On a semiparametric survival model with flexible covariate effect
The Cox regression model specifies the stochastic hazard rate at exposure time \(t\) for covariate \(z\) as \[ \lambda(z,t)= \alpha(t) \exp(\beta z), \tag{1} \] where \(\alpha\) is nonparametric while the dependency on the marker or covariate \(z\) is parametric. The authors suppose \[ \lambda(z,t)= \alpha(t; \theta)g(z), \tag{2} \] where \(\alpha\) is a parametric class of hazard functions, while \(g\) is of unknown functional form. In Section 2 are presented the counting process formulation of the model, while in Section 3 are defined estimators of \(\theta\) and \(g\) in (2), based on the profile likelihood principle. In Section 4 are considered the asymptotic properties of the parametric and nonparametric estimates outlining the general approach to the asymptotics. Section 5 contains numerical results and some extensions are discussed in Section 6. The proofs are given in the Appendix. All the sections contain a rich and impressive bibliography.
scientific article; zbMATH DE number 1359513
scientific article