Multilevel Factorial Designs in Intervention Development

Factorial designs are one of the many useful experimental tools that can be used to inform the construction of multicomponent behavioral, biobehavioral, and biomedical interventions. Clustering presents various challenges to investigators aiming to implement such designs. Clustering means that some or all individuals are nested in higher-level social or administrative units (e.g., schools, therapy groups). These multilevel settings generate dependency in data within clusters because individuals in one cluster tend to be more similar to each other than to individuals in other clusters. Such dependency has implications for the design of the factorial experiment, the model used to analyze the data, and the power for detecting the effects of interest. In this chapter, we discuss five classes of multilevel factorial designs that vary in terms of the nature of clustering (i.e., the process by which individuals become clustered or the reason why they are considered to be clustered), as well as the randomization scheme employed (i.e., whether randomization to experimental conditions is done at the individual level, the cluster level, or both). For each of the five classes, we discuss the scientific motivation for employing the multilevel factorial design, provide a model for analyzing data arising from employing a multilevel factorial design of this class, and offer formulas that investigators can use to calculate the expected power. Design considerations are also discussed with respect to each class. Our goal is to provide a comprehensive review to help investigators select the most suitable design given their scientific questions, target population, and available resources.