中文摘要
本文提出一种用于两阶段随机对照试验的自适应随机化程序。该方法利用第一轮实验的数据来确定如何在第二轮实验中进行分层，其目标是最小化平均处理效应估计量的方差。我们考虑从一类我们称之为分层树的分层随机化程序中进行选择：这些程序的层可以表示为决策树，且不同层的处理分配概率不同。通过利用第一轮数据估计一棵分层树，我们同时选择哪些协变量用于分层、如何在这些协变量上进行分层，以及各层内的分配概率。我们的主要结果表明，使用这一随机化程序并配合适当的估计量，可以得到在分层树类中渐近方差最小的结果。此外，我们的结果能够容纳层内一大类分配机制，包括分层区组随机化。在一项模拟研究中，我们发现，我们的方法配合适当的交叉验证程序，能够优于分层方案的自定式选择。最后，我们将该方法应用于Karlan和Wood (2017, Journal of Behavioral and Experimental Economics, vol. 66, 1–8)的研究，其中我们使用其第一轮实验来估计分层树。
Abstract
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.