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Local linear estimation for time-dependent coefficients in Cox’s regression model. (English) Zbl 1034.62096
The proportional hazards (Cox regression) model with time dependent coefficients is considered for the conditional hazard function \(\lambda(t\mid x)\) of a survival time \(T\): \[ \lambda(t\mid x)=\lambda_0(t)\exp \Biggl(\sum_{j=1}^p a_j(t)x_j\Biggr). \] A local linear partial maximum likelihood estimator \(\hat a_j(t)\) is proposed for the functions \(a_j\). The asymptotic normality of \(\hat a_j\) is demonstrated. Simulation examples and a case-study of gastric cancer data are presented.

MSC:
62N02 Estimation in survival analysis and censored data
62G20 Asymptotic properties of nonparametric inference
62P10 Applications of statistics to biology and medical sciences; meta analysis
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