Comparison of three-level cluster randomized trials using quantile dispersion graphs

Abstract

The purpose of this article is to evaluate and compare several three-level cluster randomized designs on the basis of their power functions. The power function of cluster designs depends on the intracluster correlations (ICCs), which are generally unknown at the planning stage. Thus, to compare these designs a prior knowledge of the ICCs is required. Three interval estimation methods are proposed for assigning joint confidence intervals to the two ICCs (corresponding to each cluster level). A detailed simulation study comparing the confidence intervals attained by the different techniques is given. The technique of quantile dispersion graphs is used for comparing the three-level cluster designs. For a given design, quantiles of the power function, are obtained for various effect sizes. These quantiles are functions of the unknown ICC coefficients. To address the dependence of the quantiles on the correlations, a confidence region is computed, and used as a parameter space. A three-level nested data set collected by the University of Michigan to study various school reforms on the achievements of students is used to illustrate the proposed methodology.