Mortality inequality in populations with equal life expectancy: Arriaga's decomposition method in SAS, Stata, and Excel

Life expectancy is used to measure population health, but large differences in mortality can be masked even when there is no life expectancy gap. We demonstrate how Arriaga's decomposition method can be used to assess inequality in mortality between populations with near equal life expectancy. We calculated life expectancy at birth for Quebec and the rest of Canada from 2005 to 2009 using life tables and partitioned the gap between both populations into age and cause-specific components using Arriaga's method. The life expectancy gap between Quebec and Canada was negligible (<0.1 years). Decomposition of the gap showed that higher lung cancer mortality in Quebec was offset by cardiovascular mortality in the rest of Canada, resulting in identical life expectancy in both groups. Lung cancer in Quebec had a greater impact at early ages, whereas cardiovascular mortality in Canada had a greater impact at older ages. Despite the absence of a gap, we demonstrate using decomposition analyses how lung cancer at early ages lowered life expectancy in Quebec, whereas cardiovascular causes at older ages lowered life expectancy in Canada. We provide SAS/Stata code and an Excel spreadsheeet to facilitate application of Arriaga's method to other settings.