Stratification Trees for Adaptive Randomisation in Randomised Controlled Trials
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随机对照试验中用于自适应随机分配的分层树
- 研究问题
- 两阶段随机试验如何利用首轮数据，联合选择分层变量、分层方式及处理分配概率，从而降低平均处理效应估计方差？
- 方法与思路
- 作者将分层方案表示为决策树，用首轮实验估计分层树与层内分配概率，再配合适当估计量用于第二轮随机试验。
- 材料陈述的贡献
- 摘要称，该程序在分层树类别内达到最小渐近方差，并容纳分层区组随机化；模拟显示结合交叉验证可改善随意分层。
- 阅读关注点
- 应核对最优性所针对的树类别、两轮样本的条件、层内分配概率限制，以及适当估计量和交叉验证的具体构造。
- 阅读边界
- 摘要的最优性限于分层树类别且属于渐近结论，未说明全部条件；不能由此断言所有有限样本或所有随机设计下均最优。
原文摘要
Abstract This paper proposes an adaptive randomisation procedure for two-stage randomised controlled trials. The method uses data from a first-wave experiment in order to determine how to stratify in a second wave of the experiment, where the objective is to minimise the variance of an estimator for the average treatment effect. We consider selection from a class of stratified randomisation procedures which we call stratification trees: these are procedures whose strata can be represented as decision trees, with differing treatment assignment probabilities across strata. By using the first wave to estimate a stratification tree, we simultaneously select which covariates to use for stratification, how to stratify over these covariates, and the assignment probabilities within these strata. Our main result shows that using this randomisation procedure with an appropriate estimator results in an asymptotic variance which is minimal in the class of stratification trees. Moreover, our results are able to accommodate a large class of assignment mechanisms within strata, including stratified block randomisation. In a simulation study, we find that our method, paired with an appropriate cross-validation procedure, can improve on ad-hoc choices of stratification. We conclude by applying our method to the study in Karlan and Wood (2017, Journal of Behavioral and Experimental Economics, vol. 66, 1–8), where we estimate stratification trees using the first wave of their experiment.