Mediation analyses in randomized controlled trials (RCTs) can unpack potential causal pathways between interventions and outcomes and help the iterative improvement of interventions. When designing RCTs investigating these mechanisms, two key considerations are (a) the sample size needed to achieve adequate statistical power and (b) the efficient use of resources. The current study has developed closed-form statistical power formulas for RCTs investigating mediation effects with and without covariates under the Sobel and joint significance tests. The power formulas are functions of sample size, sample allocation between treatment conditions, effect sizes in the treatment-mediator and mediator-outcome paths, and other common parameters (e.g., significance level, one- or two-tailed test). The power formulas allow us to assess how covariates impact the magnitude of mediation effects and statistical power. Accounting for the potential unequal sampling costs between treatment conditions, we have further developed an optimal design framework to identify optimal sample allocations that provide the maximum statistical power under a fixed budget or use the minimum resources to achieve a target power. Illustrations show that the proposed method can identify more efficient and powerful sample allocations than conventional designs with an equal number of individuals in each treatment condition. We have implemented the methods in the R package odr to improve the accessibility of the work. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

中文翻译：

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研究中介效应的随机对照试验的统计功效和优化设计。


随机对照试验（RCT）中的中介分析可以揭示干预措施和结果之间的潜在因果路径，并有助于干预措施的迭代改进。在设计研究这些机制的随机对照试验时，两个关键考虑因素是（a）实现足够统计功效所需的样本量和（b）资源的有效利用。当前的研究开发了用于随机对照试验的封闭式统计功效公式，用于调查索贝尔和联合显着性检验下有或没有协变量的中介效应。功效公式是样本大小、治疗条件之间的样本分配、治疗-中介和中介-结果路径中的效应大小以及其他常见参数（例如显着性水平、单尾或双尾检验）的函数。功效公式使我们能够评估协变量如何影响中介效应和统计功效的大小。考虑到处理条件之间潜在的不平等抽样成本，我们进一步开发了一个最佳设计框架，以确定最佳样本分配，在固定预算下提供最大统计功效或使用最少资源实现目标功效。插图表明，与在每种治疗条件下具有相同数量个体的传统设计相比，所提出的方法可以识别更有效和更强大的样本分配。我们实现了 R 包 odr 中的方法，以提高工作的可访问性。 （PsycInfo 数据库记录 (c) 2024 APA，保留所有权利）。