A A.Estimating regression parameters using linear rank tests for censored data.The Annals of Statistics,1990,18:354-372
[11]Ying Z.A large sample study of rank estimation for censored regression data.The Annals of Statistics,1993,21:76-99
[12]Jin Z,Lin D Y,Wei L J,Ying Z.Rank-based inference for the accelerated failure time model.Biometrika,2003,90:341-353
[13]Zheng M,Lin,R,Yu W.Competing risks data analysis under the accelerated failure time model with missing cause of failure.Annals of the Institute of Statistical Mathematics,2016,68(4):855-876
[14]Robins J M,Rotnitzky A,Zhao L P.Estimation of regression coefficients when some regressors are not always observed.Journal of the American Statistical Association,1994,89:846-866
[15]Cummings F J,Gray R,Tormey D C,Da,vis T E,Volk H,Harris,J,Falkson G,Bennett J M.Adjuvant tamoxifen versus placebo in elderly women with nodepositive breast cancer:long-term follow-up and causes of death.J.Clinical Oncology,1993,11:29-35
[16]Pollard.Empirical Processes:Theory and Applications.Institute of Mathematical Statistics,1990
[17]Wang S,Wang C Y.A note on kernel assisted estimators in missing covariate regression.Statistics&Probability Letters,2001,55(4):439-449
[2]Goetghebeur E,Ryan L.Analysis of competing risks survival data when some failure types are missing.Biometrika, 1995,82:821-834
[3]Hyun S,Lee J,Sun Y.Proportional hazards model for competing risks data with missing cause of failure.Journal of Statistical Planning and Inference,2012,142:1767-1779
[4]Lu,K,Tsiatis A A.Multiple imputation methods for estimating regression coefficients in the competing risks model with missing cause of failure.Biometrics,2001,57:1191-1197
[5]Gao G,Tsiatis A A.Semiparametric estimators for the regression coefficients in the linear transformation competing risks model with missing cause of failure.Biometrika, 2005,92:875-891
[6]Lu W,Liang Y.Analysis of competing risks data with missing cause of failure under additive hazards model.Statistica Sinica, 2008,18:219-234
[7]Song X,Sun L,Mu X,Dinse G E.Additive hazards regression with censoring indicators missing at random.The Canadian Journal of Statistics,2010,38:333-351
[8]Lin D Y,Wei L J,Ying Z.Accelerated failure time models for counting processes.Biometrika,1998,85:605-618
[9]Prentice R L.Linear rank tests with right censored data.Biometrika,1978,65:167-179
[10]Tsiatis A A.Estimating regression parameters using linear rank tests for censored data.The Annals of Statistics,1990,18:354-372
[11]Ying Z.A large sample study of rank estimation for censored regression data.The Annals of Statistics,1993,21:76-99
[12]Jin Z,Lin D Y,Wei L J,Ying Z.Rank-based inference for the accelerated failure time model.Biometrika,2003,90:341-353
[13]Zheng M,Lin,R,Yu W.Competing risks data analysis under the accelerated failure time model with missing cause of failure.Annals of the Institute of Statistical Mathematics,2016,68(4):855-876
[14]Robins J M,Rotnitzky A,Zhao L P.Estimation of regression coefficients when some regressors are not always observed.Journal of the American Statistical Association,1994,89:846-866
[15]Cummings F J,Gray R,Tormey D C,Da,vis T E,Volk H,Harris,J,Falkson G,Bennett J M.Adjuvant tamoxifen versus placebo in elderly women with nodepositive breast cancer:long-term follow-up and causes of death.J.Clinical Oncology,1993,11:29-35
[16]Pollard.Empirical Processes:Theory and Applications.Institute of Mathematical Statistics,1990
[17]Wang S,Wang C Y.A note on kernel assisted estimators in missing covariate regression.Statistics&Probability Letters,2001,55(4):439-449