Limitless longevity: Comment on the Contribution of rectangularization to the secular increase of life expectancy

Rossi et al. looked at the increase in life expectancy in nine European countries, including Sweden, from 1922–2006.¹ To do this, they used a method that allowed them to separate the two respective contributions to increased life expectancy of: (i) postponement of death, through rectangularization of the survival curve; and (ii) an upward shift in the maximum age at death, as a measure of longevity. They found that both factors have contributed to the increase in life expectancy in the nine countries in their study, but that increased longevity played a relatively greater role than postponement of death. They propose that changes in life-style factors, and particularly cigarette smoking, have been essential for rectangularizing the survival curve, but they have less specific suggestions for explaining the upward shift in the age at death in the countries included in their study.

We previously analyzed mortality among Swedish centenarians in a cohort study based on individual data for all persons in Sweden who reached the age of 100 years from 1969–2009 (n = 15 231).² In the analyses for this study we divided the data into a sequence of one-year cohorts. We used these data in an attempt to add some further insights to the findings by Rossi et al.

We could indeed confirm that longevity, measured as the maximum age at death, has increased steadily during the period that we studied (Figure 1), and this was also shown by others for an earlier period.³ This corroborates Rossi and colleagues’ results, although their method of discrimination of the components of life expectancy leads to a slightly different definition of longevity than maximum age at death. Interestingly, however, there was no secular trend in the average age at death in our one-year cohorts of centenarians, either for males or for females.² The mean age at death of females was ∼102 years throughout the 40-year period of the study, and about half a year less in males. This shows that the increase in maximum age at death was not caused by a decrease in mortality among the very oldest subjects in the study. Instead, the increase in maximum age at death was fueled by an increase in the number of people surviving to the age of 100 years; with a larger number of centenarians the probability that at least one dies at very old age also gets larger. A similar argument can be brought forward for the observations of Rossi et al.¹ Declining mortality at younger ages eventually leads to rectangularization of the survival curve and thus to a greater number of individuals reaching higher ages. However, it will also lead to an increase in Rossi and colleagues’ chosen longevity measure, even in the case in which mortality rates at the higher ages have remained stable.

Figure 1.

Highest age reached by cohort of centenarians (1969–2000)

Furthermore, our data suggest that the age-specific probabilities of dying may level off at some point closely above 100 years, rather than continuing to increase continuously with age. At the very end of life too few people remain in the population for proper estimations, but the observed figures would be consistent with one-year probabilities of dying stabilized at a level of about 0.5 (Figure 2). Such a level would be in agreement with previous reports, and the concept of probabilities of dying leveling off at old age would be consistent with the theory of heterogeneity of mortality introduced by Vaupel.⁴ At present there are no data available that allow an examination of mortality at much older ages, but such data will come. However, Gampe et al. have shown the leveling off of mortality after age 110 years through the use of combined data for many countries.⁵ It is perhaps natural to think of mortality as something that increases continuously with age and that the probability of dying eventually reaches 100% at a certain age, i.e., at the maximum life span. If, instead, probabilities of dying level off at old age, the maximum age at death will still increase steadily as long as the population that survives to old age increases as the result of decreased mortality at younger ages. One can only speculate about the age at which the probability of dying is no longer below 100 percent (we don't even know if a limit exists) or about the period for which the maximum age of dying may increase. The negative binomial distribution applied to persons who reach 100 years of age, with the annual probability of dying as a parameter, may provide a model for consideration.

Figure 2.

Probability of dying for Swedish men and women over 100 years of age (1969–2009)

Our data are based on the Swedish experience of mortality, for which we know from official statistics that there are downward secular trends in mortality for age groups below 100 years, but as we have shown, not for age groups above this. At present we have less information about secular trends in centenarian mortality in countries other than Sweden. However, our key point, that longevity, defined as the maximum age of death, will continue to increase, is essentially independent of actual mortality trends among centenarians.

Funding

This study was funded by the Swedish Council for Working Life and Social Research (Swedish acronym: FAS). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

Conflict of interest: None declared.