The presence of interference renders classic Fisher randomization tests infeasible due to nuisance unknowns. To address this issue, we propose imputing the nuisance unknowns and computing Fisher randomization p-values multiple times, then averaging them. We term this approach the imputation-based randomization test and provide theoretical results on its asymptotic validity. Our method leverages the merits of randomization and the flexibility of the Bayesian framework: for multiple imputations, we can either employ the empirical distribution of observed outcomes to achieve robustness against model mis-specification or utilize a parametric model to incorporate prior information. Simulation results demonstrate that our method effectively controls the type I error rate and significantly enhances the testing power compared to existing randomization tests for randomized experiments with interference. We apply our method to a two-round randomized experiment with multiple treatments and one-way interference, where existing randomization tests exhibit limited power.

翻译：由于干扰的存在，经典Fisher随机化检验因存在未知干扰项而不可行。为解决此问题，我们提出通过插补未知干扰项并多次计算Fisher随机化p值，再取其平均值的方法。我们将此方法称为基于插补的随机化检验，并给出了其渐近有效性的理论结果。该方法结合了随机化检验的优势与贝叶斯框架的灵活性：在进行多重插补时，既可采用观测结果的实证分布以增强对模型误设的稳健性，也可利用参数化模型融入先验信息。仿真结果表明，相较于现有针对存在干扰的随机实验的随机化检验方法，本方法能有效控制第一类错误率，并显著提升检验功效。我们将本方法应用于具有多处理组和单向干扰的双轮随机实验，在该场景下现有随机化检验方法表现出有限的检验功效。