An Approximation Algorithm for Blocking of an Experimental Design
An Approximation Algorithm for Blocking of an Experimental Design
复制标题
实验设计分块的近似算法
DOI：
10.1111/rssb.12545
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发表时间：
2022
期刊：
影响因子：
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通讯作者：
Karmakar, Bikram
中科院分区：
文献类型：
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作者：
Karmakar, Bikram
与完全随机化设计相比，区组随机化设计用于提高治疗效果估计的精度。区组是一组相对同质的单元，因此如果治疗无效，则往往会产生相对相似的结果。找到的问题的最佳块的单位成相等大小的块的任何给定的大小大于2是已知的是一个困难的问题，有没有多项式时间的方法保证找到最佳的阻塞。现有的解决该问题的方法都是启发式方法。我们提出的方法，在多项式时间内运行，并保证阻塞，可证明接近最佳阻塞。在我们所有的模拟研究中，所提出的方法表现更好，创建更好的同质块，与现有的方法相比。我们的分块方法的目的是最大限度地减少所有成对的单位在同一块的差异。我们表明，边界的最大差异，确保在平均治疗效果估计的误差是类似的所有治疗分配有界。相反，如果区组限制了这些差异的平均值或总和，则在几个治疗分配中，平均治疗效果估计的误差仍然很大。
Blocked randomized designs are used to improve the precision of treatment effect estimates compared to a completely randomized design. A block is a set of units that are relatively homogeneous and consequently would tend to produce relatively similar outcomes if the treatment had no effect. The problem of finding the optimal blocking of the units into equal sized blocks of any given size larger than two is known to be a difficult problem—there is no polynomial time method guaranteed to find the optimal blocking. All available methods to solve the problem are heuristic methods. We propose methods that run in polynomial time and guarantee a blocking that is provably close to the optimal blocking. In all our simulation studies, the proposed methods perform better, create better homogeneous blocks, compared with the existing methods. Our blocking method aims to minimize the maximum of all pairwise differences of units in the same block. We show that bounding this maximum difference ensures that the error in the average treatment effect estimate is similarly bounded for all treatment assignments. In contrast, if the blocking bounds the average or sum of these differences, the error in the average treatment effect estimate can still be large in several treatment assignments.