Table 4.

For the scenario depicted in Figure 3(a), the standard regression model ${\hat{y}}_S^{(i)}$ necessary for estimating the total causal effect of each exposure x_i on y, and the corresponding UR model ${\hat{y}}_{\mathit{UR}}^{(i)}$, for $1\le i\le k$.

	Standard regression model ${\hat{y}}_S^{(i)}$	UR model ${\hat{y}}_{\mathit{UR}}^{(i)}$
$i=1$:	${\hat{\alpha }}_0^{(1)}+{\hat{\alpha }}_{m1}^{(1)}{m}_1+{\hat{\alpha }}_{\mathbf{x}1}^{(1)}{x}_1$	${\hat{\lambda }}_0^{(1)}+{\hat{\lambda }}_{m1}^{(1)}{m}_1+{\hat{\lambda }}_{\mathbf{x}1}^{(1)}{x}_1$
$i=2$:	${\hat{\alpha }}_0^{(2)}+{\hat{\alpha }}_{m1}^{(2)}{m}_1+{\hat{\alpha }}_{x1}^{(2)}{x}_1+{\hat{\gamma }}_{m2}^{(2)}{m}_2+{\hat{\alpha }}_{\mathbf{x}2}^{(2)}{x}_2$	${\hat{\lambda }}_0^{(2)}+{\hat{\lambda }}_{m1}^{(2)}{m}_1+{\hat{\lambda }}_{\mathbf{x}1}^{(2)}{x}_1+{\hat{\lambda }}_{\mathit{em}2}^{(2)}{e}_{m2}+{\hat{\lambda }}_{\mathbf{ex}2}^{(2)}{e}_{x2}$
⋮	⋮	⋮
$i=k$:	$\begin{array}{c}\multicolumn{1}{c}{{\hat{\alpha }}_0^{(k)}+{\hat{\alpha }}_{m1}^{(k)}{m}_1+{\hat{\alpha }}_{x1}^{(k)}{x}_1+{\hat{\alpha }}_{m2}^{(k)}{m}_2+{\hat{\alpha }}_{x2}^{(k)}{x}_2}\\ \multicolumn{1}{c}{+\dots +{\hat{\alpha }}_{\mathit{mk}}^{(k)}{m}_k+{\hat{\alpha }}_{\mathbf{xk}}^{(\mathbf{k})}{x}_k}\end{array}$	$\begin{array}{c}\multicolumn{1}{c}{{\hat{\lambda }}_0^{(k)}+{\hat{\lambda }}_{m1}^{(k)}{m}_1+{\hat{\lambda }}_{\mathbf{x}1}^{(\mathbf{k})}{x}_1+{\hat{\lambda }}_{\mathit{em}2}^{(k)}{e}_{m2}+{\hat{\lambda }}_{\mathbf{ex}2}^{(\mathbf{k})}{e}_{x2}}\\ \multicolumn{1}{c}{+\dots +{\hat{\lambda }}_{\mathit{emk}}^{(k)}{e}_{\mathit{mk}}+{\hat{\lambda }}_{\mathbf{exk}}^{(\mathbf{k})}{e}_{\mathit{xk}}}\end{array}$