Principled analysis of crossover designs: causal effects, efficient estimation, and robust inference
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交叉设计的系统分析：因果效应、有效估计与稳健推断
- 研究问题
- 在同一单位依次接受不同处理的交叉实验中，如何识别当前处理效应与历史处理的延续效应，并降低模型误设对推断的影响？
- 方法与思路
- 作者采用潜在结果与基于设计的框架，将处理分配机制、回归系数约束和单位权重纳入统一的最小二乘分析程序。
- 材料陈述的贡献
- 摘要称，该框架统一识别、估计和方差计算，并可在工作回归模型误设时仍提供一致、有效的点估计与有效方差估计。
- 阅读关注点
- 应核对不同处理序列对应的因果目标、潜在结果限制及可识别条件，并检查权重与系数约束如何支持效率和方差结论。
- 阅读边界
- 所据为 arXiv 预印本，不能确认同行评审或期刊接收；摘要未列出各类交叉设计的具体假设及模型误设稳健性的适用边界。
原文摘要
Crossover designs randomly assign each unit to receive a sequence of treatments. By comparing outcomes within the same unit, these designs can effectively eliminate between-unit variation and facilitate the identification of both instantaneous effects of current treatments and carryover effects from past treatments. They are widely used in traditional biomedical studies and are increasingly adopted in modern digital platforms. However, standard analyses of crossover designs often rely on strong parametric models, making inference vulnerable to model misspecification. This paper adopts a design-based framework to analyze general crossover designs. We make two main contributions. First, we use potential outcomes to formally define the causal estimands and assumptions on the data-generating process. For any given type of crossover design and assumptions on potential outcomes, we outline a procedure for identification and estimation, emphasizing the central role of the treatment assignment mechanism in design-based inference. Second, we unify the analysis of crossover designs using least squares, with restrictions on the coefficients and weights on the units. Based on the theory, we recommend the specification of the regression function, weighting scheme, and coefficient restrictions to assess identifiability, construct efficient estimators, and estimate variances in a unified fashion. Crucially, the least squares procedure is simple to implement, and yields not only consistent and efficient point estimates but also valid variance estimates even when the working regression model is misspecified.