title: Comparison of subject-specific and population averaged models for count data from cluster-unit intervention trials.
abstract: 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.
authors.affiliation: Department of Biostatistics, University of North Carolina School of Public Health, Chapel Hill, NC, USA.
authors.forename: Mary L
authors.initials: ML
authors.lastname: Young
authors.forename: John S
authors.initials: JS
authors.lastname: Preisser
authors.forename: Bahjat F
authors.initials: BF
authors.lastname: Qaqish
authors.forename: Mark
authors.initials: M
authors.lastname: Wolfson
mesh_terms: D000293:Adolescent; D000328:Adult; D000428:Alcohol Drinking / Q000517:prevention & control*; D016000:Cluster Analysis; D005260:Female; D006801:Humans; D007407:Interviews as Topic; D016013:Likelihood Functions; D008297:Male; D014481:United States