Inference for Two-stage Experiments under Covariate-Adaptive Randomization
协变量自适应随机化下两阶段实验的推断AI 解读 ↓
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协变量自适应随机化下两阶段实验的推断
- 研究问题
- 先随机分配簇、再在处理簇内随机分配个体的实验中，如何利用两级协变量有效估计主要效应和溢出效应并进行推断？
- 方法与思路
- 作者在同质部分干扰假设下分析两阶段分层随机化，提出平均值再平均的差分估计量、渐近方差估计，并研究设计和额外协变量调整。
- 材料陈述的贡献
- 摘要称建立一致性、渐近正态性及有效检验，并证明特定广义配对设计使各估计量渐近方差最小；忽略协变量可能损失效率或破坏推断。
- 阅读关注点
- 应核对同质部分干扰的具体含义、两阶段随机化独立性、簇与个体的加权方式，以及最小方差结论所比较的设计集合。
- 阅读边界
- 所据为 arXiv 预印本，同行评审或期刊接收未核实；摘要未列明簇规模和渐近条件，最优设计结论不能直接推广至任意干扰结构。
原文摘要
This paper studies inference in two-stage randomized experiments under covariate-adaptive randomization. In the initial stage of this experimental design, clusters (e.g., households, schools, or graph partitions) are stratified and randomly assigned to control or treatment groups based on cluster-level covariates. Subsequently, an independent second-stage design is carried out, wherein units within each treated cluster are further stratified and randomly assigned to either control or treatment groups, based on individual-level covariates. Under the homogeneous partial interference assumption, I establish conditions under which the proposed difference-in-``average of averages'' estimators are consistent and asymptotically normal for the corresponding average primary and spillover effects and develop consistent estimators of their asymptotic variances. Combining these results establishes the asymptotic validity of tests based on these estimators. My findings suggest that ignoring covariate information in the design stage can result in efficiency loss, and commonly used inference methods that ignore or improperly use covariate information can lead to either conservative or invalid inference. Then, I apply these results to studying optimal use of covariate information under covariate-adaptive randomization in large samples, and demonstrate that a specific generalized matched-pair design achieves minimum asymptotic variance for each proposed estimator. Finally, I discuss covariate adjustment, which incorporates additional baseline covariates not used for treatment assignment. The practical relevance of the theoretical results is illustrated through a simulation study and an empirical application.