  Disparities in health or well-being experienced by minority groups can be
difficult to study using the traditional exposure-outcome paradigm in causal
inference, since potential outcomes in variables such as race or sexual
minority status are challenging to interpret. Causal decomposition analysis
addresses this gap by positing causal effects on disparities under
interventions to other, intervenable exposures that may play a mediating role
in the disparity. While invoking weaker assumptions than causal mediation
approaches, decomposition analyses are often conducted in observational
settings and require uncheckable assumptions that eliminate unmeasured
confounders. Leveraging the marginal sensitivity model, we develop a
sensitivity analysis for weighted causal decomposition estimators and use the
percentile bootstrap to construct valid confidence intervals for causal effects
on disparities. We also propose a two-parameter amplification that enhances
interpretability and facilitates an intuitive understanding of the plausibility
of unmeasured confounders and their effects. We illustrate our framework on a
study examining the effect of parental acceptance on disparities in suicidal
ideation among sexual minority youth. We find that the effect is small and
sensitive to unmeasured confounding, suggesting that further screening studies
are needed to identify mitigating interventions in this vulnerable population.
