This paper focuses on the longevity revolution as part of a broader project called the ‘M Project’ in which my co-investigators are Siu Lan Cheung from China, Shiro Horiuchi from Japan but working in New York and Roger Thatcher from UK.
Figure 1 shows broad changes over time in the distribution of ages at death in Switzerland. The data come from the Human Mortality Database (www.mortality.org/) which is a fantastic research database gathering more than 5000 period life tables for at least 26 countries starting with Sweden in 1751.
We are focusing on three indicators: (i) the modal length of life (M), which is the most important one for our study, (ii) the standard deviation above M, representing the dispersion of individual life durations above and around this central value, and of course (iii) the maximum life span.
Figure 1: Distribution of the ages at death in Switzerland 1876-1880, 1929-1932, 1988-1993
Looking at the change over time in the modal length of life, which is the most frequent life duration for adults, we observe an increase over time. We will check this in the past against the life tables gathered by the Human Mortality Database (Figure 2) for a selection of nine countries, Nordic, western European, the USA, and Japan.
There are three periods in this Figure: the first one, from 1751 to 1851, when the maximum life span is just fluctuating between 70 and 75. Sweden is the only available country for these dates.
The second period is the period of the demographic and epidemiologic transition. Some countries entered this transition early such as the UK or France, and other countries entered some 60 or 70 year later. This creates a kind of confusion, but in 1950, the demographic transition finishes and the modal length of life is close to 80 years for all the countries.
Since then, a huge increase in the modal length of life can be observed, with an increase of more than 2 months per year. Now, the modal length of life is above 90 years in some countries like Japan, but also in France and Switzerland.
The second indicator is the standard deviation above the modal length of life. This indicator measures the dispersion or compression of mortality around the central value. According to Figure 1, we are expecting to see the value of this indicator decrease over time. We check this in the past against the life tables gathered by the Human Mortality Database (Figure 3). The global picture is about the same as for the mode, basically no big change before 1950. After 1950 a clear decline can be observed beyond small fluctuations.
Figure 3: Decrease in the standard deviation of the ages at death above M (SDM+), since 1751: a selection of 9 countries
click to enlarge
So obviously, during the last 50 years, at the level of these nine most developed countries which have the lowest mortality and the longest life expectancy, a compression of mortality is observed, with an increase in the modal length of life, and a decrease in the dispersion of individual life duration around this central value.
The third indicator is the maximum life span. By definition the maximum life span is just one value per year and per country, and thus we get a lot of fluctuations.
When observing the Swiss distribution again (Figure 1), it looks almost normally distributed, in particular from the mode to the tail. This is Lexis’ idea. We can test it from the d(x) distribution in the Human Mortality Database.
If the distribution is normal, we’re expecting to observe the last normal value at about 3.5 standard deviations from the mode (Cheung and Robine, 2007). We build an indicator to estimate the highest value from the most frequent life duration and from the standard deviation around this central value (M + 3.5* SDM). We expect to have this maximum life span increasing over time (Figure 4).
Pages: 1 2
Tags: longevity revolution, shifting mortality