Longitudinal cluster randomized trials (L-CRTs) are increasingly used to evaluate the cost-effectiveness of healthcare interventions across multiple assessment periods, yet design methods for powering these trials remain underdeveloped. Existing methods for cost-effectiveness analyses in cluster settings are limited to simple parallel-arm cluster randomized trials with a single follow-up assessment period. These methods cannot accommodate the complex correlation structures in L-CRTs conducted over multiple periods, which require differentiation between within-period and between-period correlations for both clinical and cost outcomes, as well as between-outcome correlations. Moreover, while substantial methodological advances have been made for the design of L-CRTs with univariate outcomes, none specifically address cost-effectiveness objectives where clinical and cost outcomes must be jointly modeled. We provide a design-stage framework for powering cost-effectiveness L-CRTs across three design variants: parallel-arm, crossover, and stepped wedge designs. We derive closed-form variance expressions for the generalized least squares estimator of the average incremental net monetary benefit under a bivariate linear mixed model. We propose a standardized ceiling ratio that adjusts willingness-to-pay for relative outcome variability to inform optimal design. We then develop local optimal designs that maximize statistical power under known correlation parameters and MaxiMin designs that ensure robust performance across parameter uncertainty for all three design variants. Through a real stepped wedge trial data example, we demonstrate the sample size calculation for testing intervention cost-effectiveness under local optimal and MaxiMin designs.

翻译：纵向群组随机试验（L-CRTs）日益被用于评估医疗干预措施在多个评估周期内的成本效益，然而为这些试验提供统计效力的设计方法仍不成熟。现有针对群组设置中成本-效益分析的方法仅限于单次随访评估周期的简单平行臂群组随机试验。这些方法无法处理多周期L-CRTs中复杂的相关结构——既需要对临床和成本结局的周期内与周期间相关性进行区分，也需要考虑结局间的相关性。此外，尽管针对单变量结局的L-CRTs设计已取得重要方法论进展，但尚无专门针对成本-效益目标的方法，而在此类目标中临床与成本结局需联合建模。我们为三种设计变体（平行臂、交叉和阶梯楔形设计）下提供成本-效益L-CRTs统计效力的设计阶段框架。在双变量线性混合模型框架下，推导出平均增量净货币收益的广义最小二乘估计量的闭式方差表达式。提出标准化支付意愿阈值比，该比值根据相对结局变异性调整支付意愿以指导最优设计。进而针对已知相关性参数开发最大化统计效力的局部最优设计，以及确保三种设计变体在参数不确定性下保持稳健性能的MaxiMin设计。通过真实阶梯楔形试验数据实例，展示在局部最优与MaxiMin设计下检验干预成本-效益的样本量计算方法。