Table 2.

Distance Metrics Used in Analysis.

Estimator	Formula	Notes
Standardised numerical difference	$D_S=\frac{{\overline{Y}}_{NRS}^c-{\overline{Y}}_{RCT}^c}{S_{RCT}}$	$S_{RCT}$ = sample standard deviation of outcome in benchmark.
Standardised absolute difference	$\left|D_S\right|=\frac{\left|{\overline{Y}}_{NRS}^c-{\overline{Y}}_{RCT}^c\right|}{S_{RCT}}$
Percentage of treatment effect estimate (percent difference)	$\left|D_T\right|=\frac{{\widehat{\tau }}_{NRS}- {\widehat{\tau }}_{RCT}}{\left|{\widehat{\tau }}_{RCT}\right|}\mathrm{\times }100=\frac{{\overline{Y}}_{NRS}^c-{\overline{Y}}_{RCT}^c}{{\overline{|Y}}_{RCT}^t-{\overline{Y}}_{RCT}^c|}\mathrm{\times }100$
Percentage of control mean (percent bias)	$\left|D_C\right|=\frac{\left|{\overline{Y}}_{NRS}^c-{\overline{Y}}_{RCT}^c\right|}{{\overline{Y}}_{RCT}^c} \mathrm{\times } 100$
Percentage of remaining bias (percent bias removed)	$\left|D_R\right|=\left(1-\frac{{\overline{Y}}_{NRS}^c-{\overline{Y}}_{RCT}^c}{{\overline{|Y}}_{PF}^c-{\overline{Y}}_{RCT}^c|}\right)\mathrm{\times } 100$	${\overline{Y}}_{PF}^c$ = prima facie comparison mean.
Mean-squared error	$MS{E}_i=bia{s}_i^2+s_i^2=D_i^2+s_i^2$	$s_i^2$ =variance of $D_i$ .

Sources: Greenland (2000); Glazerman et al. (2003); Hansen et al. (2013); Steiner and Wong (2018).