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Biometrika Advance Access originally published online on January 24, 2008
Biometrika 2008 95(1):123-137; doi:10.1093/biomet/asm081
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© 2008 Biometrika Trust

Articles

Nonparametric regression using local kernel estimating equations for correlated failure time data

Zhangsheng Yu

Division of Biostatistics, The Ohio State University College of Public Health, Columbus, Ohio 43210, U.S.A. zyu{at}cph.osu.edu

Xihong Lin

Department of Biostatistics, Harvard School of Public Health, Boston, Massachusetts 02115, U.S.A. xlin{at}hsph.harvard.edu

Received for publication 1 January 2006. Revision received 1 June 2007.
  Abstract

We study nonparametric regression for correlated failure time data. Kernel estimating equations are used to estimate nonparametric covariate effects. Independent and weighted-kernel estimating equations are studied. The derivative of the nonparametric function is first estimated and the nonparametric function is then estimated by integrating the derivative estimator. We show that the nonparametric kernel estimator is consistent for any arbitrary working correlation matrix and that its asymptotic variance is minimized by assuming working independence. We evaluate the performance of the proposed kernel estimator using simulation studies, and apply the proposed method to the western Kenya parasitaemia data.

Key Words: Asymptotics • Clustered survival data • Marginal model • Sandwich Estimator • Weighted kernel smoothing • Working-independence kernel estimator


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