Comparing cluster-level dynamic treatment regimens using sequential, multiple assignment, randomized trials: Regression estimation and sample size considerations

Cluster-level dynamic treatment regimens can be used to guide sequential, intervention or treatment decision-making at the cluster level in order to improve outcomes at the individual or patient-level. In a cluster-level DTR, the intervention or treatment is potentially adapted and re-adapted over time based on changes in the cluster that could be impacted by prior intervention, including based on aggregate measures of the individuals or patients that comprise it. Cluster-randomized sequential multiple assignment randomized trials (SMARTs) can be used to answer multiple open questions preventing scientists from developing high-quality cluster-level DTRs. In a cluster-randomized SMART, sequential randomizations occur at the cluster level and outcomes are at the individual level. This manuscript makes two contributions to the design and analysis of cluster-randomized SMARTs: First, a weighted least squares regression approach is proposed for comparing the mean of a patient-level outcome between the cluster-level DTRs embedded in a SMART. The regression approach facilitates the use of baseline covariates which is often critical in the analysis of cluster-level trials. Second, sample size calculators are derived for two common cluster-randomized SMART designs for use when the primary aim is a between-DTR comparison of the mean of a continuous patient-level outcome. The methods are motivated by the Adaptive Implementation of Effective Programs Trial, which is, to our knowledge, the first-ever cluster-randomized SMART in psychiatry.