We propose a generalization of the standard matched pairs design in which experimental units (often geographic regions or geos) may be combined into larger units/regions called "supergeos" in order to improve the average matching quality. Unlike optimal matched pairs design which can be found in polynomial time (Lu et al. 2011), this generalized matching problem is NP-hard. We formulate it as a mixed-integer program (MIP) and show that experimental design obtained by solving this MIP can often provide a significant improvement over the standard design regardless of whether the treatment effects are homogeneous or heterogeneous. Furthermore, we present the conditions under which trimming techniques that often improve performance in the case of homogeneous effects (Chen and Au, 2022), may lead to biased estimates and show that the proposed design does not introduce such bias. We use empirical studies based on real-world advertising data to illustrate these findings.

翻译：我们提出了一种标准配对设计的推广方法，其中实验单元（通常为地理区域或地理实体）可合并为称为"超级地理区"的更大单元/区域，以提升平均匹配质量。与可在多项式时间内求解的最优配对设计（Lu等，2011）不同，此广义匹配问题属于NP难问题。我们将其构建为混合整数规划（MIP）模型，并证明：无论处理效应是同质还是异质的，通过求解该MIP获得的实验设计通常能显著优于标准设计。此外，我们给出了其中一种常见修剪技术（该技术在同质效应场景下常能提升性能，Chen和Au，2022）可能导致有偏估计的条件，并证明所提出的设计不会引入此类偏差。我们基于真实广告数据的实证研究验证了这些发现。