Before revision:  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:  We present a framework that explicitly considers what the disparity measure and hypothetical intervention adjust for (so-called allowable covariates) and the equity value judgements these choices convey, drawing from the bioethics, biostatistics, epidemiology, and health services research literatures. From this discussion, we generalize decomposition estimands and formulae to incorporate allowable covariate sets, to reflect equity choices, while still allowing for adjustment of non-allowable covariates needed to satisfy causal assumptions .