Censored Regression - Local Linear-approximations and Their Applications

Abstract Various statistical tools are available for modeling the relationship between response and covariate if the data are fully observable. In the situation of censored data, however, those tools are no longer directly applicable. This article provides an easily implemented methodology for modeling the association, based on censored data. The form of the regression relationship will be completely determined by the data; no assumptions are made about this form. Basic ideas behind the methodology are to transform the observed data in an appropriate simple way and then to apply a locally weighted least squares regression. The proposed estimator involves a variable bandwidth that automatically adapts to the design of the data points. That the methodology is very easy to implement is illustrated by several examples, including simulation studies and an analysis of the Stanford Heart Transplant Data and the Primary Biliary Cirrhosis Data. Several theoretical considerations are reflected in the examples. Fina...

[1]  E. Nadaraya.  On Estimating Regression , 1964 .

[2]  G. S. Watson,et al.  Smooth regression analysis , 1964 .

[3]  C. J. Stone,et al.  Consistent Nonparametric Regression , 1977 .

[4]  W. Cleveland.  Robust Locally Weighted Regression and Smoothing Scatterplots , 1979 .

[5]  I. James,et al.  Linear regression with censored data , 1979 .

[6]  H. Müller,et al.  Kernel estimation of regression functions , 1979 .

[7]  J. V. Ryzin,et al.  Regression Analysis with Randomly Right-Censored Data , 1981 .

[8]  Rupert G. Miller,et al.  Regression with censored data , 1982 .

[9]  Richard S. Varga,et al.  Proof of Theorem 5 , 1983 .

[10]  I. R. James,et al.  Consistency Results for Linear Regression with Censored Data , 1984 .

[11]  B. Silverman.  Density estimation for statistics and data analysis , 1986 .

[12]  Zukang Zheng.  A class of estimators of the parameters in linear regression with censored data , 1987 .

[13]  D. Dabrowska.  Non-parametric regression with censored survival time data , 1987 .

[14]  Sue Leurgans,et al.  Linear models, random censoring and synthetic data , 1987 .

[15]  M. C. Jones,et al.  Spline Smoothing and Nonparametric Regression. , 1989 .

[16]  J. Staniswalis.  Local Bandwidth Selection for Kernel Estimates , 1989 .

[17]  W. Härdle.  Applied Nonparametric Regression , 1991 .

[18]  G. Wahba.  Spline models for observational data , 1990 .

[19]  A. Tsiatis.  Estimating Regression Parameters Using Linear Rank Tests for Censored Data , 1990 .

[20]  Ya'acov Ritov,et al.  Estimation in a Linear Regression Model with Censored Data , 1990 .

[21]  Zhiliang Ying,et al.  Large Sample Theory of a Modified Buckley-James Estimator for Regression Analysis with Censored Data , 1991 .

[22]  D. Harrington,et al.  Counting Processes and Survival Analysis , 1991 .

[23]  Jianqing Fan,et al.  Variable Bandwidth and Local Linear Regression Smoothers , 1992 .

[24]  Jianqing Fan.  Design-adaptive Nonparametric Regression , 1992 .

[25]  Jianqing Fan.  Local Linear Regression Smoothers and Their Minimax Efficiencies , 1993 .

[26]  Jianqing Fan,et al.  Fast Implementations of Nonparametric Curve Estimators , 1994 .