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Biostatistics Advance Access published online on March 18, 2008
Biostatistics, doi:10.1093/biostatistics/kxm059
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© The Author 2008. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org.

A Bayesian approach to functional-based multilevel modeling of longitudinal data: applications to environmental epidemiology

Kiros Berhane*

Department of Preventive Medicine, University of Southern California, Los Angeles, CA 90033-9987, USA
kiros{at}usc.edu

Nuoo-Ting Molitor

Department of Epidemiology and Public Health, Imperial College London, Norfolk Place, London W2 1PG, UK
jassy.molitor{at}imperial.ac.uk

* To whom correspondence should be addressed.

Flexible multilevel models are proposed to allow for cluster-specific smooth estimation of growth curves in a mixed-effects modeling format that includes subject-specific random effects on the growth parameters. Attention is then focused on models that examine between-cluster comparisons of the effects of an ecologic covariate of interest (e.g. air pollution) on nonlinear functionals of growth curves (e.g. maximum rate of growth). A Gibbs sampling approach is used to get posterior mean estimates of nonlinear functionals along with their uncertainty estimates. A second-stage ecologic random-effects model is used to examine the association between a covariate of interest (e.g. air pollution) and the nonlinear functionals. A unified estimation procedure is presented along with its computational and theoretical details. The models are motivated by, and illustrated with, lung function and air pollution data from the Southern California Children's Health Study.

Keywords: Air pollution; Correlated data; Growth curves; Mixed-effects; Splines

Received January 31, 2007; revised November 7, 2007; accepted for publication December 17, 2007.


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