| The Emergence and Proliferation of |
| Centenarians |
by James W. Vaupel & Bernard Jeune
In developed countries the number of people celebrating their 100th birthday multiplied several fold from 1875 to 1950 and doubled each decade since 1950. In Denmark, for instance, an average of only 3 individuals reached age 100 in each year of the 1870s, compared with 213 new centenarians in 1990. Table 1 presents statistics on the number and annual rate of growth in number of persons attaining age 100, for 11 developed countries with highly reliable data. On average, the number of new centenarians increased at an annual rate of about 7% between the 1950s and the 1980s. This pace of increase is exceptionally rapid compared with the more stately progress of most populations.
As with any population, the multiplication of centenarians must be due to some combination of earlier changes in fertility, migration, and mortality (Preston and Coale 1982). In particular, the rate of growth in the number of 100-year-olds can be decomposed into the sum of the rate of increase in births 100 years ago, the rate of decrease in the effects of net emigration, and the rate of improvement in survival from birth to 50, 50 to 80, and 80 to 100. In the next section of this chapter we analyze the relative importance of these factors in explaining the proliferation of centenarians. The results indicate that the proliferation of centenarians is mainly due to improved survival from age 80 to 100.
We then turn to an analysis of the emergence of centenarians. Some simple calculations suggest that over the course of human existence the chance of enduring from birth to age 100 may have increased more than 100,000-fold. This radical change is also largely attributable to reductions in death rates at advanced ages. Taken together, our findings about the emergence and proliferation of centenarians challenge the tenet that mortality among the oldest-old is intractable.
Causes of the Proliferation of Centenarians
Our analysis is based on data from the Odense Archive of Population Data on Aging (Kannisto 1994). Most of the data used were compiled and organized by Väinö Kannisto and Roger Thatcher. Their data were supplemented with data on Sweden compiled by Hans Lundström, on Norway by Jens Olaf Borgan, and on Denmark by Axel Skytthe and Kirill Andreev. The numbers displayed in Table 1 are for those countries and times for which the quality of the data is excellent; there are serious problems of age misreporting in many countries before 1950 and in some countries, including the United States, more recently (Kannisto 1994, Thoms 1873, Condran et al 1991).
We used the decomposition 
, where n is the number of people
attaining age 100, n0 is the number of births in the corresponding time period 100 years earlier, a is an adjustment for the effects of migration, s50 is the
proportion of those born who survive to age 50, s80 is the proportion of these survivors who live
on to age 80, and s100 is the proportion of these octogenarians who endure to celebrate their 100th
birthday. Let 
be the
rate of growth of n, such that 
,
where y denotes time. Defining 
, and 
100 similarly, it follows (using methods explained in Preston and Coale 1982 and
Arthur and Vaupel 1984) that 
. The annual rates of growth in number of
births and number attaining age 100 were calculated as the logarithm of the ratio of the
number in the second time period to the number in the first time period, divided by the
number of years between the time periods.
For Denmark, Norway, and
Sweden values of the rate of increase in survival from birth to 50, from 50 to 80, and
from 80 to 100 were calculated from cohort lifetable values of annual probabilities of
survival, adjusted for migration. For these three countries the adjustment for emigration
was calculated as 
. For the other countries, data were available on the number of people attaining
age 80 from 1950 through 1969 and the corresponding number attaining age 100 from 1970 to
1989: the proportion surviving from 80 to 100 was estimated using these data.
In the Scandinavian countries, the cohorts born in the 1880s were larger than those born in the 1870s. Fewer of the members of the later cohorts left their homelands and death rates were lower at all ages. Hence changes in fertility, migration, and mortality at younger and older ages all contributed to the doubling of the number of centenarians between the 1970s and 1980s. The statistics in Table 2 indicate the relative importance of these various changes: the predominant cause of the rise of centenarians is greater survival from age 80 to 100.
We did not have the requisite cohort data for other countries to calculate the effect of all the various factors, but we were able to calculate the contribution of improved survival at advanced ages. In every case, as shown in Table 2, the proliferation of centenarians is mostly due to the reduction in mortality among octogenarians and nonagenarians.
The Emergence of Centenarians
Life expectancy summarizes the harshness of a mortality regime. Over most of the course of human existence life expectancy hovered between 20 and 30 years; even in Western Europe life expectancy did not reach 40 until after 1800 and 50 until after 1900. In many of the countries in Table 1, female life expectancy is now about 80 years; in Japan, female life expectancy is above 82. An analysis of how the chance of surviving to age 100 varies as life expectancy increases from 20 to 80 provides, therefore, a long-term perspective on the emergence of centenarians.
We based our analysis on data from the female "model West" lifetables estimated by Coale and Demeny, who studied hundreds of lifetables to determine the relationship between the level of life expectancy and the age-trajectory of mortality (Coale and Demeny 1983). Although the Coale-Demeny lifetables are a widely-used demographic standard, our results should be interpreted with caution because few reliable statistics are available concerning levels of mortality among the very old under conditions when life expectancy was low. The lower life expectancy is, the greater the tendency for age exaggeration at older ages (Kannisto 1994, Thoms 1873, Condran et al 1991). This may result in underestimates of death rates at older ages (because many of the alleged older people were actually younger).
Coale and Demeny were aware of data limitations at older ages and relied on a formula to extrapolate death rates from age 80 to age 105. They tested the formula against what they considered to be reliable lifetables, but even these tables are questionable. Their formula is based on the assumption that death rates increase exponentially between ages 80 and 105, attaining an estimated value at age 105. Although this assumption is questionable, so little is known about the age-trajectory of mortality at advanced ages when life expectancy is low that it is not clear whether the Coale-Demeny estimates produce overestimates or underestimates of the probability of surviving to 100. Wilmoth, elsewhere in this monograph, develops a rich array of alternative estimates.
Because of the bias caused by greater age overstatement in populations with shorter life expectancies, the probabilities of survival from age 50 to 80, from 80 to 100, and from birth to 100 in high-mortality regimes may be even lower than the Coale-Demeny data suggest. The seriousness of the problem of age exaggeration can be illustrated by examples from two countries generally considered to have highly reliable vital statistics, Sweden and Norway. Swedish statistics report twice as many Swedes in their 80s and four times in their 90s per million population in 1750 than in 1850 (Sundbärg 1907). In Norway 197 persons are reported as having attained age 100 in the 1870s: this figure is more than 5 times the numbers reported for more populous Denmark and Sweden. The relatively slow rate of growth in the number of centenarians in Norway (Table 1) and the relatively slow rate of improvement in survival from 80 to 100 (Table 2) may be artifacts of decreasing age exaggeration.
Although questionable, results based on the Coale-Demeny estimates are suggestive. Under the most brutish conditions, with a female life expectancy at birth of 20 years (and a remaining life expectancy at age 5 of 37 years), the odds against attaining age 100 are roughly 20 million to 1. When life expectancy at birth increases to 30 years and to 40 years, these odds fall to 700,000 to 1 and 80,000 to 1. Under current mortality rates in the countries with female life expectancies of about 80 years, two women in 100 will survive a century or more. Hence as life expectancy increases four-fold, from 20 to 80, the chance of surviving 100 years swells 400,000-fold. (Zhao, in this monograph, also used the Coale-Demeny estimates to derive the chances of survival to advanced ages: see, in particular, his Figure 1).
This enormous rise in survival chances is largely attributable to an increase in the probability of an octogenarian becoming a centenarian. As life expectancy increases from 20 to 80, the chance of surviving from birth to age 50 grows about 5-fold and the chance of surviving from 50 to 80 increases roughly 15-fold. Remarkable as these changes are, they are dwarfed by the 5,000-fold multiplication of the chance of surviving from 80 to 100.
Let s be the probability of survival from some age to some later age, e.g. from 80 to 100. If the force of mortality (hazard of death) is reduced or increased by the same factor a over all ages in the interval, then the chance of survival becomes sa. Suppose a is 0.5. If s is 0.01, then sa is 0.1, an improvement of 10-fold. If s is 0.000001, then sa is 0.001, an improvement of 1000-fold. Boldsen (in this monograph) suggests that mortality between ages 50 and 100 may have been 8 times higher in Medieval Denmark than in Denmark today. The chance of surviving from 50 to 100 today is roughly 1 in 100, so the chance then would have been roughly 10-16. These calculations illustrate the leverage changes in mortality can have on changes in survival over age intervals with low survival.
Before about 2000 BC, the number of births per year was under 1 million; until roughly 1000 AD annual global births ran at less than 10 million; only since 1970 have more than 100 million babies been added to the human population each year (McEvedy and Jones 1978). If the chance of surviving to age 100 is about 1 in 20 million when life expectancy is 20 and about 1 in 80,000 when life expectancy is 40 (a level not reached in Western Europe until the early 19th century), then centenarians must have been exceedingly rare in most countries before the modern era. Nearly all of the hundreds of Danish centenarians (and super-centenarians) reported in the 18th century are probably tales: in most years before 1800 there may have been no genuine celebration in Denmark of a 100th birthday (Jeune 1994, Skytthe and Jeune and Jeune in this monograph). More generally, unless there is some secret of longevity that has enabled some humans to transcend the death rates that governed the fate of nearly all their contemporaries, most accounts of centenarians in earlier centuries must be inaccurate (Thoms 1873).
Gerontological research - and much health policy - has been guided by the notions that aging is an intrinsic, intractable process, that deaths at advanced ages are "natural", and that little can be done to increase survival among the oldest-old (Fries 1980, Olshansky et al 1990). Far from being fixed, however, death rates after age 80 have declined considerably (Kannisto 1994, Kannisto et al 1994). The emergence and proliferation of centenarians dramatically illustrates the improvement in the life chances of octogenarians and nonagenarians. Because half of female and a third of male deaths in developed countries now occur after age 80, the plasticity of survival at advanced ages is of considerable significance. If the present pace of improvement in old-age survival persists, then it will be as likely for a child today to reach age 100 as it was for a child born eight decades ago to reach age 80 (Vaupel and Gowan 1986).
Acknowledgement
We thank Väinö Kannisto, Peter Laslett, Hans Lundström, Jim Oeppen, Richard Smith, Richard Suzman, A. Roger Thatcher, Shripad Tuljapurkar, Kenneth Wachter, John Wilmoth, and Anthony Wrigley for suggestions, and Kirill Andreev and Wang Zhenglian for research assistance. Supported by grants from the Danish Research Councils, the U.S. National Institute on Aging (grant AG08761), and the Wellcome Trust.