On the Local and Stratified Likelihood Approaches in Single-Index Hazards Model

Abstract

We propose the single-index hazards model for censored survival data. As an extension of the Cox model and many transformation models, this model allows nonparametric modeling of covariate effects in a parsimonious way via a single index. In addition, the relative importance of covariates can be assessed via this model. We consider two commonly used profile likelihood methods for parameter estimation: the local profile likelihood method and the stratified profile likelihood method. It is shown that both methods may give consistent estimators under certain restrictive conditions, but in general they can yield biased estimation. Simulation studies are also conducted to demonstrate these bias phenomena. The existence and nature of the failures of these two commonly used approaches is somewhat surprising.

Keywords

Bias analysis / Cox model / Local likelihood / Profile likelihood / Single-index / Stratification