标题： 用于设计具有连续效果和实施终点的混合型2型集群随机试验的方法比较 显示英文标题

标题： A comparison of methods for designing hybrid type 2 cluster-randomized trials with continuous effectiveness and implementation endpoints

摘要： 混合型2类研究因其能够将实施和健康结果作为主要终点进行评估而越来越受欢迎。 通常作为整群随机试验（CRTs）进行，有五种设计方法可以有效计算这些研究的统计功效：p值调整方法、合并结果方法、单个加权1-自由度检验、析取2-自由度检验和联合检验。 我们从理论上和数值上比较了所有方法。 对统计功效方程的理论比较使我们能够确定是否有任何方法在整体上比其他方法更强大或更弱。 结果显示，p值调整方法始终不如合并结果方法和单个1-自由度检验强大。 我们还确定了析取2-自由度检验比单个1-自由度检验弱的条件。 由于我们的理论比较显示，在某些条件下某些方法可能比其他方法更强大，而在其他条件下则不那么强大，因此我们进行了数值研究以了解这些差异。 创建了crt2power R包，用于计算具有两个连续主要终点的CRTs的统计功效或样本量。 使用这个包，我们在30,000个输入场景中进行了数值评估，以比较统计功效。 发现了特定模式，其中某种方法始终能获得最高的统计功效。 当治疗效应不同时，析取2-自由度检验往往具有更高的统计功效。 当治疗效应大小相同时，单个1-自由度检验往往具有更高的统计功效。 综上所述，这些比较提供了更清晰的见解，以指导混合型2类研究统计功效方法的选择。 显示英文摘要

摘要： Hybrid type 2 studies are gaining popularity for their ability to assess both implementation and health outcomes as co-primary endpoints. Often conducted as cluster-randomized trials (CRTs), five design methods can validly power these studies: p-value adjustment methods, combined outcomes approach, single weighted 1-DF test, disjunctive 2-DF test, and conjunctive test. We compared all of the methods theoretically and numerically. Theoretical comparisons of the power equations allowed us to identify if any method globally had more or less power than other methods. It was shown that the p-value adjustment methods are always less powerful than the combined outcomes approach and the single 1-DF test. We also identified the conditions under which the disjunctive 2-DF test is less powerful than the single 1-DF test. Because our theoretical comparison showed that some methods could be more powerful than others under certain conditions, and less powerful under others, we conducted a numerical study to understand these differences. The crt2power R package was created to calculate the power or sample size for CRTs with two continuous co-primary endpoints. Using this package, we conducted a numerical evaluation across 30,000 input scenarios to compare statistical power. Specific patterns were identified where a certain method consistently achieved the highest power. When the treatment effects are unequal, the disjunctive 2-DF test tends to have higher power. When the treatment effect sizes are the same, the single 1-DF test tends to have higher power. Together, these comparisons provide clearer insights to guide method selection for powering hybrid type 2 studies.