  Causal decomposition analysis provides a way to identify mediators that
contribute to health disparities between marginalized and non-marginalized
groups. In particular, the degree to which a disparity would be reduced or
remain after intervening on a mediator is of interest. Yet, estimating
disparity reduction and remaining might be challenging for many researchers,
possibly because there is a lack of understanding of how each estimation method
differs from other methods. In addition, there is no appropriate estimation
method available for a certain setting (i.e., a regression-based approach with
a categorical mediator). Therefore, we review the merits and limitations of the
existing three estimation methods (i.e., regression, weighting, and imputation)
and provide two new extensions that are useful in practical settings. A
flexible new method uses an extended imputation approach to address a
categorical and continuous mediator or outcome while incorporating any
nonlinear relationships. A new regression method provides a simple estimator
that performs well in terms of bias and variance but at the cost of assuming
linearity, except for exposure and mediator interactions. Recommendations are
given for choosing methods based on a review of different methods and
simulation studies. We demonstrate the practice of choosing an optimal method
by identifying mediators that reduce race and gender disparity in
cardiovascular health, using data from the Midlife Development in the US study.
