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

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.