  Causal decomposition has provided a powerful tool to analyze health disparity
problems, by assessing the proportion of disparity caused by each mediator.
However, most of these methods lack \emph{policy implications}, as they fail to
account for all sources of disparities caused by the mediator. Besides, their
estimations \emph{pre-specified} some covariates set (\emph{a.k.a}, admissible
set) for the strong ignorability condition to hold, which can be problematic as
some variables in this set may induce new spurious features. To resolve these
issues, under the framework of the structural causal model, we propose to
decompose the total effect into adjusted and unadjusted effects, with the
former being able to include all types of disparity by adjusting each
mediator's distribution from the disadvantaged group to the advantaged ones.
Besides, equipped with maximal ancestral graph and context variables, we can
automatically identify the admissible set, followed by an efficient algorithm
for estimation. Theoretical correctness and the efficacy of our method are
demonstrated on a synthetic dataset and a spine disease dataset.
