Statistical Modelling 17 (6) (2017), 423–448

Estimation of partly linear additive hazards model with left-truncated and right-censored data

Arfan Raheen Afzal
Department of Mathematics and Statistics,
University of Calgary,
Calgary, Alberta,
Canada


Cheng Dong
Department of Statistics University of Missouri,
Columbia, MO,
U.S.A.


Xuewen Lu
Department of Mathematics and Statistics,
University of Calgary,
Calgary, Alberta,
Canada
e-mail: xlu@ucalgary.ca

Abstract:

In this article, we consider an additive hazards semiparametric model for left-truncated and right-censored data where the risk function has a partly linear structure, we call it the partly linear additive hazards model. The nonlinear components are assumed to be B-splines functions, so the model can be viewed as a semiparametric model with an unknown baseline hazard function and a partly linear parametric risk function, which can model both linear and nonlinear covariate effects, hence is more flexible than a purely linear or nonlinear model. We construct a pseudo-score function to estimate the coefficients of the linear covariates and the B-spline basis functions. The proposed estimators are asymptotically normal under the assumption that the true nonlinear functions are B-spline functions whose knot locations and number of knots are held fixed. On the other hand, when the risk functions are unknown non-parametric functions, the proposed method provides a practical solution to the underlying inference problems. We conduct simulation studies to empirically examine the finite-sample performance of the proposed method and analyze a real dataset for illustration.

Keywords:

B-spline; left-truncation; linear and nonlinear effects; partly linear additive hazards model; right-censoring.

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