A Sextic Representation of the Mortlity Curve

Jon Anson , Retraité

Mortality curves, under normal conditions, follow a standard pattern, of decline and then monotonic increase into old age. We propose a global approach to modelling this curve, using a sextic (6th degree) polynomial of the log mortality rate. The curve is defined structurally to have three shape-defining parameters: the breadth, the flatness and the tilt and three scale and location parameters (see details in extended abstract). We fit this curve for all 5-year abridged life tables in the HMD data set and consider the relations between the parameters and their relation to life expectancy, to sex and to social conditions in the different countries. Initial analysis indicates: 1. The scale and location parameters are all related directly to the level of mortality 2. As mortality declines, the tilt of the curve increases 3. The breadth and the flatness paramenets are collinear and define the Shape of the curve. This varies between countries but has remained remarkably consistent over time and is not directly related to the level of mortality in the population. The sextic curve, defined in terms of three structural and three scaling parameters, provide a transparent description of the mortality curve¸which enables us to describe the changes that have taken place over time, in relation to the general level of mortality in the population and in relation to the social conditions in the different countries over time.

See extended abstract

 Presented in Session P2. Health, Mortality, Ageing - Aperitivo