Drewnowski's index to measure lifespan variation: Revisiting the Gini coefficient of the life table

TL;DR

This paper revisits Drewnowski's index as a measure of lifespan variation, analyzing its mathematical properties and relationship with life expectancy, and demonstrating its utility through theoretical and simulation studies.

Contribution

It provides a detailed mathematical analysis of Drewnowski's index, exploring its properties and relationship with mortality improvements and lifespan inequality.

Findings

Drewnowski's index is a useful indicator of mortality pattern shapes.

Threshold age determines whether mortality improvements decrease or increase lifespan variation.

Simulation confirms the index's sensitivity to changes in mortality across ages.

Abstract

The Gini coefficient of the life table is a concentration index that provides information on lifespan variation. Originally proposed by economists to measure income and wealth inequalities, it has been widely used in population studies to investigate variation in ages at death. We focus on a complementary indicator, Drewnowski's index, which is as a measure of equality. We study its mathematical properties and analyze how changes over time relate to changes in life expectancy. Further, we identify the threshold age below which mortality improvements are translated into decreasing lifespan variation and above which these improvements translate into increasing lifespan inequality. We illustrate our theoretical findings simulating scenarios of mortality improvement in the Gompertz model. Our experiments demonstrate how Drewnowski's index can serve as an indicator of the shape of mortality patterns. These properties, along with our analytical findings, support studying lifespan variation alongside life expectancy trends in multiple species.