On mitigating the analytical limitations of finely stratified experiments
On mitigating the analytical limitations of finely stratified experiments
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DOI：
10.1111/rssb.12290
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发表时间：
2018-11-01
影响因子：
5.8
通讯作者：
Fogarty, Colin B.
中科院分区：
文献类型：
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作者：
Fogarty, Colin B.
虽然从理论的角度来看是有吸引力的，精细分层的实验，如配对设计遭受某些分析的局限性，不存在于区组随机化实验与多个治疗和控制个人在每个区组。简而言之，当使用平均值的加权差异来估计样本平均治疗效应时，配对实验中的传统方差估计量是保守的，除非配对平均治疗效应在各对之间是恒定的;然而，在更粗略分层的实验中，如果治疗效应在区组内是恒定的，则相应的方差估计量是无偏的，即使它们在区组之间变化。从经典的最小二乘理论的见解，我们提出了一个改进的方差估计，是适当的精细分层实验。方差估计在期望上保持保守，但渐近地不比经典估计更保守，并且可以相当不保守。改善的幅度取决于观察到的协变量可以解释效应异质性的程度。在此估计量的辅助下，提出了一种新的恒定治疗效果的零假设检验。这些发现扩展到一些，但不是所有的，超总体模型，这取决于协变量是否被视为固定的样本。
Although attractive from a theoretical perspective, finely stratified experiments such as paired designs suffer from certain analytical limitations that are not present in block-randomized experiments with multiple treated and control individuals in each block. In short, when using a weighted difference in means to estimate the sample average treatment effect, the traditional variance estimator in a paired experiment is conservative unless the pairwise average treatment effects are constant across pairs; however, in more coarsely stratified experiments, the corresponding variance estimator is unbiased if treatment effects are constant within blocks, even if they vary across blocks. Using insights from classical least squares theory, we present an improved variance estimator that is appropriate in finely stratified experiments. The variance estimator remains conservative in expectation but is asymptotically no more conservative than the classical estimator and can be considerably less conservative. The magnitude of the improvement depends on the extent to which effect heterogeneity can be explained by observed covariates. Aided by this estimator, a new test for the null hypothesis of a constant treatment effect is proposed. These findings extend to some, but not all, superpopulation models, depending on whether the covariates are viewed as fixed across samples.