Partially Retargeted Balancing Weights for Causal Effect Estimation Under Positivity Violations

Positivity violations pose significant challenges for causal effect estimation with observational data. Under positivity violations, available methods result in either treatment effect estimators with substantial statistical bias and variance or estimators corresponding to a modified estimand and target population that is misaligned with the original research question. To address these challenges, we propose partially retargeted balancing weights, which yield reduced estimator variance under positivity violations by modifying the target population for only a subset of covariates. Our weights can be derived under a novel relaxed positivity assumption allowing the calculation of valid balancing weights even when positivity does not hold. Our proposed weighted estimator is consistent for the original target estimand when either 1) the implied propensity score model is correct; or 2) the subset of covariates whose population is not modified contains all treatment effect modifiers. When these conditions do not hold, our estimator is consistent for a slightly modified treatment effect estimand. Furthermore, our proposed weighted estimator has reduced asymptotic variance when positivity does not hold. We evaluate our weights and corresponding estimator through applications to synthetic data, an EHR study, and when transporting an RCT treatment effect to a Midwestern population.