Efficient Switchback Experiments with Surrogate Variables: Estimation and Experimental Design

Switchback experiments, in which experimental units are assigned to control and treatment interchangeably over time, have gained increasing popularity in recent years due to their ability to mitigate interference across units. Despite their wide adoption in the technology sector, drawing reliable inferences from such experiments remains challenging due to temporal interference. In this paper, we address this challenge by examining a special causal structure commonly found in a wide range of applications. Specifically, we consider scenarios where there exist surrogate variables at each experimental period that can fully capture the potential temporal interference from the past. We outline the necessary assumptions for identification in this context and propose an unbiased estimator using the technique of importance sampling. Additionally, we derive an experimental design with a near-optimal worst-case guarantee and compare it theoretically and empirically to the inverse propensity score estimator. To facilitate inferences, we introduce both an exact inference procedure based on Fisher’s randomization test and an asymptotic inference procedure based on the central limit theorem. We demonstrate by extensive numerical experiments that the proposed estimator, coupled with the experimental design, results in lower risk compared with the traditional inverse propensity score estimator.