基于精确度的顺序随机实验设计

Mattias Nordin, Mårten Schultzberg
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引用次数: 0

摘要

在本文中,我们考虑了单位依次进入实验的实验环境。我们的目标是制定停止规则,从而得出具有给定精度的治疗效果估计值。我们提出了一种固定宽度置信区间设计(FWCID),一旦达到预先指定的置信区间宽度,实验即终止。我们的研究表明,在这种设计下,均值差估计器是一个一致的平均治疗效果估计器,而且标准置信区间在几种设计版本中都有覆盖率和效率的渐近保证。此外,我们还提出了一种称为固定功率设计(FPD)的设计版本,在这种设计中,对于给定的治疗效果,给定的功率可以得到渐近保证,而无需指定治疗或对照结果的方差。此外,这种设计还给出了一致的均值差估计值,并能正确覆盖相应的标准置信区间。我们用蒙特卡罗模拟对我们的理论发现进行了补充,并将我们提出的设计与顺序实验文献中的标准设计进行了比较,结果表明我们的设计在几个重要方面优于这些设计。我们相信,我们的研究结果适用于许多单位依次进入的实验环境,例如临床试验,以及科技和电子商务行业使用的在线 A/B 测试。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Precision-based designs for sequential randomized experiments
In this paper, we consider an experimental setting where units enter the experiment sequentially. Our goal is to form stopping rules which lead to estimators of treatment effects with a given precision. We propose a fixed-width confidence interval design (FWCID) where the experiment terminates once a pre-specified confidence interval width is achieved. We show that under this design, the difference-in-means estimator is a consistent estimator of the average treatment effect and standard confidence intervals have asymptotic guarantees of coverage and efficiency for several versions of the design. In addition, we propose a version of the design that we call fixed power design (FPD) where a given power is asymptotically guaranteed for a given treatment effect, without the need to specify the variances of the outcomes under treatment or control. In addition, this design also gives a consistent difference-in-means estimator with correct coverage of the corresponding standard confidence interval. We complement our theoretical findings with Monte Carlo simulations where we compare our proposed designs with standard designs in the sequential experiments literature, showing that our designs outperform these designs in several important aspects. We believe our results to be relevant for many experimental settings where units enter sequentially, such as in clinical trials, as well as in online A/B tests used by the tech and e-commerce industry.
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