最佳化Tie-Breaker回归不连续设计
Optimizing the tie-breaker regression discontinuity design
摘要：
受客户忠诚度计划和奖学金计划的激励，我们研究了由随机对照试验（RCT）和回归不连续设计（RDD）混合而成的决胜设计。我们量化了平局决胜设计的统计效率，其中观察的受试者中有一部分$Δ$在RCT中。在双线回归中，统计效率随$Δ$单调增加，因此RCT可使效率最大化。我们指出了决胜局与RDD相比的其他优势：对于非参数回归，边界偏差要小得多，对于二次回归，方差大大减小。对于双线模型，我们可以量化治疗分配的短期价值，该比较有利于较小的$Δ$，RDD最佳。我们解决这些探索和开发目标之间的最佳权衡。通常的决胜局设计对按分配变量排序的中间$Δ$受试者应用RCT。我们量化了其他设计的效率，例如只在从顶部开始的第二个十分位中进行实验。我们还表明，在一些一般的参数模型的蒙特卡罗评估可以取代矩阵代数。
英文摘要：
Motivated by customer loyalty plans and scholarship programs, we study tie-breaker designs which are hybrids of randomized controlled trials (RCTs) and regression discontinuity designs (RDDs). We quantify the statistical efficiency of a tie-breaker design in which a proportion $Δ$ of observed subjects are in the RCT. In a two line regression, statistical efficiency increases monotonically with $Δ$, so efficiency is maximized by an RCT. We point to additional advantages of tie-breakers versus RDD: for a nonparametric regression the boundary bias is much less severe and for quadratic regression, the variance is greatly reduced. For a two line model we can quantify the short term value of the treatment allocation and this comparison favors smaller $Δ$ with the RDD being best. We solve for the optimal tradeoff between these exploration and exploitation goals. The usual tie-breaker design applies an RCT on the middle $Δ$ subjects as ranked by the assignment variable. We quantify the efficiency of other designs such as experimenting only in the second decile from the top. We also show that in some general parametric models a Monte Carlo evaluation can be replaced by matrix algebra.
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