Analyzing two-stage experiments in the presence of interference

TL;DR

This paper develops unbiased estimators and connects analysis methods for two-stage experiments with interference, addressing complexities like varying household sizes and covariate inclusion, validated through simulations and real data.

Contribution

It introduces unbiased estimators for two-stage experiments with interference, clarifies the relationship between regression and inference approaches, and explores covariate integration for improved precision.

Findings

Unbiased estimators for various estimands are proposed.

Linear regression and randomization inference yield identical results with proper standard errors.

In application, significant spillover effects were detected.

Abstract

Two-stage randomization is a powerful design for estimating treatment effects in the presence of interference; that is, when one individual's treatment assignment affects another individual's outcomes. Our motivating example is a two-stage randomized trial evaluating an intervention to reduce student absenteeism in the School District of Philadelphia. In that experiment, households with multiple students were first assigned to treatment or control; then, in treated households, one student was randomly assigned to treatment. Using this example, we highlight key considerations for analyzing two-stage experiments in practice. Our first contribution is to address additional complexities that arise when household sizes vary; in this case, researchers must decide between assigning equal weight to households or equal weight to individuals. We propose unbiased estimators for a broad class of individual- and household-weighted estimands, with corresponding theoretical and estimated variances. Our second contribution is to connect two common approaches for analyzing two-stage designs: linear regression and randomization inference. We show that, with suitably chosen standard errors, these two approaches yield identical point and variance estimates, which is somewhat surprising given the complex randomization scheme. Finally, we explore options for incorporating covariates to improve precision. We confirm our analytic results via simulation studies and apply these methods to the attendance study, finding substantively meaningful spillover effects.