摘要翻译：
本文研究了随机对照试验中存在多个治疗时的协变量-自适应随机推理。更具体地说，我们研究一个或多个治疗相对于其他治疗或一个对照的平均效果的推论。如Bugni等人。(2018)，协变量-自适应随机化是指先根据基线协变量分层，再分配治疗状态，从而实现各阶层内部平衡的随机化方案。与Bugni等人形成对比。(2018)，我们不仅允许多个治疗，而且进一步允许分配给每个治疗的单位比例跨层变化。我们首先研究了完全饱和线性回归估计量的性质，即每个处理的指标和每个层的指标之间所有相互作用的结果的线性回归。我们证明了基于这些估计的检验是无效的，使用通常的渐近方差的异方差相合估计；另一方面，基于这些估计量的检验和我们提供的渐近方差的适当估计量是精确的。对于分配给每个处理的单位的目标比例不随层而变化的特殊情况，我们还考虑了基于从具有层固定效应的线性回归导出的估计量的检验，即每个处理的指标和每个层的指标的结果的线性回归。我们证明了基于这些估计的检验是保守的，而基于这些估计的检验和我们提供的适当的渐近方差估计是精确的。一个模拟研究说明了我们的理论结果的实际相关性。
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英文标题：
《Inference under Covariate-Adaptive Randomization with Multiple
  Treatments》
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作者：
Federico A. Bugni and Ivan A. Canay and Azeem M. Shaikh
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最新提交年份：
2019
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分类信息：

一级分类：Economics        经济学
二级分类：Econometrics        计量经济学
分类描述：Econometric Theory, Micro-Econometrics, Macro-Econometrics, Empirical Content of Economic Relations discovered via New Methods, Methodological Aspects of the Application of Statistical Inference to Economic Data.
计量经济学理论，微观计量经济学，宏观计量经济学，通过新方法发现的经济关系的实证内容，统计推论应用于经济数据的方法论方面。
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一级分类：Statistics        统计学
二级分类：Methodology        方法论
分类描述：Design, Surveys, Model Selection, Multiple Testing, Multivariate Methods, Signal and Image Processing, Time Series, Smoothing, Spatial Statistics, Survival Analysis, Nonparametric and Semiparametric Methods
设计，调查，模型选择，多重检验，多元方法，信号和图像处理，时间序列，平滑，空间统计，生存分析，非参数和半参数方法
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英文摘要：
  This paper studies inference in randomized controlled trials with covariate-adaptive randomization when there are multiple treatments. More specifically, we study inference about the average effect of one or more treatments relative to other treatments or a control. As in Bugni et al. (2018), covariate-adaptive randomization refers to randomization schemes that first stratify according to baseline covariates and then assign treatment status so as to achieve balance within each stratum. In contrast to Bugni et al. (2018), we not only allow for multiple treatments, but further allow for the proportion of units being assigned to each of the treatments to vary across strata. We first study the properties of estimators derived from a fully saturated linear regression, i.e., a linear regression of the outcome on all interactions between indicators for each of the treatments and indicators for each of the strata. We show that tests based on these estimators using the usual heteroskedasticity-consistent estimator of the asymptotic variance are invalid; on the other hand, tests based on these estimators and suitable estimators of the asymptotic variance that we provide are exact. For the special case in which the target proportion of units being assigned to each of the treatments does not vary across strata, we additionally consider tests based on estimators derived from a linear regression with strata fixed effects, i.e., a linear regression of the outcome on indicators for each of the treatments and indicators for each of the strata. We show that tests based on these estimators using the usual heteroskedasticity-consistent estimator of the asymptotic variance are conservative, but tests based on these estimators and suitable estimators of the asymptotic variance that we provide are exact. A simulation study illustrates the practical relevance of our theoretical results.
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PDF链接：
https://arxiv.org/pdf/1806.04206