Statistical estimation in the proportional hazards model with risk set sampling

Details Statistical estimation in the proportional hazards model with risk set sampling Statistical estimation in the proportional hazards model with risk set sampling

2004-10-05

arxiv.org/abs/math/0410086v1

Annals of Statistics 2004, Vol. 32, No. 4, 1513-1532

Mathematics

Statistics Theory

Published by the Institute of Mathematical Statistics (http://www.imstat.org) in the Annals of Statistics (http://www.imstat

Scientific paper

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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