A tutorial on conducting sample size and power calculations for detecting treatment effect heterogeneity in cluster randomized trials with linear mixed models
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用线性混合模型检测整群随机试验处理效应异质性：样本量与功效教程
- 研究问题
- 整群随机试验计划检验处理与协变量交互或亚群体效应差异时，如何确定群数和群大小，并考虑比总体平均效应更复杂的设计参数？
- 方法与思路
- 作者汇总不同整群随机设计及连续、二元结局下线性混合模型的既有功效和样本量方法，配套 R Shiny 计算器并以真实试验示范。
- 材料陈述的贡献
- 摘要称，教程提供统一参考与在线计算工具，重点讨论结局和协变量的群内相关系数如何影响预先设定的异质性检验功效。
- 阅读关注点
- 应核对不同设计和结局对应的公式、交互效应尺度、群内相关参数的设定依据，以及计算器采用的近似与真实试验示范的适用条件。
- 阅读边界
- 这是 arXiv 预印本，同行评审及期刊接收未核验。摘要未列出公式、设计参数或计算器验证结果，不能直接据此确定具体试验样本量。
原文摘要
Cluster-randomized trials (CRTs) are a well-established class of designs for evaluating community-based interventions. An essential task in planning these trials is determining the number of clusters and cluster sizes needed to achieve sufficient statistical power for detecting a clinically relevant effect size. While methods for evaluating the average treatment effect (ATE) for the entire study population are well-established, sample size methods for testing heterogeneity of treatment effects (HTEs), i.e., treatment-covariate interaction or difference in subpopulation-specific treatment effects, in CRTs have only recently been developed. For pre-specified analyses of HTEs in CRTs, effect-modifying covariates should, ideally, be accompanied by sample size or power calculations to ensure the trial has adequate power for the planned analyses. Power analysis for testing HTEs is more complex than for ATEs due to the additional design parameters that must be specified. Power and sample size formulas for testing HTEs via linear mixed effects (LME) models have been separately derived for different cluster-randomized designs, including single and multi-period parallel designs, crossover designs, and stepped-wedge designs, and for continuous and binary outcomes. This tutorial provides a consolidated reference guide for these methods and enhances their accessibility through an online R Shiny calculator. We further discuss key considerations for conducting sample size and power calculations to test pre-specified HTE hypotheses in CRTs, highlighting the importance of specifying advanced estimates of intracluster correlation coefficients for both outcomes and covariates, and their implications for power. The sample size methodology and calculator functionality are demonstrated through a real CRT example.