Open Access
August 2004 Statistical estimation in the proportional hazards model with risk set sampling
Kani Chen
Ann. Statist. 32(4): 1513-1532 (August 2004). DOI: 10.1214/009053604000000517


Thomas’ partial likelihood estimator of regression parameters is widely used in the analysis of nested case-control data with Cox’s model. This paper proposes a new estimator of the regression parameters, which is consistent and asymptotically normal. Its asymptotic variance is smaller than that of Thomas’ estimator away from the null. Unlike some other existing estimators, the proposed estimator does not rely on any more data than strictly necessary for Thomas’ estimator and is easily computable from a closed form estimating equation with a unique solution. The variance estimation is obtained as minus the inverse of the derivative of the estimating function and therefore the inference is easily available. A numerical example is provided in support of the theory.


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Kani Chen. "Statistical estimation in the proportional hazards model with risk set sampling." Ann. Statist. 32 (4) 1513 - 1532, August 2004.


Published: August 2004
First available in Project Euclid: 4 August 2004

zbMATH: 1047.62089
MathSciNet: MR2089132
Digital Object Identifier: 10.1214/009053604000000517

Primary: 62F12
Secondary: 62J05

Keywords: asymptotic relative efficiency. , empirical approximation , Extended nested case-control data , time-restricted nested case-control data

Rights: Copyright © 2004 Institute of Mathematical Statistics

Vol.32 • No. 4 • August 2004
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