Cluster randomized trials (CRTs) are studies where treatment is randomized at the cluster level but outcomes are typically collected at the individual level. When CRTs are employed in pragmatic settings, baseline population characteristics may moderate treatment effects, leading to what is known as heterogeneous treatment effects (HTEs). Pre-specified, hypothesis-driven HTE analyses in CRTs can enable an understanding of how interventions may impact subpopulation outcomes. While closed-form sample size formulas have recently been proposed, assuming known intracluster correlation coefficients (ICCs) for both the covariate and outcome, guidance on optimal cluster randomized designs to ensure maximum power with pre-specified HTE analyses has not yet been developed. We derive new design formulas to determine the cluster size and number of clusters to achieve the locally optimal design (LOD) that minimizes variance for estimating the HTE parameter given a budget constraint. Given the LODs are based on covariate and outcome-ICC values that are usually unknown, we further develop the maximin design for assessing HTE, identifying the combination of design resources that maximize the relative efficiency of the HTE analysis in the worst case scenario. In addition, given the analysis of the average treatment effect is often of primary interest, we also establish optimal designs to accommodate multiple objectives by combining considerations for studying both the average and heterogeneous treatment effects. We illustrate our methods using the context of the Kerala Diabetes Prevention Program CRT, and provide an R Shiny app to facilitate calculation of optimal designs under a wide range of design parameters.

翻译：整群随机试验（CRT）是将处理随机化分配到整群层级、但结局通常在个体层面收集的研究。当CRT应用于务实环境中时，基线人群特征可能调节处理效应，从而产生所谓的异质性处理效应（HTE）。在CRT中进行预先指定、基于假设的HTE分析，可帮助理解干预措施如何影响亚组人群的结局。尽管近期已提出假设协变量与结局的组内相关系数（ICC）已知的闭合式样本量公式，但关于如何确保预设HTE分析具有最大检验效能的优化整群随机化设计指导仍属空白。我们推导出新的设计公式，用于确定在预算约束下最小化HTE参数估计方差的局部最优设计（LOD）所需的整群规模与整群数量。由于LOD基于通常未知的协变量ICC和结局ICC值，我们进一步开发了评估HTE的最大最小设计，识别在最坏情景下最大化HTE分析相对效率的设计资源组合。此外，鉴于平均处理效应分析常为主要关注点，我们还通过综合考量平均与异质性处理效应研究，建立了适配多目标的最优设计。我们以喀拉拉邦糖尿病预防计划CRT为背景演示方法，并提供R Shiny应用程序以促进在广泛设计参数下的最优设计计算。