## The bottom line

At it's core, the study of mortality is based on a simple ratio — the number of deaths, D, divided by the population exposed to the risk of death, E:

mortality rate = D / E

While this seems simple and straightforward, there are important subtleties concerning the quality of the data used.  One of these is illustrated by a series of revelations about unreported deaths in Japan, where a recent audit has cast doubt on the reliability of Japanese population statistics for the elderly.  Unreported deaths reduce mortality rates both by under-counting deaths and by inflating the population at risk.  Time will tell if Japan's famously low mortality rates have been under-stated as a result.

The top line of a mortality rate is the number of deaths.  In a country like the United Kingdom, this is usually reasonably reliable: all deaths have to be registered within a few days of occurring, and weekly mortality statistics are collected by local registrars' offices and forwarded to the General Register Office for England & Wales, Scotland or Northern Ireland.  Deaths are effectively counted continuously with a high degree of accuracy.

However, the population figures on the bottom line are much trickier.  Instead of being counts, the population figures are actually just estimates, usually drawing upon census information.  However, in the UK a census is only carried out once a decade.  Despite the legal obligation to do so, not everyone fills out a census form, so various adjustments have to be made to the census figures to allow for this.  For inter-census years, the population has to be estimated using indirect methods.  Population figures are therefore calculated much less frequently than deaths data, and with a lower degree of accuracy as well.

This must all be borne in mind when performing projections of future mortality rates.  There is effectively an additional source of uncertainty to reckon with: how accurate are the data on which you are basing your projections?  Do you understand the limitations of the data you are using?

Assume we have a random variable, $$X$$, with expected value ... Read more