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.

翻译：自适应干预，亦称动态治疗方案，是根据个体基线信息及动态变化需求（包括对先前干预的响应）来指导治疗方案的预定义决策规则序列。分组自适应干预通过将干预指导扩展至集群层面（如诊所），其目标是改善集群内个体层面的结果（如诊所中的临床医生或患者）。分组序贯多分配随机试验是一种多阶段、多层次随机试验设计，用于构建高质量的分组自适应干预。在分组序贯多分配随机试验中，集群在多个干预决策点被随机分配；每个决策点的随机分配概率可能取决于先前数据的响应。在包括分组序贯多分配随机试验在内的集群随机试验中，一个关键挑战是集群样本量较小对统计推断造成的负面影响，特别是通过标准误估计体现。\par 本文开发了有限样本调整方法，用于改进分组序贯多分配随机试验中分组自适应干预因果效应的统计推断。本文提出的有限样本调整方法包括：(i) 基于自由度调整缩放方差估计量，(ii) 采用t分布（而非正态分布）作为参考分布，(iii) 使用“偏差校正”方差估计量。方法(iii)需要针对分组序贯多分配随机试验分析进行独特扩展。通过大量模拟实验检验了这些方法的性能。本文以基于学校的适应性认知行为疗法实施研究为例进行方法说明，该研究是一项分组序贯多分配随机试验，旨在构建分组自适应干预，以改善密歇根州高中内学校心理健康专业人员实施认知行为疗法的效果。