Estimating the total treatment effect in randomized experiments with unknown network structure.

Randomized experiments are widely used to estimate the causal effects of a proposed treatment in many areas of science, from medicine and healthcare to the physical and biological sciences, from the social sciences to engineering, and from public policy to the technology industry. Here we consider situations where classical methods for estimating the total treatment effect on a target population are considerably biased due to confounding network effects, i.e., the fact that the treatment of an individual may impact its neighbors' outcomes, an issue referred to as network interference or as nonindividualized treatment response. A key challenge in these situations is that the network is often unknown and difficult or costly to measure. We assume a potential outcomes model with heterogeneous additive network effects, encompassing a broad class of network interference sources, including spillover, peer effects, and contagion. First, we characterize the limitations in estimating the total treatment effect without knowledge of the network that drives interference. By contrast, we subsequently develop a simple estimator and efficient randomized design that outputs an unbiased estimate with low variance in situations where one is given access to average historical baseline measurements prior to the experiment. Our solution does not require knowledge of the underlying network structure, and it comes with statistical guarantees for a broad class of models. Due to their ease of interpretation and implementation, and their theoretical guarantees, we believe our results will have significant impact on the design of randomized experiments.