Table 1 below (which is based Table 1 of BSPS 2006) illustrates the issues. It shows a situation where an intervention shifts the risk distributions of two groups with different baseline adverse outcome rates by half a standard deviation (with the advantaged group (AG) rate in BSPS 2006 Table 1 used as the treated rate and the disadvantaged group (DG) rate used as the control rate). In other words, according to the reasoning above and on other pages of this site, the intervention affects the two groups in exactly the same way. But the penultimate column shows that the intervention effects a greater proportionate reduction in the adverse outcome rate in the group with the lower adverse outcome baseline rate (Group A). The final column, on the other hand, shows a larger proportionate increase in the favorable outcome rate for the group with the higher adverse outcome baseline rate (Group B).
Table 1: Comparative Effects of .5 Standard Deviation Change in Risk Distributions of Groups with Different Baseline Rates
Group Point Control Treated Relative Risk Adv Risk Reduc Fav Risk
A M 12.71% 5.00% 0.39 60.67% 8.84%
B L 21.77% 10.00% 0.46 54.06% 15.04%