  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.
