Experimental Design and Analysis of Multiple Group Individually-Randomized Group Trials

Abstract Information: We consider a class of individually-randomized group trials that introduces a (partially) cross-classified structure in the treatment condition (only). The novel feature of this design is that the nature of the treatment induces a clustering structure that involves two or more non-nested groups among individuals in the treatment condition that does not exist in the control condition. Although a review of prior substantive literature suggests that multiple group individually-randomized group trials are present in theory and practice, the appropriate analysis of this structure has largely gone unexamined and undeveloped. For example, contemporary interventions in education often combine multiple interventions (e.g., tutoring and small group mindset training) to more holistically address student needs (e.g., Wanzek et al., 2020). Similarly, interventions in health often coordinate and integrate multiple services to supplement health needs with social or psychological needs. (e.g., reduction of opioid use through an intervention that combines health education coursework with social support groups; Sandhu, et al., 2023). In this study, we develop the statistical theory that motivates this design, map out its use in practice, and develop estimation methods and closed-form expressions to track treatment effects, their sampling variability and the statistical power to detect the treatment effect. Collectively, the results provide the core tools to effectively and efficiently design and analyze studies drawing on multiple group individually-randomized group trials.