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Comparison of subject-specific and population averaged models for count data from cluster-unit intervention trials

Department of Biostatistics, University of North Carolina School of Public Health, Chapel Hill, NC, USA

John S. Preisser

Department of Biostatistics, University of North Carolina School of Public Health, Chapel Hill, NC, USA,jpreisse{at}bios.unc.edu

Bahjat F. Qaqish

Department of Biostatistics, University of North Carolina School of Public Health, Chapel Hill, NC, USA

Mark Wolfson

Department of Social Sciences and Health Policy, Division of Public Health Sciences, Wake Forest University School of Medicine, Winston-Salem, NC, USA

Maximum likelihood estimation techniques for subject-specific (SS) generalized linear mixed models and generalized estimating equations for marginal or population-averaged (PA) models are often used for the analysis of cluster-unit intervention trials. Although both classes of procedures account for the presence of within-cluster correlations, the interpretations of fixed effects including intervention effect parameters differ in SS and PA models. Furthermore, closed-form mathematical expressions relating SS and PA parameters from the two respective approaches are generally lacking. This paper investigates the special case of correlated Poisson responses where, for a log-linear model with normal random effects, exact relationships are available. Equivalent PA model representations of two SS models commonly used in the analysis of nested cross-sectional cluster trials with count data are derived. The mathematical results are illustrated with count data from a large non-randomized cluster trial to reduce underage drinking. Knowledge of relationships among parameters in the respective mean and covariance models is essential to understanding empirical comparisons of the two approaches.

Statistical Methods in Medical Research, Vol. 16, No. 2, 167-184 (2007)
DOI: 10.1177/0962280206071931


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