Q -Learning with clustered-SMART (cSMART) data: examining moderators in the construction of clustered adaptive interventions

Abstract A clustered adaptive intervention (cAI) is a prespecified sequence of decision rules that guides practitioners on how best—and based on which measures—to tailor cluster-level intervention to improve outcomes at the level of individuals within the clusters. A clustered sequential multiple assignment randomized trial (cSMART) is a type of trial that is used to inform the empirical development of a cAI. A common analytic goal in a cSMART focuses on assessing causal effect moderation by candidate tailoring variables. We introduce a clustered Q-learning framework with the M-out-of-N cluster bootstrap using data from a cSMART to evaluate whether a set of candidate tailoring variables may be useful in defining an optimal cAI. This approach could construct confidence intervals (CIs) with near-nominal coverage to assess parameters indexing the causal effect moderation function. Specifically, it allows reliable inferences concerning the utility of candidate tailoring variables in constructing a cAI that maximizes a mean end-of-study outcome even when “non-regularity,” a well-known challenge, exists. Simulations demonstrate the numerical performance of the proposed method across varying non-regularity conditions and investigate the impact of varying numbers of clusters and intra-cluster correlation coefficients on CI coverage. Methods are applied on the ADEPT dataset to inform the construction of a clinic-level cAI for improving evidence-based practice in treating mood disorders.