Sankhya: The Indian Journal of Statistics
Varying-Coefficient Marginal Models and Applications in Longitudinal Data Analysis
Sichuan University, Chengdu, Sichuan, P.R.China
Peter X.-K. Song and Qian M. Zhou University of Waterloo, Waterloo, Ontario, Canada
SUMMARY. We consider a class of nonparametric marginal models in which the regression coefficients are assumed to be time-varying smooth functions. Such models are appealing in longitudinal data analysis to characterize the timedependent effects of covariates on the expected value of the response variable. A local quasi-likelihood method is employed to estimate the coefficient functions, based on the nonparametric technique of local polynomial kernel regression. We establish the asymptotic distribution theory for the estimators considered. We conduct Monte Carlo simulation studies to compare two types of kernel-based GEE methods with global and local variance structures, respectively. We illustrate the proposed models via three real-world data sets from a clinical trial of multiple sclerosis, a quality of life study in chemotherapeutic treatments on breast cancer, and a genomic fine-scale mapping association study on chromosomal region 5q31 for Crohn’s disease.
AMS (2000) subject classification. Primary 62G08, 62J12, 62P10.
Key words and phrases. Estimating equation, kernel, local-linear fitting, nonparametric regression.