Mortality at very old ages

France Meslé, Jean-Marie Robine, Jacques Vallin

Mortality at very advanced ages is hard to observe using conventional methods. This is because after the age of 90 - and even more so after 100 - the numbers in each year of age are too small to monitor yearly mortality without large random fluctuations. Moreover, current theories of human longevity leave unanswered the question of whether longevity is limited to Jeanne Calment’s 122 years or whether it could be even higher, thus increasing the potential number of supercentenarians (people aged over 110).

Given high future demand for specialized medical and social services for this population, it is becoming crucial to generate better estimates of the number of very old people in order to anticipate needs more effectively. An international research project involving most OECD countries has therefore been set up to provide a global benchmark on mortality after 110 that would enable more accurate modelling, on the national level, of the survival curve between 90 and 110 and its annual change in recent decades, the aim being to extrapolate the observed trend to the decades ahead.

The process will involve identifying all the people who are believed to have reached the age of 110 since 1950 in as many developed countries as possible and verifying their exact dates of birth and death on the basis of a strict protocol with a view to calculating an accurate mortality rate at 110, which national demographic research projects can then use to forecast the elderly population. In 2002 the international network of research on supercentenarians officially became a three-party consortium (MPIDR/INSERM/INED) with a scientific board (15 researchers from 10 countries), whose main responsibility is to monitor confidentiality aspects and define the standards for verifying age.

In France, France Meslé, Jacques Vallin and Jean-Marie Robine, working with Guy Desplanques, gathered data from several imperfect sources: death statistics from municipal civil registers, data from the National Directory for the Identification of Natural Persons (RNIPP), and a list of names from print media reports of celebrations of very old birthdays. These three data sources were matched case by case to compile as exhaustive a list as possible of the presumed supercentenarians. Each case was then verified by a survey at the registry in the municipality of birth. Some 69 supercentenarians have been confirmed to date.

In order to confirm the supercentenarians, we need an identifier to locate the municipal registry where their births were recorded. For deaths recorded in the RNIPP, INSEE has twice provided us with a file including the dates of birth of the deceased. However, this process must not leave anyone out. We are therefore waiting for two other files from INSEE: the RNIPP file of "les immortels" and the file of deaths at age 110 or later from the municipal registries, providing dates of birth, dates of death and municipalities of birth.

Paradoxically, measures of mortality after 110 are now more accurate than those of mortality between 105 and 110, for which existing data are not very reliable. Verifying ages case by case is a much more expensive exercise for the latter age group, which is far more numerous. At their last meeting in Montreal in September 2008, the supercentenarians research group decided to undertake the same task for these ages, at least on the basis of a sample.

Nicolas Brouard

Epidemiological research into calculations of healthy life expectancy, such as that undertaken by the REVES network, has demonstrated a considerable discrepancy between the point prevalence measured on a particular date by a single survey or a census, and the period prevalence over a year or between two rounds of a survey calculated for a hypothetical cohort that would have experienced the incidence rates observed at a given point over its entire lifetime.

Regarding mortality, obviously we cannot speak of the prevalence of death, which is a single event rather than a condition. However, demographers do define prevalence of life (usually called prevalence of survival). They calculate (albeit not often enough) the prevalence of life observed at each age at a point in time when they calculate the percentage of people in a cohort that reach that age at that point in time for the purpose of constructing cohort-specific life tables. However, they do not usually turn the point prevalence into an indicator of the prevalence of life in a population. Conversely, the age-specific point prevalence of life is the percentage of survivors to a given age in a hypothetical cohort that would have experienced the mortality rates up to that age measured at that point, from which we commonly deduce life expectancy (e0) by summing. In the same way, we can work out a mean length of life (d0) from the prevalence observed. The difference between d0 and e0 can be eight to ten years in developed countries like France, Italy and Japan, but two to three years in countries that have not suffered wars or where the mortality transition began earlier and is progressing more slowly.

While the point prevalence is highly predictive of future human life expectancy, the observed prevalence reflects the past history of mortality in a country and is thus more similar to an indicator of population ageing due to the mortality component alone (i.e. excluding the birth rate and migration) than to an indicator of mortality in the conventional sense. The discrepancy between the two types of mortality prevalence is greatest at the oldest ages, when the past history of the cohorts diverges the most from projected mortality based on current mortality conditions. The project involves calculating the mean length of life in all the countries where cohort-specific mortality data are available or can be estimated.
Projections of mean length of life based on different hypothetical mortality rates at old ages will be calculated and compared with life expectancy projections. In France, the mean length of life is now rising much faster than life expectancy. Therefore it is interesting to study the impact of different decreases in mortality at old ages on those rates of increase.

Nicolas Brouard

Some authors maintain that the Gompertz function - whereby mortality increases exponentially with age - no longer holds at very old ages because the rate of growth in mortality slows down. Back in the late 1970s, Jean Bourgeois-Pichat warned of the risks of error when estimating mortality after age 90 on the basis of the probability of dying rather than the incremental mortality rate. Unlike the initial calculations performed in other countries, Bourgeois-Pichat showed that in France the curve of the logarithm of age-specific mortality became concave at advanced ages.

Nothing has changed since then, except that as mortality has declined, the percentage of survivors to an advanced age is increasing over time and at much faster rates than the decline in the mortality rate at the same age (wave crest effect). However, in all the cohorts of centenarians that we have been able to examine, particularly the IPSEN survey, the survey period of two months on average is long enough for people who are two months from death to be omitted from either the numerators or the denominators, thus biasing mortality rates.

Consequently, the under-representation of centenarians who are close to death will have a bigger impact on mortality at 110 than at 100, including a false slowdown in mortality with age. Furthermore, a mortality rate cannot be estimated at a single point (time or age) on the Lexis diagram, but only over an area with a certain width and height around that point so that there are enough deaths and enough person-years for the relationship between the two quantities to be meaningful. However, because the number of people surviving at very advanced ages becomes very small and the number of deaths is random, there is a tendency to broaden the estimation area both in terms of age (annual or five-year mortality rate) and exposure time. Not only does it become increasingly difficult to estimate the denominators, the calculated rate can no longer be considered an estimate of mortality at the average age of the interval but as an estimate of the age of the beginning of the interval. At very advanced ages, the annual rate - even correctly estimated - can be biased by as much as half a year. In addition to identifying the biases that contribute to the decline in the mortality rate at very old ages, we have developed an estimation method and a software program (an ImaCh version later than 0.97) that can estimate the mortality rate in a cross-sectional longitudinal survey such as the LSOA and HID surveys, on the basis of a prior modelling of the mortality law (Gompertz, Makeham, etc.) and an estimate using the maximum likelihood method when the sample is representative of the population of advanced age at a given age on a given date and when an exhaustive inventory of deaths that have occurred in this population is also known. The impact of the increase, which varies with age because of the decline in past mortality, on the initial structure of the pyramid, will receive special attention.

Authors who reject the validity of the Gompertz function after age 85 attribute the divergence to a heterogeneity effect and individual adaptation to life stress. It is too simplistic to ascribe the inversion of the mortality curve at advanced ages to heterogeneity, however, because the numbers at these ages decrease, which makes estimates of mortality uncertain and induces biases such as those in the IPSEN survey. The impact of heterogeneity on the length of survival is unclear. Its role in the measurement of mortality at advanced ages needs to be clarified. This issue should therefore be discussed to establish the connection between our research on the mortality of centenarians in France and the methods we have developed for calculating healthy life expectancy, which assume that people have different risks of dying. People with disabilities exhibit higher mortality than healthy people. However, mortality increases more slowly with age among the former group.