Local linear regression on correlated survival data

• Published in: Journal of multivariate analysis Vol. 147; pp. 285 - 294
• Main Authors: Jin, Zhezhen, He, Wenqing
• Format: Journal Article
• Language: English
• Published: New York Elsevier Inc 01.05.2016; Taylor & Francis LLC
• Subjects: Asymptotic bias; Asymptotic methods; Correlated survival data; Data analysis; Estimating techniques; Kernel function; Local linear regression; Mean squared error; Nonparametric curve estimation; Regression analysis; Studies; Unbiased data transformation; Variance analysis; Kernel function; Asymptotic bias; 62G08; 62N01; Local linear regression; Nonparametric curve estimation; 62H99; Correlated survival data; Mean squared error; Unbiased data transformation
• ISSN: 0047-259X; 1095-7243
• DOI: 10.1016/j.jmva.2016.02.006

Correlated survival data arise in many contexts, and the regression analysis of such data is often of interest in practice. In this paper, we study a weighted local linear regression method for the analysis of correlated censored data, which is a natural extension of classical nonparametric regression that models directly the effect of covariates on survival time, using an unknown smooth nonparametric function. The estimation and inference are based on local linear regression and a class of unbiased data transformations. The most important feature of the proposed method is to weight local observations with local variance, which is the key to improve the estimation efficiency. We derive the asymptotic properties of the resulting estimator and show that the asymptotic variance of the nonparametric estimator is minimized with the correct specification of correlation structure. We evaluate the performance of the proposed method using simulation studies, and illustrate the proposed method with an analysis of data from the Busselton Health Study.