论文标题
与一般响应的平等和不等分配的随机实验中阻断设计的最佳性
The Optimality of Blocking Designs in Equally and Unequally Allocated Randomized Experiments with General Response
论文作者
论文摘要
我们考虑了在共同的实验终点（例如连续（回归），发病率，比例和生存）下的两臂随机实验中差异估计器的性能。我们检查了对治疗组的平等分配和不平等分配的绩效，我们考虑了Neyman随机模型和人口模型。我们表明，在Neyman模型中，唯一的随机性是治疗操作，没有免费的午餐：完全随机分组是估算器的平均误差的最小值。在人群模型中，每个主题的均值均值为零，最佳设计是确定性的完美平衡分配。但是，该分配通常是计算和进一步的NP-硬化，这取决于未知的响应参数。在考虑Kapelner等人的尾标准时。 （2021），我们显示的最佳设计不如完全随机化，而不是确定性的完美平衡分配。我们证明Fisher的阻塞设计提供了渐近最佳的实验随机性。理论上的结果得到了所有被考虑的实验设置中的模拟支持。
We consider the performance of the difference-in-means estimator in a two-arm randomized experiment under common experimental endpoints such as continuous (regression), incidence, proportion and survival. We examine performance under both equal and unequal allocation to treatment groups and we consider both the Neyman randomization model and the population model. We show that in the Neyman model, where the only source of randomness is the treatment manipulation, there is no free lunch: complete randomization is minimax for the estimator's mean squared error. In the population model, where each subject experiences response noise with zero mean, the optimal design is the deterministic perfect-balance allocation. However, this allocation is generally NP-hard to compute and moreover, depends on unknown response parameters. When considering the tail criterion of Kapelner et al. (2021), we show the optimal design is less random than complete randomization and more random than the deterministic perfect-balance allocation. We prove that Fisher's blocking design provides the asymptotically optimal degree of experimental randomness. Theoretical results are supported by simulations in all considered experimental settings.
