Table 1.

Summary of simulation scenarios used to explore performance of quantile g-computation and WQS regression for small ($n=100$)- or moderate ($n=500$)-sized samples.

Simulation scenarioa	${\mathrm{\beta }}_1$	${\mathrm{\beta }}_2$	${\mathrm{\beta }}_{\mathrm{1,1}}$	${\mathrm{\beta }}_{\mathrm{1,2}}$	${\mathrm{\beta }}_C$	${\mathrm{\psi }}_1$	${\mathrm{\psi }}_2$	${\mathrm{\rho }}_{X_1,X_2}$	${\mathrm{\rho }}_{X,C}$
1	0	0	0	0	0	0	0	0	0
2	0.25	$-0.25$	0	0	0	0	0	0	0
3	0.25	0	0	0	0	0.25	0	0	0
4b	0.25/d	0.25/d	0	0	0	0.25	0	0	0
5	0.25	$-0.2$, $-0.1$, $-0.05$	0	0	0	0.05, 0.15, 0.2	0	0.0, 0.4, 0.75	0
6	0.25	0	0	0	0.5	0.25	0	0	0.75
7	0.25	0.25	0	$-0.15$	0	0.5	$-0.15$	0	0
8	0.25	0.25	$-0.15$	0	0	0.5	$-0.15$	0	0

Note: Table columns are as follows: ${\mathrm{\beta }}_C$, true coefficient for unmeasured confounder C; ${\mathrm{\beta }}_1$, true coefficient for $X_1$; ${\mathrm{\beta }}_2$, true coefficient for $X_2$; ${\mathrm{\beta }}_{\mathrm{1,2}}$, true coefficient for interaction term $X_1{X}_2$; ${\mathrm{\rho }}_{X,C}$, true correlation between $X_1$ and unmeasured confounder C; ${\mathrm{\rho }}_{X_1,X_2}$, true correlation between $X_1\mathrm{and}{X}_2$; ${\mathrm{\psi }}_1$, true mixture effect (main term); ${\mathrm{\psi }}_2$ true mixture effect (quadratic term).

^aEach scenario was repeated for sample sizes of 100 and 500 and a total number of exposures of 4, 9, and 14. Outcomes are simulated according to the model $Y=0+\sum _{j=1}^d{\mathrm{\beta }}_j{X}_j+{\mathrm{\beta }}_{\mathrm{1,1}}{X}_1{X}_1+{\mathrm{\beta }}_{\mathrm{1,2}}{X}_1{X}_2+{\mathrm{\beta }}_{C}C+\mathrm{\epsilon };\text{where epsilon is the error term, and}\mathrm{\epsilon }\sim N\left(\mathrm{0,1}\right)$.

^bd refers to the total number of exposures.