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Biometrika 2002 89(1):111-128; doi:10.1093/biomet/89.1.111
© 2002 by Biometrika Trust
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Varying-coefficient models and basis function approximations for the analysis of repeated measurements

Jianhua Z.Huang1, Colin O.Wu2 and Lan Zhou3

1 Department of Statistics, University of Pennsylvania, Philadelphia, Pennsylvania 19104, U.S.Ajianhua{at}wharton.upenn.edu 2 Department of Mathematical Sciences, The Johns Hopkins University, Baltimore, Maryland 21218, U.S.A.colin{at}mts.jhu.edu 3 Center for Clinical Epidemiology and Biostatistics, University of Pennsylvania, Philadelphia, Pennsylvania 19104, U.S.A. lzhou{at}cceb.upenn.edu

A global smoothing procedure is developed using basis function approximations for estimating the parameters of a varying-coefficient model with repeated measurements.Inference procedures based on a resampling subject bootstrap are proposed to construct confidence regions and to perform hypothesis testing. Conditional biases and variances of our estimators and their asymptotic consistency are developed explicitly. Finite sample properties of our procedures are investigated through a simulation study. Application of the proposed approach is demonstrated through an example in epidemiology. In contrast to the existing methods, this approach applies whether or not the covariates are time-invariant and does not require binning of the data when observations are sparse at distinct observation times.

Key Words: Basis function; Confidence band; Hypothesis testing; Least squares; Longitudinal data; Polynomial spline; Resampling subject bootstrap; Varying-coefficient model

Received June 2000. Revised March 2001


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