14. The changing survival curve
Being of relatively short duration, survival in old age follows a rapidly falling line which in arithmetic scale slows downs as it approaches zero but in logarithmic scale continues to fall ever more precipitously. The former case, a sweeping curve, is easily recognized as the last part of the survival function describing the entire human life. In a study limited to the oldest old, the starting level at age 80 is in all cases equal and this fact conditions all comparisons because we observe only the effects of mortality after this age.
The various survival curves in Figure 29, based on Annex Table 3, may at first sight look rather similar but at closer examination show that by age 90 or soon thereafter, the level of one curve may be twice that of another, and that this relative difference keeps growing even larger at still older ages. In fact, each of the decennial curves of the group of thirteen countries falls more slowly than the preceding one. Such differences are more marked among women, particularly between the last decades. The differences between the three groups of countries are also quite noticeable.
A closer look at the change is awarded when examining the first differences of the survival functions over time in Tables 30 and 31 and in Figure 30. Instead of the function 1x, these tables and figures are based on the life-year function Lx which gives virtually the same result and has the advantage of being additive, thus allowing a better appreciation of the age pattern. The sum of the increase in Lx by age equals the increase in life expectancy at 80.
In the group of thirteen (Table 30), 80-year-old men gained between the first two decades on the average 0.2 years of life-time, between the next two, 0.3 years, and between the last two, 0.5 years, all this adding up to just over one year(see bottom line). Among women, the total gain was 1.8 years and also in this case roughly half of it took place between the last two decades. The acceleration was thus considerable.
In all cases, the greatest benefits befell ages 86 or 87 and, more generally, the 85-89 group. The relative age distribution of the gains tended to move over time to higher ages. This shift, visible in Figure 30, was very pronounced among women: in the course of time, the 90-94-year-old became much greater beneficiaries of additional life-time than the 80-84-year-old. It must, however, be kept in mind that this is the case only regarding mortality decline above age 80. What happened at the same time below 80, probably affected the age groups in a different way. The gap in Figure 30 between age 80 and the peak would undoubtedly be filled if the gains were measured beginning with a younger age.
In relative terms, the gains increased extremely sharply with age. By early 90s, the number of survivors had doubled and after age 100 it had grown several times over.
Table 31 reveals wide differences between the three groups of countries: for men the total gain was in countries of low mortality 1.3 years, of medium mortality 0.7 years and in high mortality populations barely 0.1 year. This stark international contrast is present, though somewhat more subdued, among women.
It was seen in Chapter 5 that for women, mortality reductions were heavily concentrated at "younger" ages close to 80 years while for men they were more evenly distributed. This was the case with relative reductions. Here, in absolute terms, the situation is the opposite as can be ascertained by comparing age groups 80-84 and 90-94 either in Table 30 or in the top two frames of Figure 30 (areas below the bold line). Men have made greater gains at ages 80-84 than 90-94, women at ages 90-94 more than at 80-84. The reason is that the survival situation of female octogenarians is more "mature", survival ratios already much higher leaving less room for further gains.
The slight shift in the peak age of gain which was observed among females of the group of thirteen, is replicated in the international comparison (last frame in Figure 30). When we proceed from high to lower mortality, the gains move to older age where there still is more room for improvement.
The men in the high-mortality group were an exception to this rule for particular reasons. The survival conditions of middle-aged men in these countries actually deteriorated sending ripple effects which produced stagnation among octogenarians, and only still older men drew any benefit at all.
It can be concluded that the main impact of the decline in old age mortality is being felt between ages 85 and 90, and that there is a tendency for it to move slowly higher as the situation matures.
Updated by V. Castanova, 1 November 1999