Efficient estimation of the partly linear additive Cox model

The partly linear additive Cox model is an extension of the (linear) Cox model and allows flexible modeling of covariate effects semiparametrically. We study asymptotic properties of the maximum partial likelihood estimator of this model with right-censored data using polynomial splines. We show that, with a range of choices of the smoothing parameter (the number of spline basis functions) required for estimation of the nonparametric components, the estimator of the finite-dimensional regression parameter is root-n consistent, asymptotically normal and achieves the semiparametric information bound. Rates of convergence for the estimators of the nonparametric components are obtained. They are comparable to the rates in nonparametric regression. Implementation of the estimation approach can be done easily and is illustrated by using a simulated example.

[1]  Dorota M. Dabrowska,et al.  Smoothed Cox regression , 1997 .

[2]  F. Coolen,et al.  Statistical Models Based on Counting Processes. , 1996 .

[3]  Jon A. Wellner,et al.  Weak Convergence and Empirical Processes: With Applications to Statistics , 1996 .

[4]  T M Therneau,et al.  Diagnostic plots to reveal functional form for covariates in multiplicative intensity models. , 1995, Biometrics.

[5]  K. Do,et al.  Efficient and Adaptive Estimation for Semiparametric Models. , 1994 .

[6]  W. Wong,et al.  Convergence Rate of Sieve Estimates , 1994 .

[7]  C. J. Stone,et al.  The Use of Polynomial Splines and Their Tensor Products in Multivariate Function Estimation , 1994 .

[8]  P. Bickel.  Efficient and Adaptive Estimation for Semiparametric Models , 1993 .

[9]  Finbarr O'Sullivan,et al.  Nonparametric Estimation in the Cox Model , 1993 .

[10]  R. Tibshirani,et al.  Exploring the nature of covariate effects in the proportional hazards model. , 1990, Biometrics.

[11]  P. Grambsch,et al.  Martingale-based residuals for survival models , 1990 .

[12]  C. J. Stone,et al.  The Dimensionality Reduction Principle for Generalized Additive Models , 1986 .

[13]  J. Friedman,et al.  Estimating Optimal Transformations for Multiple Regression and Correlation. , 1985 .

[14]  C. J. Stone,et al.  Additive Regression and Other Nonparametric Models , 1985 .

[15]  R. Prentice,et al.  Commentary on Andersen and Gill's "Cox's Regression Model for Counting Processes: A Large Sample Study" , 1982 .

[16]  CensoringJian Huang.  Efficient Estimation for the Cox Model with Interval Censoring , 1996 .

[17]  Young K. Truong,et al.  The L2 rate of convergence for hazard regression , 1995 .

[18]  P. Sasieni,et al.  Information Bounds for the Conditional Hazard Ratio in a Nested Family of Regression Models , 1992 .

[19]  P. Sasieni,et al.  Non-orthogonal projections and their application to calculating the information in a partly linear Cox model , 1992 .

[20]  Aad Van Der Vbart,et al.  ON DIFFERENTIABLE FUNCTIONALS , 1988 .

[21]  L. Schumaker.  Spline Functions: Basic Theory , 1981 .

[22]  A. Tsiatis.  A Large Sample Study of Cox's Regression Model , 1981 .

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