Quantifying inequality in health in the absence of a natural reference group

When quantifying inequality in health, the excess fraction (i.e. the proportional reduction in the outcome in question that would occur if all groups had the same, lowest, risk rate) is an appealing measure. If the population contains a natural, healthiest reference group, the excess fraction is straightforward to estimate. In the absence of an a priori reference group, calculating the excess fraction requires reflection, since using the group with the lowest observed risk rate as reference can lead to erroneous conclusions. This paper proposes a simple simulation procedure for calculating the excess fraction, without fixing a reference group.