Discussion of the paper
"Living to age 100 in Canada in 2000" presented by Louis G. Doray
at the International Symposium "Living to 100 and Beyond: Survival at Advanced Ages"
(Lake Buena Vista, Florida, January 17-18, 2002)

Discussant: Leonid A. Gavrilov
Center on Aging, NORC and the University of Chicago

This is an interesting an important study of the oldest-old mortality in Canada, which includes construction of reliable life tables by the method of extinct generations, testing different statistical models to explain mortality age-trajectories, and analysis of temporal improvement in survival to advanced ages.

In my opinion, this study has the following important strengths:

(1) The study is based on survival data generated by the method of extinct generations. This is the best possible method to study survival at extreme ages, because traditional methods based on census data and age claims by nonagenarians and centenarians are extremely unreliable. Now, when a profound changes in the oldest-old mortality are observed in many developed countries, it is important to organize a continuous international monitoring of mortality trends at advanced ages (which is also important for regular correction of forecasts), and the method of extinct generations is the best possible way to address the problem of data quality.

(2) The study uses several alternative models (mortality laws) that are applied to survival data and compared to each other. This is an important approach that needs to be developed further in the future studies.  There are many different mortality models available in the scientific literature (Gavrilov, Gavrilova, 1991;  2001), which deserve to be compared with each other using the same data sets. This is how "the best mortality law" for extreme old ages could be eventually found.

(3) The mortality models used in this study are not just arbitrary combinations of symbols and parameters, but rather the "theories" having fundamental justification in statistics and mathematical biology. For example, the Perks model used in the study directly follows from the mathematical theory of aging assuming the avalanche-like mechanism of age-related destruction of an organism (Gavrilov, Gavrilova, 1991).  This mechanism of “domino effect” in aging can be illustrated by the following scheme:

avalanche-like destruction


One suggestion for further developments of this study is to address the problem of secular mortality trends (period effects).  This is because the life tables calculated by the method of extinct generations are cohort life tables, where deleterious effects of aging on mortality are confounded by simultaneous mortality improvement over time. It is this type of confounding that may result in the failure of tested models, which was observed in the study.  The tested models were developed for situations where the age was the only predictor variable for mortality, while all other covariates were supposed to be fixed.  This assumption is violated in the case of cohort life tables when the calendar time is also increasing with the age of surviving cohort.  One way to overcome this problem is to use a set of generated cohort life tables in order to calculate the current (cross-sectional) life tables for the oldest-old. Then the models can be tested with these current life tables, where mortality rates are calculated for the same time periods and are, therefore, not confounded by secular mortality trends and fluctuations. Another interesting approach is to analyze the oldest-old mortality surface (at the Lexis diagram) by the 'age-period-cohort' models (APC models), where the changes in mortality rates are partitioned into the effects of age, period (calendar time), and cohort (birth year).

It is interesting to discuss possible limitations of this study, because this may be useful for future work. The method of extinct generations used in this study assumes that there is no migration of the population, and I agree with the author that this assumption seems to be reasonable for nonagenarians and centenarians. In fact some of them are even not able to leave the house where they live. However, it would be interesting to ask a question whether there are any real data proving negligible migration of the oldest-old in Canada. Canada is an interesting country with population mostly concentrated at the US border, and this border is not a Berlin Wall at all.  There may be incentives for those who live in Canada and have aged parents in the United States to move aged parents in Canadian nursing homes, which may be cheaper and more convenient in care providing. On the other hand, those who live in the United States and have aged parents in Canada may also be interested to move aged parents closer to them, particularly if they believe that they can afford better care for their parents in the United States.  It would be interesting to explore these issues in the future, and perhaps to conduct a survey in order to estimate migration among the Canadian oldest-old.

Another interesting question is how reliable are the data on ages at death, recorded in Canadian death certificates for the oldest-old, which are used by the method of extinct generations. There are significant differences between different countries in the way on how this information (age at death) is reported. For example, in Russia everybody is supposed to have an internal passport (with exact birth date recorded there) and this passport has to be surrendered by the relatives in order to obtain death certificate for deceased person. In other words, age at death in a death certificate comes from the document (internal passport), rather then claims from the relatives or physicians. The situation is different in the United States, where ages at death in death certificates are sometimes taken from recollections of relatives or physician claims, and therefore may be less accurate for the oldest-old.  It would be interesting to know what is the situation in Canada with age at death reporting and how accurate is this information in the case of the oldest-old death certificates.

Finally, there is a technical question related to application of the method of extinct generations to the Canadian data, where the annual numbers of deaths above age 100 are aggregated (denoted 100+).  Since the annual numbers of deaths above age 100 may be different from the number of deaths (above age 100) in cohort life tables generated by the method of extinct generations, it would be interesting to know, how this problem (caused by data aggregation) has been addressed.

Overall, this is an interesting, important and thought-provoking study, which raises a number of new methodological issues for the future research.


Gavrilov L.A., Gavrilova N.S. The Biology of Life Span: A Quantitative Approach, NY: Harwood Academic Publisher, 1991, 385p.

Gavrilov L.A., Gavrilova N.S. The reliability theory of aging and longevity.  Journal of Theoretical Biology, 2001, 213(4): 527-545.

Contact address of the discussant:

Dr. Leonid A. Gavrilov, Center on Aging
NORC/University of Chicago
1155 East 60th Street
Chicago, IL 60637-2745
Fax: (773) 256-6313, Phone: (773) 256-6359