Covariate balancing strategy for single and multiple exposures with interaction

\nBalancing the distribution of covariates (Z) among exposure levels is a crucial step for establishing causality between the exposure and the outcome in observational studies. Standard approaches utilizing propensity score typically focus on a single exposure, yet it is not uncommon for the exposure to interact with other variables on the outcome. Ignoring such interactions and applying standard balancing procedures solely on a single exposure can lead to significant bias. For instance, consider the Georgia Capital Charging and Sentencing Study, which sought to examine whether the race of the defendant and the race of the victim influenced the severity or length of the sentence (Y). In such a study, there are two exposures of interest on the outcome with significant interaction. Analysing each exposure separately may produce biased results. Base on the simulation results we suggest to use covariate-partition strategy for single-exposure scenario and all-covariate strategy for multiple-exposure scenario.\n