Data: Population and Deaths Findings

3 Method

3.1 Method of Extinct Generations

An important part of our paper thus consists of evaluating the quality of Canadian mortality data for those aged 80 years and over. Drawing on mortality statistics, which generally offer greater coverage, we reconstitute the population with the help of the method of extinct generations [6] [38]. This method has been used by many researchers to study mortality at age 80 and above and is useful to estimate the population at advanced ages using only mortality statistics classified by year of birth and age at death. The principle of the method is very simple; when a cohort has died out, its size for any past year (and, consequently, at any given age) is simply calculated by summing the deaths, beginning with the oldest. Obviously, this method assumes the absence of international migration - a safe assumption at these extreme ages.

Although the extinct generation method can account for the problem of age misreporting in census data, there are still problems of age misreporting at death in vital statistics, mainly net age overstatement in particular at very old ages (100 and over). Depending on the degree of error, this problem may affect estimates of mortality at older ages. In a recent paper, Preston et al. [30] have examined this problem and have shown that the extinct generation method, as well as four other methods, produce the same effect on mortality, a downward bias. However, the degree of error related to the patterns of age misreporting chosen in that study (pattern for African American decedents) was quite extreme, which is not the case for Canada. In fact, the Canadian situation is more comparable to that of white Americans for which the quality of data is sufficiently high that extinct generation methods of estimating mortality produce reliable results [16] [17] [29].

These considerations suggest that the extinct generation method is a sound method to estimate mortality for the oldest-old in Canada. Another consideration is a matter of consistency, since the purpose of our study is to compare mortality of oldest-old in Canada to results from other studies where the extinct generation method has been used.

Graduation methods are not necessary in the context of our study, though they are still very useful. In fact, official life tables (like the Canadian or the U.S. Life Tables) will always require some graduation because of small numbers of deaths at very old ages (above 100 years old).


3.2 Estimating the Deaths of Non Extinct Generations: The Survival Ratio Method.

One drawback of the method of extinct generations is the need to wait until all members of the same cohort have died before being able to fully estimate the population at a given age. However, the Survival Ratio method can be used to estimate population figures for non-extinct cohorts at a given moment in time [20] [34] [43]. Depoid [10] claims to obtain very adequate results based on the assumption that the deaths of non-extinct cohorts are distributed by age until extinction in the same way as deaths of earlier, already extinct, cohorts; in other words, it assumes that mortality is invariable. In this study, we have chosen 110 years as the age at which cohorts become extinct; for the cohorts born between 1841 to 1884, very few deaths reportedly occurred at the age of 110 and over (66 for women and 27 for men).


Data: Population and Deaths Findings

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Mortality Statistics for the Oldest-Old: An Evaluation of Canadian Data
Robert Bourbeau and André Lebel
© 2000 Max-Planck-Gesellschaft ISSN 1435-9871