Table 1.

Allowability Designations of Estimators

	${\mathit{A}}_{\mathbf{1}}^{\mathit{y}}$	${\mathit{A}}_{\mathbf{1}}^{\mathit{m}}$	${\mathit{N}}_{\mathbf{1}}$
1. Oaxaca–Blinder Decomposition via Linear Models52,53: All covariates are considered non-allowable	$\oslash$	$\oslash$	$X_0^{age},X_0^{sex},X_0^{edu},X_0^{ins},X_0^{dia},L_1$
2. Oaxaca–Blinder Decomposition Estimator via Reweighting Functions: No covariates considered outcome-allowable; all covariates are considered target-allowable38,39	$\oslash$	$X_0^{age},X_0^{sex},X_0^{edu},X_0^{ins},X_0^{dia},L_1$	$\oslash$
3. Natural Direct/Indirect Effect Analogue Estimators33,41–43,48,56–58: All covariates are considered outcome- and target-allowable	$X_0^{age},X_0^{sex},X_0^{edu},X_0^{ins},X_0^{dia},L_1$	$\oslash$	$\oslash$
4. Path-Specific Effect Analogue (I & II) Estimator5,36,46: Demographic covariates considered outcome- and target-allowable; remaining covariates considered non-allowable	$X_0^{age},X_0^{sex}$	$\oslash$	$X_0^{edu},X_0^{ins},X_0^{dia},L_1$
5. Path-Specific Effect Analogue (III) Estimator44,47: Demographic covariates outcome- and target-allowable; remaining covariates considered target-allowable	$X_0^{age},X_0^{sex}$	$X_0^{edu},X_0^{ins},X_0^{dia},L_1$	$\oslash$
6. A Meaningful Estimator: Demographic covariates considered outcome- and target-allowable; clinical covariates considered target-allowable; socioeconomic covariates considered non-allowable	$X_0^{age},X_0^{sex}$	$X_0^{dia},L_1$	$X_0^{edu},X_0^{ins}$

Abbreviations: ${\mathit{A}}_{\mathbf{1}}^{\mathit{y}}$ outcome- (and target-) allowable covariates, ${\mathit{A}}_{\mathbf{1}}^{\mathit{m}}$ exclusively target-allowable covariates, ${\mathit{N}}_{\mathbf{1}}$ non-allowable covariates, $\oslash$ the empty set; List of covariates include $X^{age}$ age, $X^{sex}$ sex, $X^{edu}$ educational attainment, $X^{ins}$ private health insurance, $X^{dia}$ diabetes, $L_1$ baseline blood pressure