Primary Submission Category: Matching, Weighting
A Weighting Framework for Clusters as Confounders In Observational Studies
Authors: Luke Keele,
Presenting Author: Luke Keele*
Units in observational studies are often clustered in groups, such as students in schools and patients in hospitals. Researchers then seek to adjust for (possibly unmeasured) cluster-level covariates and contexts that may influence both treatment assignment and outcomes. In this paper, we introduce a unified framework to evaluate the constraints assumed by estimation methods that adjust for cluster membership. We develop a weighting framework to show that different approaches differentially control global balance (differences between treated and control units across clusters) and local balance (differences within clusters). We first review traditional model-based inverse propensity score weighting (IPW) focusing on IPW with a hierarchical propensity score model, which is the current standard in the literature. We show that this approach does not impose any constraints on local balance. We then outline a more general balancing weight estimator that include constraints on global and local balance but uses regularization within these constraints. We next show that a form of the newly proposed Generalized Mundlak approach also fits into this framework, with model-based IP weights that adjust for cluster-level attributes rather than cluster indicators. We also propose a novel Mundlak balancing weights estimator, which is well-suited to this context and can be applied even if there are smaller clusters where all the units are treated or untreated. We then compare these methods in