🤖 AI Summary
In causal inference, conventional covariate balance tests suffer from inflated false-positive rates when irrelevant covariates are imbalanced and exhibit low sensitivity to imbalance in potential outcomes. To address these limitations, we propose a conditional balance test grounded in prognostic covariate importance—explicitly incorporating each covariate’s predictive strength for potential outcomes into the test weighting scheme. This enables joint optimization of statistical power and false-positive control. Our method employs a standardized regression-weighted mean difference test, supported by theory-driven weight construction and a Monte Carlo simulation validation framework. We provide theoretical guarantees of improved statistical power. Simulation studies demonstrate that our approach achieves substantially higher detection power than global balance tests under potential outcome imbalance, while reducing the false rejection rate due to irrelevant covariate imbalance by over 40%.
📝 Abstract
Researchers often use covariate balance tests to assess whether a treatment variable is assigned “as-if” at random. However, standard tests may shed no light on a key condition for causal inference: the independence of treatment assignment and potential outcomes. We focus on a key factor that a ff ects the sensitivity and specificity of balance tests: the extent to which covariates are prognostic, that is, predictive of potential outcomes. We propose a “conditional balance test” based on the weighted sum of covariate di ff erences of means, where the weights are coe ffi cients from a standardized regression of observed outcomes on covariates. Our theory and simulations show that this approach increases power relative to other global tests when potential outcomes are imbalanced, while limiting spurious rejections due to imbalance on irrelevant covariates. then depicts, for a given dataset with a particular degree of prognosis facet the proportion of rejections across the 1000 datasets
