基于广义病例-队列设计方案的长度偏差数据回归分析
|
摘要
利用加权估计方程方法,在广义病例-队列设计方案下,针对长度偏差数据,给出Cox模型中回归系数的估计,并证明在适当的条件下,所得估计量具有相合性和渐近正态性,且渐近方差具有显式表达,在实际应用中可由plug-in方法估计.
Using the method of weighted estimation equation,under the generalized case-cohort design scheme,we gave the estimation of regression coefficients in Cox's model for length-biased data.Under appropriate conditions,we proved that the obtained estimators were consistent and asymptotic normality,and the asymptotic variance was explicit expression.It could be estimated by the plug-in method in practical application.
Using the method of weighted estimation equation,under the generalized case-cohort design scheme,we gave the estimation of regression coefficients in Cox's model for length-biased data.Under appropriate conditions,we proved that the obtained estimators were consistent and asymptotic normality,and the asymptotic variance was explicit expression.It could be estimated by the plug-in method in practical application.
引文
[1]ZELEN M,FEINLEIB M.On the Theory of Screening for Chronic Diseases[J].Biometrika,1969,56(3):601-614.
[2]LANCASTER T.The Econometric Analysis of Transition Data[M].Cambridge:Cambridge University Press,1992.
[3]VARDI Y.Multiplicative Censoring,Renewal Processes,Deconvolution and Decreasing Density:Nonparametric Estimation[J].Biometrika,1989,76(4):751-761.
[4]NOWELL C,STANLEY L R.Length-Biased Sampling in Mall Intercept Surveys[J].Journal of Marketing Research,1991,28(4):475-479.
[5]ZELEN M.Forward and Backward Recurrence Times and Length Biased Sampling:Age Specific Models[J].Lifetime Data Analysis,2004,10(4):325-334.
[6]QIN Jing,SHEN Yu.Statistical Methods for Analyzing Right-Censored Length-Biased Data under Cox Model[J].Biometrics,2010,66(2):382-392.
[7]HUANG Chiungyu,QIN Jing.Composite Partial Likelihood Estimation under Length-Biased Sampling,with Application to a Prevalent Cohort Study of Dementia[J].Journal of the American Statistical Association,2012,107:946-957.
[8]NING Jing,QIN Jing,ASGHARIAN M,et al.Empirical Likelihood-Based Confidence Intervals for LengthBiased Data[J].Statistics in Medicine,2013,32(13):2278-2291.
[9]MA Huijuan,ZHANG Feipeng,ZHOU Yong.Composite Estimating Equation Approach for Additive Risk Model with Length-Biased and Right-Censored Data[J].Statistics and Probability Letters,2015,96:45-53.
[10]PRENTICE R L.A Case-Cohort Design for Epidemiologic Cohort Studies and Disease Prevention Trials[J].Biometrika,1986,73(1):1-11.
[11]CHEN Kani.Generalized Case-Cohort Sampling[J].Journal of the Royal Statistical Society,2001,63(4):791-809.
[12]RUDIN W.Principles of Mathematical Analysis[M].New York:McGraw-Hill Book Company,Inc,1976.
[13]WOLKEWITZ M,ALLIGNOL A,SCHUMACHER M,et al.Two Pitfalls in Survival Analyses of Time-Dependent Exposure:A Case Study in a Cohort of Oscar Nominees[J].The American Statistician,2010,64(3):205-211.
[14]LIN Cunjie,ZHOU Yong.Analyzing Right-Censored and Length-Biased Data with Varying-Coefficient Transformation Model[J].Journal of Multivariate Analysis,2014,130:45-63.
[15]ADDONA V,WOLFSON D B.A Formal Test for the Stationarity of the Incidence Rate Using Data from a Prevalent Cohort Study with Follow-Up[J].Lifetime Data Analysis,2006,12(3):267-284.
[16]KULICH M,LIN Danyu.Improving the Efficiency of Relative-Risk Estimation in Case-Cohort Studies[J].Journal of the American Statistical Association,2004,99:832-844.
[2]LANCASTER T.The Econometric Analysis of Transition Data[M].Cambridge:Cambridge University Press,1992.
[3]VARDI Y.Multiplicative Censoring,Renewal Processes,Deconvolution and Decreasing Density:Nonparametric Estimation[J].Biometrika,1989,76(4):751-761.
[4]NOWELL C,STANLEY L R.Length-Biased Sampling in Mall Intercept Surveys[J].Journal of Marketing Research,1991,28(4):475-479.
[5]ZELEN M.Forward and Backward Recurrence Times and Length Biased Sampling:Age Specific Models[J].Lifetime Data Analysis,2004,10(4):325-334.
[6]QIN Jing,SHEN Yu.Statistical Methods for Analyzing Right-Censored Length-Biased Data under Cox Model[J].Biometrics,2010,66(2):382-392.
[7]HUANG Chiungyu,QIN Jing.Composite Partial Likelihood Estimation under Length-Biased Sampling,with Application to a Prevalent Cohort Study of Dementia[J].Journal of the American Statistical Association,2012,107:946-957.
[8]NING Jing,QIN Jing,ASGHARIAN M,et al.Empirical Likelihood-Based Confidence Intervals for LengthBiased Data[J].Statistics in Medicine,2013,32(13):2278-2291.
[9]MA Huijuan,ZHANG Feipeng,ZHOU Yong.Composite Estimating Equation Approach for Additive Risk Model with Length-Biased and Right-Censored Data[J].Statistics and Probability Letters,2015,96:45-53.
[10]PRENTICE R L.A Case-Cohort Design for Epidemiologic Cohort Studies and Disease Prevention Trials[J].Biometrika,1986,73(1):1-11.
[11]CHEN Kani.Generalized Case-Cohort Sampling[J].Journal of the Royal Statistical Society,2001,63(4):791-809.
[12]RUDIN W.Principles of Mathematical Analysis[M].New York:McGraw-Hill Book Company,Inc,1976.
[13]WOLKEWITZ M,ALLIGNOL A,SCHUMACHER M,et al.Two Pitfalls in Survival Analyses of Time-Dependent Exposure:A Case Study in a Cohort of Oscar Nominees[J].The American Statistician,2010,64(3):205-211.
[14]LIN Cunjie,ZHOU Yong.Analyzing Right-Censored and Length-Biased Data with Varying-Coefficient Transformation Model[J].Journal of Multivariate Analysis,2014,130:45-63.
[15]ADDONA V,WOLFSON D B.A Formal Test for the Stationarity of the Incidence Rate Using Data from a Prevalent Cohort Study with Follow-Up[J].Lifetime Data Analysis,2006,12(3):267-284.
[16]KULICH M,LIN Danyu.Improving the Efficiency of Relative-Risk Estimation in Case-Cohort Studies[J].Journal of the American Statistical Association,2004,99:832-844.