Isotonized smooth estimators of a monotone baseline hazard in the Cox model

Journal article (2017)

Authors

H.P. Lopuhaä Statistics - EEMCS
E. Musta Statistics - EEMCS
Research Group
Statistics (EEMCS) (TU Delft)
Isotonic estimation Kernel smoothing Cox regression model Asymptotic normality Hazard rate Isotonized smoothed Breslow estimator Maximum smoothed likelihood estimator
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Published Date

2017

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Statistics

Abstract

We consider two isotonic smooth estimators for a monotone baseline hazard in the Cox model, a maximum smooth likelihood estimator and a Grenander-type estimator based on the smoothed Breslow estimator for the cumulative baseline hazard. We show that they are both asymptotically normal at rate nm∕(2m+1), where m≥2 denotes the level of smoothness considered, and we relate their limit behavior to kernel smoothed isotonic estimators studied in Lopuhaä and Musta (2016). It turns out that the Grenander-type estimator is asymptotically equivalent to the kernel smoothed isotonic estimators, while the maximum smoothed likelihood estimator exhibits the same asymptotic variance but a different bias. Finally, we present numerical results on pointwise confidence intervals that illustrate the comparable behavior of the two methods.