Shortest Age Interval of Deaths Is there a Limit to Compression?

5. Inter-Quartile Age

In a recent article, Wilmoth and Horiuchi analysed ten possible indicators for the compression of mortality and concluded that the inter-quartile range (IQR) was the best choice for general use, being highly correlated with most of the other nine as well as being convenient and easily interpretable [Wilmoth and Horiuchi 1999].

As both IQR and C50 are measures of an age interval in which half of all deaths take place, it is of interest to compare the results they give. By definition, C50 cannot have a larger value than IQR and, in fact, in the countries shown in Table 1 as well as in about 30 others that we have studied, C50 gives consistently, without exception, a lower value then IQR, thus pointing out the existence of a shorter age interval for the same number of deaths. We accept this as proof that C50 is more successful than IQR in locating the greatest concentration of deaths. For different proportions of deaths, the other C-indicators locate similarly the greatest concentrations.

The difference between IQR and C50 is generally larger in high mortality populations. It has therefore narrowed down substantially during the great mortality transition. It nevertheless persists and is today in the leading countries usually about one to three years. This is in some cases sufficient to affect the relative position of different countries or to change the direction of the apparent trend.

In order to examine more closely the nature of the wide differences between IQR andC50 in high- and medium-mortality populations, we present in Figure 6 the age-at-death distribution of Swedish males before and after the mortality transition.

(Figure 6 here)

In 1861-70, C50 measured an age span of 38 years in the mature ages from 47 to 85. While undoubtedly long, this span nevertheless corresponded to the greatest concentration of deaths in late life in the epoch. In sharp contrast with this, IQR failed to catch any concentration of deaths which existed and fell flat between the two modes into an age range where deaths were actually least concentrated. This resulted in an IQR of 64.7 years. When this is used as a starting point, the magnitude of ensuing compression is of course vastly exaggerated.

In the fundamentally transformed d-distribution of 1991-95, the two indicators are much closer together and partly overlap. However, a visual inspection is sufficient to show that C50 covers in a more balanced manner the greatest concentration of deaths while IQR remains slightly out of focus in a somewhat wider age interval.

As a rule, C50 is situated at an older age than IQR. It would, however, be a mistake to conclude from this that it is by nature an indicator of compression in old age while IQR is one for the entire age range. C50 is so constructed that it is entirely neutral regarding both age and survival ranking. It falls generally, and increasingly, into old age for the simple reason that as the survival curve begins to assume an even remotely rectangular form, of which the left end is anchored at age zero, and as life expectancy at birth is well over 70 years, the right end of the rectangle cannot possibly be in young or middle age. In high-mortality populations, however, C50 actually tends to fall into younger age than IQR. In the Egyptian life table 1944-46 for males, IQR was 64.78 years between ages 1.74 and 66.51 while C50 was 35.40 years between ages 0.00 and 35.40.

Unless the age-at-death distribution has only one dominant mode, the C-indicators may, because of their age-neutrality, present more than one compression area. It is particularly likely that a high-mortality population will have two separate peaks for both C10 and C25, one in early childhood, the other in late life, as shown in Table 3. It is virtually impossible that two C50s would exist side by side but the only C50 could conceivably start at birth and thus contain a large element of child mortality. This proves that C-indicators are capable of identifying compression at any age and should therefore be recognized as valid for the entire age range.

(Table 3 here)

To conclude, we find C50 a better compression indicator than IQR because it consistently points out a narrower age interval for the same number of deaths - in other words, greater compression. IQR is particularly ill suited to measure compression in high-mortality populations. C50 has the additional advantage that it can be supplemented by other C-indicators which together give a more complete and many-sided picture of compression.


Shortest Age Interval of Deaths Is there a Limit to Compression?

Measuring the Compression of Mortality
Väinö Kannisto
© 2000 Max-Planck-Gesellschaft ISSN 1435-9871