Sensitivity analysis for causal decomposition analysis: Assessing robustness toward omitted variable bias

Abstract A key objective of decomposition analysis is to identify a factor (the “mediator”) contributing disparities in an outcome between social groups. In analysis, scholarly interest often centers on estimating how much the disparity (e.g., health Black women and White men) would be reduced/remain if we set mediator education) distribution one group equal another. However, causally identifying reduction remaining depends no omitted mediator–outcome confounding assumption, which not empirically testable. Therefore, propose sensitivity analyses assess robustness possible unobserved confounding. We derived general bias formulas for reduction, can used beyond particular statistical model do require any functional assumptions. Moreover, same apply with measured before after status. On basis formulas, provide techniques based regression coefficients R 2 {R}^{2} values by extending existing approaches. The -based offers straightforward interpretation parameters standard way report research findings. Although introduce context they utilized mediation setting interventional indirect effects when exposure randomized (or conditionally ignorable given covariates).