Polynomial Spline Estimation and Inference of Proportional Hazards
Regression Models with Flexible Relative Risk Form

Jianhua Z. Huang and Linxu Liu

Abstract:

The Cox proportional hazards model usually assumes
an exponential form for the dependence of the hazard function
on covariate variables. However, in practice this assumption may be
violated and other relative risk forms may be more appropriate. In
this paper, we consider the proportional hazards model with an
unknown relative risk form. Issues in model interpretation
are addressed. We propose a method to estimate the
relative risk form and the regression parameters simultaneously
by first approximating the logarithm of the relative risk form by a spline
and then employing the maximum partial likelihood estimation. An iterative
alternating optimization procedure is developed for efficient
implementation. Statistical inference of the regression coefficients
and of the relative risk form based on parametric asymptotic theory
is discussed. The proposed methods
are illustrated using simulation and an application to the Veteran's
Administration lung cancer data.


Nonparametric regression; Partial likelihood;
Proportional hazards model; Single index model; Spline.