The arithmetic of reducing relative and absolute inequalities in health: a theoretical analysis illustrated with European mortality data

Background Reducing inequalities in health is a great challenge for public health, but how relative and absolute inequalities in mortality respond to changes in mortality by socioeconomic group is not well understood. Methods We derived arithmetically what combinations of changes and starting levels of mortality by socioeconomic group produce narrowing, and what combinations produce widening of relative and absolute inequalities in mortality. We then determined empirically how often these scenarios actually occur with data on inequalities in cause-specific mortality in five European countries spanning four decades (1970-2010). Results Changes in the rate ratio depend exclusively on the ratio of relative mortality change between socioeconomic groups, whereas changes in the rate difference depend on whether the ratio of relative mortality change between socioeconomic groups is larger or smaller than the rate ratio. This implies that, in case of declining mortality and faster relative mortality decline in higher socioeconomic groups, the rate difference will increase until the rate ratio becomes equal to the ratio of relative mortality decline, but will then start to decline. In the most common scenario in our data set (starting rate ratio above 1.00 and faster relative mortality decline in higher than lower socioeconomic groups), the rate ratio indeed always goes up but the rate difference goes down in about half of all cases, sometimes after a period of growth. Conclusions A narrowing of absolute inequalities occurs under a wider range of conditions than a narrowing of relative inequalities in mortality.