“Sample size calculation in three-level cluster randomized trials using generalized estimating equation models”

Abstract: A cluster randomized trial (CRT) design is utilized when the randomization at the subject level is not practical. The unit of randomization might be hospitals, clinics, classrooms, etc. Such trials have two levels: subjects are nested into clusters. Three-level CRTs have been introduced recently. For example, interventions are randomly assigned to medical centers (“clusters”). Health care professionals within the same medical center are trained with the assigned intervention to provide care to participants in a trial. Thus twofold-nested-correlated data arise when there is a two-level-grouped structure. Teeremstra et al proposed a nested exchangeable correlation structure that accounts for two levels of clustering within the generalized estimating equations (GEE) approach. In this paper, we utilize GEE models to test the treatment effect in a two-group comparison for continuous, binary, or count data in three-level CRTs. Given the nested exchangeable correlation structure, the asymptotic variances of the estimator of the treatment effect are derived for different types of outcomes. Relative efficiency (RE) is defined as the ratio of variance of the estimator of the treatment effect for equal to unequal cluster sizes. A percentage increase in the number of clusters is proposed due to efficiency loss from unequal cluster sizes.

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