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# Global Partial Likelihood for Nonparametric Proportional Hazards Models

Kani Chen, Shaojun Guo, Liuquan Sun and Jane-Ling Wang
Journal of the American Statistical Association
Vol. 105, No. 490 (June 2010), pp. 750-760
Stable URL: http://www.jstor.org/stable/29747080
Page Count: 11
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## Abstract

As an alternative to the local partial likelihood method of Tibshirani and Hastie and Fan, Gijbels, and King, a global partial likelihood method is proposed to estimate the covariate effect in a nonparametric proportional hazards model, $\lambda (t/x)=\text{exp}\{\psi (x)\}\lambda _{0}(t)$. The estimator, $\hat{\psi}(x)$, reduces to the Cox partial likelihood estimator if the covariate is discrete. The estimator is shown to be consistent and semiparametrically efficient for linear functionals of ψ(x). Moreover, Breslow-type estimation of the cumulative baseline hazard function, using the proposed estimator $\hat{\psi}(x)$, is proved to efficient. The asymptotic bias and variance are derived under regularity conditions. Computation of the estimator involves an iterative but simple algorithm. Extensive simulation studies provide evidence supporting the theory. The method is illustrated with the Stanford heart transplant data set. The proposed global approach is also extended to a partially linear proportional hazards model and found to provide efficient estimation of the slope parameter. This article has the supplementary materials online.

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