Analysis of Two-Stage Rollout Designs with Clustering for Causal Inference under Network Interference

TL;DR

This paper introduces a two-stage experimental design with clustering to improve causal effect estimation under network interference, balancing bias and variance through clustering strategies.

Contribution

It proposes a novel two-stage rollout design that incorporates clustering to reduce variance and bias in causal inference under interference.

Findings

Bias increases with more network edges cut during clustering.

Variance depends on clustering qualities like homophily and covariate balance.

Simulations demonstrate a bias-variance trade-off with different clustering strategies.

Abstract

Estimating causal effects under interference is pertinent to many real-world settings. Recent work with low-order potential outcomes models uses a rollout design to obtain unbiased estimators that require no interference network information. However, the required extrapolation can lead to prohibitively high variance. To address this, we propose a two-stage experiment that selects a sub-population in the first stage and restricts treatment rollout to this sub-population in the second stage. We explore the role of clustering in the first stage by analyzing the bias and variance of a polynomial interpolation-style estimator under this experimental design. Bias increases with the number of edges cut in the clustering of the interference network, but variance depends on qualities of the clustering that relate to homophily and covariate balance. There is a tension between clustering objectives that minimize the number of cut edges versus those that maximize covariate balance across clusters. Through simulations, we explore a bias-variance trade-off and compare the performance of the estimator under different clustering strategies.