Semiparametric quantile-difference estimation for length-biased and right-censored data
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摘要
Prevalent cohort studies frequently involve length-biased and right-censored data, a fact that has drawn considerable attention in survival analysis. In this article, we consider survival data arising from lengthbiased sampling, and propose a new semiparametric-model-based approach to estimate quantile differences of failure time. We establish the asymptotic properties of our new estimators theoretically under mild technical conditions, and propose a resampling method for estimating their asymptotic variance. We then conduct simulations to evaluate the empirical performance and efficiency of the proposed estimators, and demonstrate their application by a real data analysis.
Prevalent cohort studies frequently involve length-biased and right-censored data, a fact that has drawn considerable attention in survival analysis. In this article, we consider survival data arising from lengthbiased sampling, and propose a new semiparametric-model-based approach to estimate quantile differences of failure time. We establish the asymptotic properties of our new estimators theoretically under mild technical conditions, and propose a resampling method for estimating their asymptotic variance. We then conduct simulations to evaluate the empirical performance and efficiency of the proposed estimators, and demonstrate their application by a real data analysis.
Prevalent cohort studies frequently involve length-biased and right-censored data, a fact that has drawn considerable attention in survival analysis. In this article, we consider survival data arising from lengthbiased sampling, and propose a new semiparametric-model-based approach to estimate quantile differences of failure time. We establish the asymptotic properties of our new estimators theoretically under mild technical conditions, and propose a resampling method for estimating their asymptotic variance. We then conduct simulations to evaluate the empirical performance and efficiency of the proposed estimators, and demonstrate their application by a real data analysis.
引文
1 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.Lifetime Data Anal,2006,12:267-284
2 Andersen P K,Gill R D.Cox’s regression model for counting processes:A large sample study.Ann Statist,1982,10:1100-1120
3 Arnold B C,Strauss D.Bivariate distributions with exponential conditionals.J Amer Statist Assoc,1988,83:522-527
4 Asgharian M.On the singularities of the information matrix and multipath change-point problems.Theory Probab Appl,2014,58:546-561
5 Asgharian M,Wolfson D B.Asymptotic behavior of the unconditional NPMLE of the length-biased survivor function from right censored prevalent cohort data.Ann Statist,2005,33:2109-2131
6 Asgharian M,Wolfson D B,Zhang X.Checking stationarity of the incidence rate using prevalent cohort survival data.Stat Med,2006,25:1751-1767
7 Chen X R,Zhou Y.Quantile regression for right-censored and length-biased data.Acta Math Appl Sin Engl Ser,2012,28:443-462
8 Gijbels I,Wang J L.Strong representations of the survival function estimator for truncated and censored data with applications.J Multivariate Anal,1993,47:210-229
9 Huang C Y,Qin J.Composite partial likelihood estimation under length-biased sampling with application to a prevalent cohort study of dementia.J Amer Statist Assoc,2012,107:946-957
10 Kosorok M R.Introduction to Empirical Processes and Semiparametric Inference.New York:Springer,2008
11 Lin C,Zhou Y.Analyzing right-censored and length-biased data with varying-coefficient transformation model.JMultivariate Anal,2014,130:45-63
12 Lin C,Zhou Y.Semiparametric varying-coefficient model with right-censored and length-biased data.J Multivariate Anal,2016,152:119-144
13 Qin J,Shen Y.Statistical methods for analyzing right-censored length-biased data under Cox model.Biometrics,2010,66:382-392
14 Reiss R D.Approximate Distributions of Order Statistics.New York:Springer,1989
15 Shen Y,Ning J,Qin J.Analyzing length-biased data with semiparametric transformation and accelerated failure time models.J Amer Statist Assoc,2009,104:1192-1202
16 Tsai W Y.Pseudo-partial likelihood for proportional hazards models with biased-sampling data.Biometrika,2009,96:601-615
17 Tsai W Y,Jewell N P,Wang M C.A note on the product-limit estimator under right censoring and left truncation.Biometrika,1987,74:883-886
18 van der Vaart A W.Asymptotic Statistics.Cambridge:Cambridge University Press,2000
19 Wang H J,Wang L.Quantile regression analysis of length-biased survival data.Stat,2014,3:31-47
20 Wang M C.Nonparametric estimation from cross-sectional survival data.J Amer Statist Assoc,1991,86:130-143
21 Wang M C,Brookmeyer R,Jewell N.Statistical models for prevalent cohort data.Biometrics,1993,49:1-11
22 Wang Y X,Liu P,Zhou Y.Quantile residual lifetime for left-truncated and right-censored data.Sci China Math,2015,58:1217-1234
23 Winter B B,Foldes A.A product-limit estimator for use with length-biased data.Canad J Statist,1988,16:337-355
24 Xun L,Shao L,Zhou Y.Efficiency of estimators for quantile differences with left truncated and right censored data.Statist Probab Lett,2017,121:29-36
25 Yang H,Zhao Y.Smoothed jackknife empirical likelihood for the one-sample difference of quantiles.Comput Statist Data Anal,2018,120:58-69
26 Zelen M.Forward and backward recurrence times and length biased sampling:Age specific models.Lifetime Data Anal,2004,10:325-334
27 Zelen M,Feinleib M.On the theory of screening for chronic diseases.Biometrika,1969,56:601-614
28 Zeng D,Lin D Y.Efficient resampling methods for nonsmooth estimating function.Biostatistics,2008,9:355-363
29 Zhang F,Chen X,Zhou Y.Proportional hazards model with varying coefficients for length-biased data.Lifetime Data Anal,2014,20:132-157
30 Zhou W,Jing B.Smoothed empirical likelihood confidence intervals for the difference of quantiles.Statist Sinica,2003,13:83-95
31 Zhou Y,Yip P.A strong representation of the product-limit estimator for left truncated and right censored data.JMultivariate Anal,1999,69:261-280
2 Andersen P K,Gill R D.Cox’s regression model for counting processes:A large sample study.Ann Statist,1982,10:1100-1120
3 Arnold B C,Strauss D.Bivariate distributions with exponential conditionals.J Amer Statist Assoc,1988,83:522-527
4 Asgharian M.On the singularities of the information matrix and multipath change-point problems.Theory Probab Appl,2014,58:546-561
5 Asgharian M,Wolfson D B.Asymptotic behavior of the unconditional NPMLE of the length-biased survivor function from right censored prevalent cohort data.Ann Statist,2005,33:2109-2131
6 Asgharian M,Wolfson D B,Zhang X.Checking stationarity of the incidence rate using prevalent cohort survival data.Stat Med,2006,25:1751-1767
7 Chen X R,Zhou Y.Quantile regression for right-censored and length-biased data.Acta Math Appl Sin Engl Ser,2012,28:443-462
8 Gijbels I,Wang J L.Strong representations of the survival function estimator for truncated and censored data with applications.J Multivariate Anal,1993,47:210-229
9 Huang C Y,Qin J.Composite partial likelihood estimation under length-biased sampling with application to a prevalent cohort study of dementia.J Amer Statist Assoc,2012,107:946-957
10 Kosorok M R.Introduction to Empirical Processes and Semiparametric Inference.New York:Springer,2008
11 Lin C,Zhou Y.Analyzing right-censored and length-biased data with varying-coefficient transformation model.JMultivariate Anal,2014,130:45-63
12 Lin C,Zhou Y.Semiparametric varying-coefficient model with right-censored and length-biased data.J Multivariate Anal,2016,152:119-144
13 Qin J,Shen Y.Statistical methods for analyzing right-censored length-biased data under Cox model.Biometrics,2010,66:382-392
14 Reiss R D.Approximate Distributions of Order Statistics.New York:Springer,1989
15 Shen Y,Ning J,Qin J.Analyzing length-biased data with semiparametric transformation and accelerated failure time models.J Amer Statist Assoc,2009,104:1192-1202
16 Tsai W Y.Pseudo-partial likelihood for proportional hazards models with biased-sampling data.Biometrika,2009,96:601-615
17 Tsai W Y,Jewell N P,Wang M C.A note on the product-limit estimator under right censoring and left truncation.Biometrika,1987,74:883-886
18 van der Vaart A W.Asymptotic Statistics.Cambridge:Cambridge University Press,2000
19 Wang H J,Wang L.Quantile regression analysis of length-biased survival data.Stat,2014,3:31-47
20 Wang M C.Nonparametric estimation from cross-sectional survival data.J Amer Statist Assoc,1991,86:130-143
21 Wang M C,Brookmeyer R,Jewell N.Statistical models for prevalent cohort data.Biometrics,1993,49:1-11
22 Wang Y X,Liu P,Zhou Y.Quantile residual lifetime for left-truncated and right-censored data.Sci China Math,2015,58:1217-1234
23 Winter B B,Foldes A.A product-limit estimator for use with length-biased data.Canad J Statist,1988,16:337-355
24 Xun L,Shao L,Zhou Y.Efficiency of estimators for quantile differences with left truncated and right censored data.Statist Probab Lett,2017,121:29-36
25 Yang H,Zhao Y.Smoothed jackknife empirical likelihood for the one-sample difference of quantiles.Comput Statist Data Anal,2018,120:58-69
26 Zelen M.Forward and backward recurrence times and length biased sampling:Age specific models.Lifetime Data Anal,2004,10:325-334
27 Zelen M,Feinleib M.On the theory of screening for chronic diseases.Biometrika,1969,56:601-614
28 Zeng D,Lin D Y.Efficient resampling methods for nonsmooth estimating function.Biostatistics,2008,9:355-363
29 Zhang F,Chen X,Zhou Y.Proportional hazards model with varying coefficients for length-biased data.Lifetime Data Anal,2014,20:132-157
30 Zhou W,Jing B.Smoothed empirical likelihood confidence intervals for the difference of quantiles.Statist Sinica,2003,13:83-95
31 Zhou Y,Yip P.A strong representation of the product-limit estimator for left truncated and right censored data.JMultivariate Anal,1999,69:261-280