Before revision:  Second, current approaches have ignored what hypothetical interventions should condition on and thus may not reflect equity concerns that actual interventionists would respect . Third, there are several estimators across the epidemiology and economics literature but their incorporation of equity value judgements has not been examined, and these do not cover many of the ways in which disparities and hypothetical interventions may be defined. In this paper , motivated by the clinical example of treatment intensification and hypertension control disparities, we address these issues of defining and estimating meaningful causal decompositions. We present a framework that explicitly considers what the disparity measure and hypothetical intervention account for and how these choices can be mapped to notions of equity .
After revision:  Second, current approaches have ignored what hypothetical interventions should condition on and thus may not reflect equity concerns that actual interventionists would respect , limiting their relevance and practical value. This paper addresses these concerns by explicitly considering what covariates the outcome disparity and hypothetical intervention account for and how these choices can be mapped to notions of equity .