16. Seven ways of looking at mortality change

In the following, an attempt is made to sort out some of the more important indicators of mortality change which have been discussed in earlier chapters and which are particularly relevant to old age. The list includes only parameters which can be calculated for each individual age and therefore excludes all summary measures and does not, of course, pretend to exhaust all points of view.

Seven indicators were selected for the review and are given here with a brief characterization which will be explained below.

Indicator		Characterization

1.Relative decrease/increase in age-specific mortality		The public health approach

2. Absolute decrease/increase in age-specific mortality per population at risk		An individual's chances between life and death

3. Relative increase/decrease in age-specific survival		The biological view

4. Lives saved/lost in stationary population		Point 2 related to a population model

5. Life-years gained/lost in stationary population		"Fall-out" of point 4. The desired end result

6. Relative gain/loss of life-years in stationary population		Expansion of survival

7. Age shift in mortality up/down		Delay/acceleration in the aging process

The seven indicators will be examined by age and sex in the light of a single set of data, the life tables for 1960-70 and 1980-90 in the group of thirteen countries with data of good quality. The calculations are based on the annual probability of dying q_x or its derivatives. Indicators 1 - 6 will be expressed in percent, indicator 7 in years.

Indicator 1, percentage decline in age-specific mortality is given in Table 33 and illustrated in Figure 32, Graph 1, for each sex. We call this the public health approach fully knowing that public health investigation does not necessarily end there. It is, however, as a rule, the first approach and often sufficient to describe epidemiological events and cycles and the response to preventive or curative measures. In this particular case, mortality has declined very substantially for both sexes, more for women than men. The decline has been age-selective in favour of the relatively young - and much more strongly so for women. Close to age 100, the decline has been equal for both sexes.

Graph 2 shows the same data per population-at-risk and thereby also for a single individual. The striking difference from Graph 1 is that in these terms the change has been greater for older persons. This means that an individual's chances to survive have improved more around age 100 than at 80. The female advantage in the recent development is confirmed here for ages below 95 but with a narrower margin. This demonstration may be taken to show that when probabilities are high, indicator 2 suitably complements the evidence of indicator 1.

At high ages, death is less and less often the result of an external agent and increasingly that of the failure of a vital organ, its endurance exhausted. It may therefore be more appropriate to speak of the ebbing force of life than the growing force of mortality. It is perhaps not pure semantics to say that it is the likelihood of further survival which then becomes the centerpiece of observation and speculation. We call this the biological point of view and it is demonstrated in Graph 3 by the survival probability p_x. Around age 80 where p is high, there is little difference between indicators 2 and 3 but when p grows smaller, a change in it becomes relatively larger. When the chances of survival are 50:50, indicators 1 and 3 are equal. In the history depicted here, indicator 3 has a steeply ascending slope meaning that the chances of survival have improved most for the centenarians. The females have further improved their relative position in the age range 80-90 but at still higher ages the likelihood of survival has increased equally for both sexes and finally more for men.

When mortality declines, lives are saved, and Graph 4 is an attempt to quantify them by applying the change in q_x to a population standard. This raises the question to which the population it should be applied when the changing q_x constantly modifies l_x and when d_x is the product of the two. Actually, a life saved is not an unambiguous concept. However, the choice of the standard does not radically affect the result and hardly at all its age pattern which is of primary interest here. We have used as the standard the stationary population which corresponds to the mean of the two lifetables. According to this estimate, or any other made along the same lines, lives were saved mostly in the lower eighties but a measurable number much later, even around age 100.

In old age, a more meaningful indicator than the number of lives saved is the length of time added to life. This is obtained directly as the difference in parameter L_x in the mortality regimes which are compared. In our example, they are given in Table 33 as "Years gained per 100 80-year-old" and illustrated in Graph 5 of Figure 32. This equals the increase in life expectancy at age 80 and gives its distribution to different ages. While Graph 4 shows where the lives are saved, Graph 5 shows where they are lived. The total gain in life-years was for each sex slightly more than four per each life saved.

The age distribution of indicators 4 and 5 is radically different from the relative gain in life-years by age in Graph 6. While the gains are mostly made at ages 80 to 85 and spent at ages 85 to 90 or 95, their relative impact is greatest well above these ages. In our example, the gain in years lived was about 50 percent at age 90, 100 percent at 95, 100 percent at 95, 200 percent at 100 and about 250 percent at age 105.

Our last indicator is the age shift of mortality, developed in Chapter 8. It measures a different dimension of mortality change, one closer to the aging process. It has the property of being adapted to the particular age pattern of mortality of the population in question. Presented in Graph 7, it is the composite of thirteen different patterns which, as was shown, do diverge a great deal. As an adverage, mortality has shiftet among the oldest-old about 2.5 - 3 years for women and 2 - 2.5 years for men.

For a final comparison the indicators are brought together in Figure 33. Only the female indicators are shown because the pattern is closely similar for men but the development has been more regular and more uniform for women and, we believe, more indicative of the broad background factors which have caused the recent extraordinary mortality decline in old age. It is believed that, as discussed above, each of the seven indicators has a story to tell. It is felt that, in particular, indicator 1 (relative decline of mortality) is in old age usefully supplemented by indicator 2 (absolute decline) and by a measure of the desired end result, indicator 5 (years of life gained). When studying the fundamentals of longevity, life expectancy can be complemented by indicators 3 (age-specific survival) and 7 (age shift).

We should be aware that the study of life and death needs to be complemented by study of healthy, or disease-free, life. A prime promoter of this emerging branch of science is the project REVES, acronym of the French initials of Network on Health Expectancy (see ROBINE et al. 1993). This becomes more and more compelling as survival is extended to ever higher ages. As also this branch of study uses life table techniques, the seven indicators may find applications in it.