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April 2007 Local partial likelihood estimation in proportional hazards regression
Songnian Chen, Lingzhi Zhou
Ann. Statist. 35(2): 888-916 (April 2007). DOI: 10.1214/009053606000001299

Abstract

Fan, Gijbels and King [Ann. Statist. 25 (1997) 1661–1690] considered the estimation of the risk function ψ(x) in the proportional hazards model. Their proposed estimator is based on integrating the estimated derivative function obtained through a local version of the partial likelihood. They proved the large sample properties of the derivative function, but the large sample properties of the estimator for the risk function itself were not established. In this paper, we consider direct estimation of the relative risk function ψ(x2)−ψ(x1) for any location normalization point x1. The main novelty in our approach is that we select observations in shrinking neighborhoods of both x1 and x2 when constructing a local version of the partial likelihood, whereas Fan, Gijbels and King [Ann. Statist. 25 (1997) 1661–1690] only concentrated on a single neighborhood, resulting in the cancellation of the risk function in the local likelihood function. The asymptotic properties of our estimator are rigorously established and the variance of the estimator is easily estimated. The idea behind our approach is extended to estimate the differences between groups. A simulation study is carried out.

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Songnian Chen. Lingzhi Zhou. "Local partial likelihood estimation in proportional hazards regression." Ann. Statist. 35 (2) 888 - 916, April 2007. https://doi.org/10.1214/009053606000001299

Information

Published: April 2007
First available in Project Euclid: 5 July 2007

zbMATH: 1117.62108
MathSciNet: MR2336873
Digital Object Identifier: 10.1214/009053606000001299

Subjects:
Primary: 62G05
Secondary: 60G44 , 62E02 , 62G08 , 62G20

Keywords: asymptotic property , local partial likelihood , relative risk , statistical inference , treatment effects

Rights: Copyright © 2007 Institute of Mathematical Statistics

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Vol.35 • No. 2 • April 2007
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