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Nielsen, Jens P.; Linton, Oliver; Bickel, Peter J.

On a semiparametric survival model with flexible covariate effect. (English) Zbl 0953.62107

Ann. Stat. 26, No. 1, 215-241 (1998).
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.
Reviewer: G.G.Vrănceanu (Bucureşti)

Cited in 22 Documents

MSC:

62N02 Estimation in survival analysis and censored data
62M09 Non-Markovian processes: estimation
62G05 Nonparametric estimation
62F12 Asymptotic properties of parametric estimators
62G20 Asymptotic properties of nonparametric inference

Keywords:

counting processes; kernel estimation; predictability; semiparametric survival analysis; bibliography
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References:

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