  A key objective of decomposition analysis is to identify a factor (the
'mediator') contributing to disparities in an outcome between social groups. In
decomposition analysis, a scholarly interest often centers on estimating how
much the disparity (e.g., health disparities between Black women and White men)
would be reduced/remain if we set the mediator (e.g., education) distribution
of one social group equal to another. However, causally identifying disparity
reduction and remaining depends on the no omitted mediator-outcome confounding
assumption, which is not empirically testable. Therefore, we propose a set of
sensitivity analyses to assess the robustness of disparity reduction to
possible unobserved confounding. We provide sensitivity analysis techniques
based on regression coefficients and $R^2$ values. The proposed techniques are
flexible to address unobserved confounding measured before and after the group
status. In addition, $R^2$-based sensitivity analysis offers a straightforward
interpretation of sensitivity parameters and a standard way to report the
robustness of research findings. Although we introduce sensitivity analysis
techniques in the context of decomposition analysis, they can be utilized in
any mediation setting based on interventional indirect effects.
