Multisite Partially Nested Designs: Estimation, Inference, and Design

We develop design and analysis methods for the multisite replication of partially nested experiments. A novel feature in this design is that replicating partially nested designs across multiple sites can create site-level random effects that are correlated yet distinct across treatment conditions. Such site- and condition-specific effects can arise because, for example, the treatment condition introduces an intermediate layer of clustering—such as shared provider influences—that introduces dependencies among individuals within the treatment condition in ways that are absent in the control group. Although a review of prior substantive literature suggests that multisite partially nested designs are embedded in both theory and practice, the deliberate design and proper analysis of these structures have largely been overlooked. In this study, we outline the motivation for this design, map out its use in practice, and develop methods to estimate treatment effects, quantify cross-site heterogeneity, and assess statistical power to detect both the treatment effect and the cross-site heterogeneity. Collectively, the results provide the tools to effectively and efficiently design and analyze studies drawing on multisite partially nested experiments.