Data-Adaptive Exposure Thresholds under Network Interference
Vydhourie Thiyageswaran, Tyler H. McCormick, Jennifer Brennan
Randomized controlled trials often suffer from interference, a violation of the Stable Unit Treatment Values Assumption (SUTVA), where a unit's outcome is influenced by its neighbors' treatment assignments. This interference biases naive estimators of the average treatment effect (ATE). A popular method to achieve unbiasedness pairs the Horvitz-Thompson estimator of the ATE with a known exposure mapping, a function that identifies units in a given randomization unaffected by interference. For example, an exposure mapping may stipulate that a  unit experiences no interference if at least an $h$-fraction of its neighbors share its treatment status. However, selecting this threshold $h$ is challenging: domain experts may struggle to specify it accurately, and a misspecified threshold can introduce bias. In this work, we propose a data-adaptive method to select the $h$-fractional threshold that minimizes the mean-squared-error (MSE) of the Hortvitz-Thompson estimator. Our approach estimates the bias and variance of the Horvitz-Thompson estimator under candidate thresholds by leveraging a first-order approximation, specifically, linear regression of potential outcomes on exposures. We present simulations illustrating that our method improves upon non-adaptive threshold choices, and an adapted Lepski's method. We further illustrate the performance of our estimator by running experiments on a village network dataset, and on a publicly-available Amazon product similarity graph. Furthermore, we demonstrate that our method remains robust to deviations from the linear potential outcomes model.