Finite-sample adjustments for comparing clustered adaptive interventions using data from a clustered SMART

Adaptive interventions, aka dynamic treatment regimens, are sequences of pre-specified decision rules that guide the provision of treatment for an individual given information about their baseline and evolving needs, including in response to prior intervention. Clustered adaptive interventions (cAIs) extend this idea by guiding the provision of intervention at the level of clusters (e.g., clinics), but with the goal of improving outcomes at the level of individuals within the cluster (e.g., clinicians or patients within clinics). A clustered, sequential multiple-assignment randomized trials (cSMARTs) is a multistage, multilevel randomized trial design used to construct high-quality cAIs. In a cSMART, clusters are randomized at multiple intervention decision points; at each decision point, the randomization probability can depend on response to prior data. A challenge in cluster-randomized trials, including cSMARTs, is the deleterious effect of small samples of clusters on statistical inference, particularly via estimation of standard errors. \par This manuscript develops finite-sample adjustment (FSA) methods for making improved statistical inference about the causal effects of cAIs in a cSMART. The paper develops FSA methods that (i) scale variance estimators using a degree-of-freedom adjustment, (ii) reference a t distribution (instead of a normal), and (iii) employ a ``bias corrected" variance estimator. Method (iii) requires extensions that are unique to the analysis of cSMARTs. Extensive simulation experiments are used to test the performance of the methods. The methods are illustrated using the Adaptive School-based Implementation of CBT (ASIC) study, a cSMART designed to construct a cAI for improving the delivery of cognitive behavioral therapy (CBT) by school mental health professionals within high schools in Michigan.