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

• Published in: Statistical methods in medical research Vol. 16; no. 2; pp. 167 - 184
• Main Authors: Young, Mary L., Preisser, John S., Qaqish, Bahjat F., Wolfson, Mark
• Format: Journal Article
• Language: English
• Published: London, England SAGE Publications 01.04.2007; Sage Publications Ltd
• Subjects: Adolescent; Adult; Alcohol consumption; Alcohol Drinking - prevention & control; Cluster Analysis; Female; Humans; Intervention; Interviews as Topic; Likelihood Functions; Male; Maximum likelihood estimation; Parameters; Random effects; Underage; United States; United States
• ISSN: 0962-2802; 1477-0334
• DOI: 10.1177/0962280206071931

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.