Data-adaptive exposure thresholds for the Horvitz-Thompson estimator of the Average Treatment Effect in experiments with network interference

TL;DR

This paper introduces a data-adaptive approach to select exposure thresholds in network experiments, reducing bias and mean squared error in estimating the average treatment effect under interference.

Contribution

We develop a method to automatically choose exposure thresholds that minimize estimation error, improving upon fixed, manually specified thresholds in network interference settings.

Findings

Our method reduces bias and MSE compared to non-adaptive thresholds.

Simulations show improved estimator performance with the adaptive approach.

Experiments on a real-world graph demonstrate robustness to model deviations.

Abstract

Randomized controlled trials often suffer from interference, a violation of the Stable Unit Treatment Values Assumption (SUTVA) in which a unit's treatment assignment affects the outcomes of its neighbors. This interference causes bias in naive estimators of the average treatment effect (ATE). A popular method to achieve unbiasedness is to pair the Horvitz-Thompson estimator of the ATE with a known exposure mapping: a function that identifies which units in a given randomization are not subject to interference. For example, an exposure mapping can specify that any unit with at least $h$-fraction of its neighbors having the same treatment status does not experience interference. However, this threshold $h$ is difficult to elicit from domain experts, and a misspecified threshold can induce bias. In this work, we propose a data-adaptive method to select the "$h$"-fraction threshold that minimizes the mean squared error of the Hortvitz-Thompson estimator. Our method estimates the bias and variance of the Horvitz-Thompson estimator under different thresholds using a linear dose-response model of the potential outcomes. We present simulations illustrating that our method improves upon non-adaptive choices of the threshold. We further illustrate the performance of our estimator by running experiments on a publicly-available Amazon product similarity graph. Furthermore, we demonstrate that our method is robust to deviations from the linear potential outcomes model.