Smoothed Rank Regression With Censored Data

A weighted rank estimating function is proposed to estimate the regression parameter vector in an accelerated failure time model with right censored data. In general, rank estimating functions are discontinuous in the regression parameter, creating difficulties in determining the asymptotic distribution of the estimator. A local distribution function is used to create a rank based estimating function that is continuous and monotone in the regression parameter vector. A weight is included in the estimating function to produce a bounded influence estimate. The asymptotic distribution of the regression estimator is developed and simulations are performed to examine its finite sample properties. A lung cancer dataset is used to illustrate the methodology.

[1]  K R Hess,et al.  Hazard function estimators: a simulation study. , 1999, Statistics in medicine.

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

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

[4]  Yijian Huang,et al.  Calibration Regression of Censored Lifetime Medical Cost , 2002 .

[5]  Tightness of Monotone Random Fields , 1987 .

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

[7]  P. Grambsch,et al.  Proportional hazards tests and diagnostics based on weighted residuals , 1994 .

[8]  Laurence L. George,et al.  The Statistical Analysis of Failure Time Data , 2003, Technometrics.

[9]  David R. Cox,et al.  Regression models and life tables (with discussion , 1972 .

[10]  B. M. Brown,et al.  Standard errors and covariance matrices for smoothed rank estimators , 2005 .

[11]  J. Wellner,et al.  Empirical Processes with Applications to Statistics , 2009 .

[12]  Zhiliang Ying,et al.  A Large Sample Study of Rank Estimation for Censored Regression Data , 1993 .

[13]  Y. Ritov,et al.  Monotone Estimating Equations for Censored Data , 1994 .

[14]  Joshua D. Naranjo,et al.  Bounded influence rank regression , 1994 .

[15]  D.,et al.  Regression Models and Life-Tables , 2022 .

[16]  Z. Ying,et al.  Rank-based inference for the accelerated failure time model , 2003 .

[17]  J. Kalbfleisch,et al.  The Statistical Analysis of Failure Time Data , 1980 .