Primary Submission Category: Multilevel Causal Inference
Estimation, Inference, and Sensitivity for Spillover Effects in Two-Stage Observational Studies via Matching
Authors: Zhiwei Xiao, Samuel Pimentel,
Presenting Author: Zhiwei Xiao*
Spillover effects play a crucial role in driving large-scale substantive impacts of treatments in the health and social science, yet their estimation remains challenging in observational studies with complex interference. Two-stage observational designs, in which both clusters and units within clusters select into treatment, provide valuable opportunities to measure such treatment effects. However, standard tools for confounding control and permutation inference do not apply directly to these studies because of the two-stage structure. We introduce two new study designs for two-stage observational studies that enable unbiased point estimation of spillover effects, valid finite-sample permutation inference, and sensitivity analysis for unobserved confounding. The first design leverages cluster-level matching followed by random selection of a subset of control subjects under a propensity model. This estimator is compatible with permutation tests, and we show that it is marginally unbiased across all possible realizations of the random subset. The second design employs multi-level matching, eliminating the need for random selection of controls at the cost of a reduced sample size. The two-stage sensitivity analyses we develop for both designs allow separate quantification of unmeasured confounding at the cluster and individual levels. We demonstrate our methods using a two-stage study of deworming medication in Kenyan primary schools.