4.1 Data Quality of Deaths and Population
Using a variety of measures of reliability, we first evaluate the quality of mortality data. We then attempt to assess whether or not the censuses provide accurate figures for the population aged eighty and over by comparing these figures with those of populations calculated from deaths.
4.1.1 Age Heaping and Generation Heaping for Deaths
We tested the quality of Canadian data on deaths at advanced ages for the problems of age heaping at ages 80, 85, 90 years and so on, by calculating the Whipples index used to measure this type of attraction; results revealed no significant signs of age heaping either for the population aged 80 years and above or among centenarians.
It was also possible to verify an attraction for the younger generation at death, often resulting from calculating the year of birth as the difference between the date of the current year and the age at death. For instance, a person dying at 100 years in 1995 was not necessarily born in 1895 (1995-100=1885); he might just as easily have been born in 1884. We would expect deaths to be distributed equally between the younger (1885) and older (1884) cohorts [Note 2]. We used the Generation Heaping Indicator (GHI) - the ratio of deaths attributed to the older cohort to deaths attributed to the younger one - to estimate the accuracy of cohort declaration.
Canadian mortality statistics on deaths of centenarians for the periods 1951-1960 and 1961-1970 are subject to a strong attraction for the younger cohort. The quality of death declarations for the year of birth appears to improve at extreme ages, although the number of deaths attributed to the older cohort are still underestimated. Moreover, an improvement over time meant that for the 1991-1995 period, the GHI was close to unity for octogenarians and is comparable to those of France, Sweden and Japan (countries with high quality data) over the age of 90 years.
4.1.2 Highest Age at Death Comparison
The reliability of mortality statistics in Canada can be estimated by comparing the number of registered deaths at oldest ages to the equivalent figures for other countries known to have high quality data (countries where age at death is carefully scrutinized and accurately recorded). Table 1 shows that the highest age at death reported in Canada exceeds that recorded in all countries except the United States. The highest age at death among the European countries and Japan over a long period of observation rarely exceeded 110 years. There were, in fact, only few cases on record: one woman who died aged 112 in Sweden (1985-1995); two others aged 112 and 111 in Japan (1953 and 1993) and a few who died between age 112 and 116 in France (1970-1995). For men, the highest reported age at death was 114 years old in France during the period 1970-1995 [Note 3]. In Canada, the highest age of registered deaths for the period 1951-1995 was substantially higher, at 118 years for men and 116 years for women.
In these reference countries, the maximum age at death tended to increase over time, with growing numbers of individuals surviving to old ages. In Canada, this trend is absent, even though, according to the Canadian life tables, 25% more women and 15% more men survived until 80 years in 1991 than in 1951. Moreover, the oldest age at death in Canada was observed in the male population, an unexpected finding given the mortality patterns it shares with other industrialized nations: higher mortality at advanced ages for men than women, and a lower number of male than female centenarians. Finally, this table also shows that the second and third highest ages at death were considerably higher for Canada than for all other countries except the United States, confirming that the highest reported age at death was not a unique case of misstatement of age.
4.1.3 Overstatement of Age at Death among Centenarians
Kannisto  has demonstrated the utility of other indicators developed to measure the reliability of data on centenarians. Those pertaining to age overstatement, age heaping and sex selection have been tested in countries with reliable data. In those countries, the rapid depletion of the population at these ages, on the one hand, and the increasing size of successive cohorts of centenarians, on the other, mean that the proportion of those aged 105 and over among all centenarians is expected to be less than 5 %, and to be smaller for men than women (table 2). Reference countries with population registers judged to have a high standard of mortality statistics, such as Sweden, Finland, France, England and Wales, adhere to this norm. The ratio for Canadian data, however, exceeds it, at 7.8 % for men and 8.5 % for women during the 1951-1995 period, indicating overstatement of age at death in Canadian data.
The second indicator expects that the percentage aged 110 and over among those aged 105 and over will be smaller than the first indicator (105 years + / 100 years +). This condition was respected only among the female populations of Japan, England and Finland. On this point, Canadian data fulfills the assumption, except during the fifties when data reliability was lower. Nonetheless, there is evidence of some overstatement of age in the fact that the first criterion was not respected.
The third indicator is based on the observation that the probability of death at age 101 is higher than at age 100, and thus that the ratio of mortality risks at 100 and 101 years should be below unity (q100 / q101 < 1). An indicator significantly higher than 1 signals an attraction towards declaring death at the exact age of 100 years. This type of error is absent in the majority of reference countries. To verify this indicator for Canadian data, the probabilities from the population estimated by the method of extinct generations were preferred to those published by Statistics Canada. Our tests showed that, at least during the fifties and sixties, Canadian data was subject to this declaration error, particularly for the male population. From 1970 onwards, however, the problem disappears, pointing to a gradual improvement in Canadian mortality statistics at advanced ages over the last half of the twentieth century.
The final indicator is the ratio of womens deaths to those of men. For Canada, this ratio remained stable at around 2 for the decades 1951-1960 and 1961-1970, but had doubled by the period 1991-1995. This provides further evidence of an age overstatement in death declarations among males over 100 years old in earlier decades. The improvement in data quality has raised this ratio to levels that are probably more accurate for Canada and comparable to those of France, Japan and Finland, in recent years.
In summary, Canadian data on deaths do indeed suffer from age overstatement at extreme ages, over 100 or 110 years old, and more so for men than women. The comparison does suggest, however, that Canadian data are more reliable than US mortality statistics that show an even stronger tendency to overestimate age at death. Moreover, since 1951, the quality of death data seems to have improved in Canada.
4.1.4 Overestimation of Centenarians in Canadian Censuses
Table 3 presents the ratio of enumerated population (census population) to population calculated from deaths (population estimates) for Canada by single year of age or age group, sex, and census year. A ratio superior to 1 indicates that the census figures are higher than the estimated population. The accuracy of the figures varies from one census to another but in general, the ratio oscillates around unity between the ages of eighty and one hundred years for women and ninety-five years for men. From then on, however, census counts clearly overestimate the population. Nonetheless, this problem has decreased over the period 1971-1991 by one third for female centenarians (from 1.98 to 1.22) and by half for males (from 2.72 to 1.43).
The evolution of population estimates at advanced ages, by age group, for Canada and for a group of industrialized countries with high quality data are compared in Table 4. Kannistos database  is the source of information for these reference countries. The proportion of individuals aged 90-99 years to those aged 80 years and over is clearly higher in Canada in 1950 and 1990. In 1991, the proportion of centenarians to the population aged 80 years and over in Canada was five times that in the other industrialized nations: one centenarian for 200, compared with one for 1000 in the reference countries. It is possible that overestimating the age of the oldest-old in Canada may have caused this discrepancy.
The highest proportion of centenarians in Europe, in 1990, reached between 60-70 per million in the total population, in countries where the demographic transition occurred early and where mortality at advanced ages had been low for some time . According to the estimated populations, Canada had 2884 centenarians in 1991: 106 centenarians per million of the total population [Note 4]. This is twice the average level known in the reference countries, at 45 centenarians per million of population. Thus, although the population estimation has reduced the overestimation of the number of centenarians, the number still appears quite high compared to other industrialized countries.
4.2 Canadian Mortality and International Comparison
4.2.1 Canadian Mortality at Advanced Ages
Figure 2 illustrates the evolution of estimated probabilities of dying (qx) at advanced ages for Canada, by age and sex, for certain five-year periods in the last half of the twentieth century. These probabilities, rising gradually with age, display a pattern similar to that found in the official life tables; nonetheless, from 100 years onwards, important fluctuations appear, linked to the absence of smoothing, to the small number of deaths at extreme ages, and to the complete absence of deaths at some ages.
Figure 3 makes it easier to appreciate the recent development of mortality estimated at advanced ages, by presenting a series of ratios relating probabilities for more recent periods to those for the period 1952-1955, which becomes therefore the point of comparison, and takes the value of 100. Female mortality between 80 and 100 years dropped sharply during the period (35%: 80-89 years, 25 % and less: 90+). For males, it is more difficult to distinguish a clear pattern in mortality decline over time because of great fluctuations from one age to another; but it has clearly declined much less markedly since the fifties than has female mortality. The greatest progress for men has been among octogenarians for whom mortality has declined between 10% and 20% during the period. For each decade, male mortality up to 95 years was substantially higher than that of females, and this difference has increased in magnitude over the last forty years, passing from 20% for octogenarians in the fifties to 40% for the period 1991-94.
4.2.2 Canadian Life Tables and estimated probabilities of dying
The ratios of the official life table probabilities of dying (1950-1952 to 1990-1992) to our estimated ones (1952-1955 to 1991-1994), by age and sex, are presented in Figure 4. A ratio inferior to 1 indicates that estimated mortality is higher than that published in the official life tables. With the improved quality of mortality data, we expected our estimated measures for more recent periods to be higher, as Statistics Canadas tables are likely to underestimate mortality at advanced ages. The results were not as obvious as predicted: in 1991 only, the estimated probabilities exceeded those published by Statistics Canada and the difference is not very large, less than 10%.
In 1991, for instance, the probability that individuals reaching the age of 80 survive to 100 years is slightly overestimated in the official life tables. For a woman, the estimated probability was 40 compared with 43 in the official life tables; the equivalent probabilities for men are 13 and 15 , respectively.
4.2.3 International comparisons on the basis of estimated probabilities of dying
In this section, estimated probabilities of dying for Canada are compared with other countries for which these probabilities, calculated by the same method, are available in the Berkeley Mortality Database . Figure 5 illustrates the relationship between Canadian probabilities and those of the USA, France, Sweden and Japan, by age (from 80 to 100 years), sex, and time period (1971-1975 and 1991-1995). A ratio inferior to 1 signifies that Canadian mortality is lower than that of the country under comparison.
Canadian probabilities of dying resemble those observed in the United States; both countries stand out as having distinctly lower levels than those of Sweden, France and Japan, at all ages over 80 years in 1971-1975 and, more particularly, over 90 years in 1991-1995. During the earlier period, female mortality in Canada was, on average, 15 to 20% lower than that observed in the other countries at that time. For the 1991-1995 period, mortality is lower in France and in Japan from age 80 to 85; then, the gap between Canada and the other countries widens gradually, in Canadas favor, up to 95 years old where, as for the period 1971-75, the mortality of Canadian women is about 10 to 20% lower. For men, the small numbers at each age lead to greater fluctuations in the mortality ratios, making it more difficult to perceive a distinct profile. However, the mortality of American males is still lower than that estimated for Canada. For the first period, Swedish, French and Japanese probabilities of dying are clearly higher than Canadian ones, from 10% to 20%. For the 1991-1995 period, Canada shows a lower mortality above age 85 only. These results hint at the possibility of a profile peculiar to North American mortality.
4.2.4 International comparisons on the basis of age-standardized death rates
Kannisto  has suggested using Age-Standardized Death Rates for individuals aged between 80 and 99 years [Note 5]. Out of a pre-selected sample of countries with high quality data, four groups were created according to the level and evolution of mortality: low (Denmark, The Netherlands, Norway and Sweden), medium (Austria, Belgium, England, Finland and West Germany), high (Czechoslovakia, East Germany and Hungary), and rapid decline (France and Switzerland).
In Figure 6, Canadian data indicate a very low level of mortality, inferior to that of the countries categorized as having low mortality. This difference lessens during the period, in particular for the female population. In 1985-1989, for example, Canadian rates stood at 89 for women and at 133 for men, compared with only 104 and 150 , respectively for the low mortality countries. Between 1955-1959 and 1985-89, Canadian mortality at advanced ages declined by 26%: 32% for women, and 16% for men. This reduction is similar to that of countries with low and medium mortality levels and slightly lower than that of countries with sharply declining mortality. For the high mortality nations, grouped geographically in Eastern Europe, the reduction in mortality rates at advanced ages during the period was of - 9%. Mortality decreased at a faster pace from the period 1970-74 onwards for all four groups of countries, and for Canada. On average, the speed of decline for those aged over 80 years was twice as fast for Canada and the reference countries. Female mortality at advanced ages for the low mortality group, for example, declined by 8.9% between 1955 and 1969, and by 19.1% between 1970 and 1989. Advances in Canadian female mortality during the latter period were also higher than during the first, at 11% and 18% respectively.
For the period 1985-89, Canada, with an age-standardized death rate for the age range 80-99 of 103.5 , rated before Iceland (105.0 ), Japan (111.2 ), and before the two countries classed as having rapidly declining mortality, Switzerland (114.0 ) and France (115.9 ). Iceland, like Japan, has been classified among the countries with excellent data quality, and is even recognized as the country with the most reliable mortality statistics at advanced ages in the world. In the light of these results, therefore, Canada does indeed have exceptionally low mortality levels among the oldest-old.
Mortality Statistics for the Oldest-Old: An Evaluation of Canadian Data
Robert Bourbeau and André Lebel
© 2000 Max-Planck-Gesellschaft ISSN 1435-9871