Propensity Scores for Causal Inference under Partial Interference

Abstract

In observational studies across fields like public health, education, and social science, treatment assignments often influence each other. While recent research in causal inference has focused more extensively on spillover effects, where one person's treatment affects another person's outcomes, far less attention has been paid to how treatment assignments themselves might interact. This oversight is particularly problematic in settings where peer influence is likely to occur, as resulting causal inferences may be significantly biased or flawed. This thesis develops novel methods for modeling dependent binary treatment assignments under partial interference, a setting where units only interact within known clusters, although our approach can be extended to arbitrary known networks. We propose a flexible Ising model framework that captures pairwise treatment dependencies as functions of observed covariates, generalizing standard logistic regression and including mixed-effects logistic regression as a special case. To address computational challenges, we develop a maximum pseudo-likelihood estimator (MPLE) with theoretical consistency guarantees and explore approximation techniques like loopy belief propagation for computing joint distributions. Through extensive simulations and an empirical analysis of COVID-19 vaccination data from Nigeria, we demonstrate that models neglecting within-cluster dependencies produce biased and high-variance estimates. Our Ising model consistently outperforms standard approaches, offering robust performance across prediction, treatment effect estimation, and individualized policy learning tasks. To help with efficient predictions, we also introduce a novel algorithm for computing the most likely cluster-level treatment assignment under mixed-effects logistic regression.