A Scottish question

The Scots are an innovative bunch, including the inventor of the telephone and the discoverer of penicillin.  Not all of our innovations have been positive, however.  Human welfare did not advance with the invention of the deep-fried Mars bar, for example.

With such dietary crimes it comes as no surprise that the Scots are known for having the shortest life expectancy within the four countries of the United Kingdom.  This even extends to select sub-groups, such as the portfolio of pension annuitants behind Table 1.

Table 1.  Time lived between ages 60 and 95 for males in United Kingdom (curtate life expectancies for holders of pension annuities).

The question is whether the shorter life expectancy shown in Table 1 is due to being Scottish, living in Scotland, unhealthy Scottish lifestyles, or something else entirely.  At this stage I should of course declare an interest: as a person of Scottish ancestry living in Scotland, I very much hope that being Scottish or being in Scotland is not the cause!  And no, I have never seen a deep-fried Mars bar, let alone eaten one.

We will use the data behind Table 1 to fit a series of survival models allowing for age, gender and time trends, together with UK region and geodemographic profile.  These latter two factors are both determined by the pensioner's postcode, and we are restricting ourselves to pensioners with a valid UK residential postcode.  The results are shown in Table 2.

Table 2.  Selected models using Perks' Law of mortality for a portfolio of pension annuitants.

Fortunately for non-statisticians, you don't need to understand either the model syntax or what an AIC is to work out what is going on.  Most obviously, geodemographic group (Acorn) is much more powerful at explaining mortality variation than region: Model 4 is a much bigger improvement than Model 2.  Furthermore, the only difference between Models 1 and 2, and Models 3 and 4,  is the region factor, yet the difference from including the region factor falls from 356 in the former case to just 129 (=1601-1472) in the latter. This leads us to the following two conclusions:

1. Socio-economic group or lifestyle is a much more important rating factor for longevity than region.
2. More than half of the apparent regional differences are in fact due to varying socio-economic mix around the UK.

These conclusions are of interest for insurers using postcodes to price annuities.  If you are using geodemographic profiles, then you are correctly allowing for socio-economic or lifestyle differences in longevity.  However, if you are just using region as a rating factor then you are missing an important trick.  Indeed, you may be losing money as a result: if your competitors use geodemographic profiles, then conclusion (2) above suggests that you are being selected against.