In cluster-randomized trials, groups of subjects (clusters) are assigned to treatments, whereas observations are taken on the individual subjects. Since observations on subjects in the same cluster are typically more similar than observations from different clusters, analyses of such data must take intracluster correlation into account rather than assuming independence among all observations. Random effects models are useful for this purpose. The problem becomes more complicated if, in addition, repeated observations are taken on subjects over time. This introduces intraindividual correlation, which is typical for longitudinal studies. The Waterloo Smoking Prevention Project, study 3 (WSPP3), 1989-1996, is a study giving rise to cluster-correlated longitudinal data, where schools were randomized to either a smoking intervention program or to a control condition. Smoking status was assessed on grade 6 students in these schools, with annual follow-up observations throughout elementary and high school years. The authors illustrate the use of a generalized random effects model for analyzing this type of data. This model obtains appropriate estimates and standard errors for both individual-level covariates and those at the level of the cluster.

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American Journal of Epidemiology
School of Mathematics and Statistics

Sashegyi, A.I. (Andreas I.), Brown, K.S. (K. Stephen), & Farrell, P. (2000). Application of a generalized random effects regression model for cluster-correlated longitudinal data to a school-based smoking prevention trial. American Journal of Epidemiology, 152(12), 1192–1200. doi:10.1093/aje/152.12.1192