Validation of Exceptional Longevity
|
Validation of Exceptional Longevity Assessing the Information on Age at Death of Old Persons in National Vital Statisticsby V. Kannisto |
[ References ]
Mortality statistics are vulnerable to age errors which are most common in old age. The method of choice for calculation of death rates at high ages is the extinct-cohort method in which the populations-at-risk are obtained by summing up the deaths in each cohort beginning with the oldest. If the age data are correct, this method gives very precise results. If they are not, the errors are cumulated to lower ages.
Among old persons, two kinds of age error are found to occur: rounding and overstatement. Rounding often results in what is called age heaping: larger numbers of cases at ages ending in 0 or 5 than in between. Of age understatement which is often observed at younger ages, there is no evidence among the old. The errors, if selective, may also lead to sex bias as can be observed when age overstatement is rife.
In the following we shall assess the reliability of mortality data from official vital statistics of about 30 countries, assembled into the Kannisto-Thatcher database at Odense University Medical School in Odense, Denmark. The data have been used for detailed mortality analysis in monographs listed under references. We shall assess mortality data for heaping at ages 80, 90 and 100.
When data below age 80 are lacking, it is difficult to measure heaping at 80 using absolute numbers. Instead, we have used the ratio q(80)/q(81) as a heaping indicator because of the relatively firm relationship observed to exist between the two values when the data are accurate. Whether heaping is caused by rounding up or rounding down or both, it raises the ratio of q(80) to q(81).
Demographers have found that mortality generally rises at these ages by somewhat less than 10 percent per year of age (life table aging rate). Our data do not contradict this but indicate a tendency of this rate to increase in recent times and to be higher for women than men. This is the result of slower decline in mortality of the very oldest and of men as compared with women. When the life table aging rate increases, the q(80)/q(81) ratio falls. In thirteen countries with the most reliable information of age at death, the ratio averaged in the 1970-90 period 0.918 for men and 0.893 for women. Table 1 gives the ratios for different countries. We may consider a ratio of 0.95 or higher to indicate the existence of some age heaping, and a ratio which exceeds unity, a mark of serious distortion. Since 1950, the ratio never exceeded 0.95 in 20 countries while heaping occurred initially in eight countries, detailed in Table 2. In Canada, Estonia, Latvia, Portugal and Spain the heaping later disappeared. In Australia and among New Zealand non-Maoris it weakened considerably but remained strong in Ireland and among the Maoris. The ratios for Iceland and Luxembourg were volatile due to small numbers.
We measure heaping at other ages than 80 by comparing recorded deaths to deaths expected on the basis of numbers at adjacent ages:
where 
is the exponential of:
This indicator has the advantage that its significance is easily measurable (see Table 5). It has to be noted, on the other hand, that absence of heaping does not result in an indicator close to unity but higher due to the well-known bend of the mortality curve in logarithmic scale. At age 90, this creates an excess of about 2 percent, at age 100, closer to 10 percent.
Table 3 shows age heaping at 90 to be rare among the countries of the database. The average values for accurate data being 1.020 for men and 1.023 for women, we may consider a value of 1.05 to represent substantial heaping if the difference is significant. Among the indicators which exceed this limit are those for men in Switzerland and Iceland but their difference from 1.02 is not statistically significant and they are not confirmed by ratios for other periods. Examining the indicators during earlier decades in Table 4, we find in four countries clear evidence of initial heaping which later disappeared except among the Maoris and possibly in Spain.
Table 5 gives the recorded and the expected numbers of deaths at age 100 as well as the H(100) in 20 countries and, as a standard, the same for the group of thirteen. The recorded values are generally close to the expected ones and even Ireland has negative indicators. The only significantly elevated value is for French males but in the 1980-95 period it was normal.
When there is a tendency to age overstatement, it becomes progressively more serious as the age advances. The age distribution of the population and of deaths becomes distorted. This distortion can be used to detect age overstatement. Recorded age distributions can be compared with mathematical models or with observed distributions known to be accurate.
An elevated ratio 100+/85+ should not be taken to mean that the data below 100 or 85 are accurate. A high ratio is symptomatic of age overstatement which is likely to affect the data of the younger elderly as well, though with diminishing intensity.
Table 6 shows the proportion of centenarian deaths among those aged 85 and over, and the proportion over 105 among centenarians. As a standard, we give the same proportions in a stable population which enjoys low mortality and is growing at the average rate observed in the database at old ages. A population may exceed these values if it is subject to still lower mortality and/or if it is growing more slowly.
Most of the centenarian ratios (the first two columns in Table 6) fall below the norm. As is to be expected, they tend to be lowest in countries with higher mortality and to approximate the norm where mortality is lowest. As an exception, Japan has low ratios because its low mortality is so recent that the number of centenarians is still quite small.
Very high - and therefore suspect - values are seen for the Maori in New Zealand, for both races in the U.S. and for Canada. In these populations, also the 105+/100+ ratio is above the norm, confirming the tendency. For these ratios to be correct, mortality would have to be exceedingly low. Moderately elevated ratios of centenarians are also recorded for the non-Maori of New Zealand but the second set of ratios is roughly normal. On the other hand, these ratios are slightly elevated for Australia.
Table 7 gives further insight into age ratios. In the thirteen countries and Japan with their reliable data, the ratios have been increasing along with the decline in mortality. Among U.S. whites the centenarian ratio is on a much higher level and growing further while the second ratio is stagnating or falling, suggesting improvement in data quality which, however, probably still has a long way to go. If the 105+/100+ ratio is too high, so is almost certainly also the 100+/85+ ratio. The U.S. other races show similar tendencies on levels which are totally unrealistic. The same applies to the Maori but with the proviso that with the small base numbers the improvement is less clear.
The series for Portugal begin with obviously exaggerated ratios in the 1950s which then improve in quality until they reach or dip below general European levels. After that has happened, we can note in the centenarian ratios a moderate increase which may be real. Likewise, the data for Spain display improvement in quality, manifest as an apparent increase of mortality.
A detailed distribution of centenarian deaths in Table 8 illustrates the case of deaths recorded to have occurred at extremely high ages. The data for Japan appear normal and the distribution credible with the exception that in 1950-69 the ages over 106 were probably overrepresented and the ages over 110 certainly so since they were almost as many as in 1970-89 when the total of centenarians had grown five-fold. In Portugal age exaggeration was rife in the 1930s and heaping was manifest at age 100. Fifty years later these irregularities had virtually disappeared with the possible exception of the very oldest. The data for Ireland seem to reach too high in the age scale to be trustworthy.
The massive and accurate data for the group of thirteen countries display a logical form where the drop in numbers from one age to the next is at first a little over 40 percent and then becomes gradually larger. It is a good standard against which to compare other populations. The U.S. white females begin with a drop of little more than 30 percent which increases only slowly, and the distribution ends with a long tail which obviously cannot be true. The data for non-white males are even more heavily distorted.
The age distribution of deaths over age 100 reflects in an approximate way the centenarian mortality though it overstates it slightly when more recent cohorts are larger to begin with. Overlooking this factor which is larger in more youthful populations, we find that in the thirteen countries with most accurate data, about 0.06 percent of women aged 100 reach the "supercentenarian" age 110. For U.S. white women, the proportion is 0.6 percent and for U.S. non-white males, 6 percent. In other words, compared with the thirteen, U.S. women would have from age 100 to 110 a survival probability ten times as high, and the non-white males, a hundred times as high. For the Maori population of New Zealand the data are not more credible than those for U.S. non-whites, and finally, the data for Spain are comparable to those for U.S. whites.
Sex bias in recorded data results from differential age overstatement between the sexes. It is very widely observed that where age overstatement is common, it is considerably more serious regarding men than women. Pride in old age seems to be a predominantly male vanity which leads to its exaggeration. Family members also are often more proud of an aged patriarch than of an old grandmother. In populations with serious age overstatement this tendency leads to a significant bias in the proportions of males and females who are recorded as dying in old age, and this bias increases with advancing age.
When the age at death is correctly recorded, the ratio of females to males increases rapidly with age as is exemplified in Table 9 by the series of ratios in thirteen countries with good data. Compared with it, the ratios for Chile lag significantly behind and those for Maoris even more.
The ratios for the United States are also consistently lower than those for the group of thirteen. There is a wide difference between the races, the non-white showing much less credible proportions. The ratios have increased between the 1970s and 1980s suggesting improvement in data quality.
The indicators proposed above do not often allow rigorous judgment on data quality. While the presence of age heaping can be detected easily and without much doubt, age overstatement is less amenable to assessment by analytical means. Unusual demographic conditions may produce unusual values which are nevertheless true. Yet, for a large majority of the populations of this database, the observed age ratios conform to a distinct pattern in which variations are minor and explainable by demographic characteristics of each population. Indicators for countries in which birth registration had in the period concerned already been universal for at least 100 years, fall into this category while significant deviations have been produced by data from countries where this is not the case. The magnitude of the deviations is moreover related to what is known about the length of birth registration, the practice of death registration and the requirement to prove one's date of birth at various times in life.
Declining mortality raises the proportion of older deaths. Yet, almost all unusually high age ratios are showing reverse development and are decreasing towards the general pattern. Taken at face value, this would indicate mortality increase while the obvious reason is improvement in data quality which in several cases is proven by simultaneous disappearance of age heaping and of improbable tail end distributions of the very highest ages at death. Some of these ratios have reached the general average while others still seem to have some way to go. Portugal has gone full circle since 1950: an initially very high ratio of centenarians fell until it dipped below average and then began to increase.
All this builds up to a strong case of treating with caution statistics which produce unusual values of the kind often associated with data of demonstrably poor quality.
|
Table 1. Heaping at age 80 in 1970-1990 q(80)/q(81) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
|
Table 2. Countries with evidence of heaping at age 80 in any period | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
|
Table 3. Indicator of heaping at age 90 in 1980-1990 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
|
Table 4. Countries with evidence of heaping at age 90 in any period | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
|
Table 5. Recorded and expected numbers of deaths and heaping indicator at age 100, 1970-1990 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
|
Table 6. Certain age ratios of deaths, 1980-1989 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
|
Table 7. Development of age ratios of deaths, 1950-1989 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
|
Table 8. Centenarian deaths by recorded age | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
|
Table 9. Sex ratio (F/M) of persons reaching specified ages | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
[ Home | Contents | Return to previous page ]
Max-Planck-Gesellschaft 2003
