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Primary Submission Category: Weighting

Approximate Balancing Weights for Clustered Observational Study Designs

Authors: Luke Keele, Eli Ben-Michael,

Presenting Author: Luke Keele*

In a clustered observational study, a treatment is assigned to groups and all units within the group are exposed to the treatment. We develop a new method for statistical adjustment in clustered observational studies using approximate balancing weights, a generalization of inverse propensity score weights that solve a convex optimization problem to find a set of weights that directly minimize a measure of covariate imbalance, subject to an additional penalty on the variance of the weights. We tailor the approximate balancing weights optimization problem to both adjustment sets by deriving an upper bound on the mean square error for each case and finding weights that minimize this upper bound, linking the level of covariate balance to a bound on the bias. We implement the procedure by specializing the bound to a random cluster-level effects model, leading to a variance penalty that incorporates the signal signal-to-noise ratio and penalizes the weight on individuals and the total weight on groups differently according to the the intra-class correlation. We also develop two extensions to the procedure for cases where overlap between treated and control clusters is poor and it is difficult to balance covariates: (i) bias-correction via an outcome model, and (ii) changing the target estimand to the maximally overlapping set. In a series of simulation studies, we inspect the performance of these estimators compared. We provide further comparisons with two empirical applications.