Saturation in G: simple & robust causal inference in cluster randomized trials with informative cluster sizes
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簇规模饱和与 g 计算：信息性簇规模下的稳健因果推断
- 研究问题
- 簇随机试验中，若簇规模关联结局或治疗效应，如何避免常规模型产生含义不清的加权对比，并区分个体与簇平均效应？
- 方法与思路
- 作者在适当加权的混合模型或 GEE 中加入簇规模主效应及治疗交互的饱和项，再通过 g 计算得到目标边际效应。
- 材料陈述的贡献
- 摘要称该方法可一致估计多种边际目标量，与模型稳健标准化估计有限样本等价，模拟中还显示效率与检测能力改善。
- 阅读关注点
- 应核对饱和项的精确定义、权重与目标量的对应关系，以及允许模型误设的范围、等价性证明和标准误计算方式。
- 阅读边界
- 这是 arXiv 预印本，同行评审或期刊接收未获核实；摘要未列出一致性的完整条件，误设稳健性不能据此无限推广。
原文摘要
Cluster randomized trials (CRTs) can exhibit informative cluster sizes (ICS) where cluster size is associated with outcomes and/or treatment effects. Under ICS, the individual and cluster-average treatment effects (iATE, cATE) can diverge, and the conventional linear mixed-effects model (LMM) and generalized estimating equation (GEE) with an exchangeable working correlation can produce data-dependent weighted contrasts that are not consistent for either estimand. In these settings with ICS, we propose easy to implement "cluster-size saturated models with g-computation" (CS-g), which employ a simple two-step adjustment to standard practice: (1.) augment the appropriately weighted working LMM or GEE with a saturated continuous cluster-size main effect and treatment x cluster-size interaction, and (2.) apply g-computation to target an interpretable marginal estimand. We prove that the appropriately weighted cluster-size saturated LMM with g-computation and more general cluster-size saturated GEE with g-computation can consistently target the iATE and cATE, among a broad class of interpretable estimands, while allowing for ICS. Crucially, this consistency holds under arbitrary misspecification of other model components, including the functional form of the saturated cluster-size terms. Furthermore, we demonstrate exact finite-sample equivalence between these consistent CS-g estimators and their model-robust standardization counterparts. Across simulations with continuous and binary outcomes, the proposed CS-g estimators were unbiased, more efficient than other consistent estimators, and returned greater power to detect ICS. A re-analysis of the PPACT P-CRT further illustrates the approach. Altogether, CS-g offers a simple, robust, and efficient route to target interpretable marginal effects in P-CRTs with ICS.