Skip to main content Accessibility help

Modelling the Age Dynamics of Chronic Health Conditions: Life-Table-Consistent Transition Probabilities and their Application*

  • Frank T. Denton (a1) and Byron G. Spencer (a1)


Surveys of chronic health conditions provide information about prevalence but not incidence and the process of change within the population. Our study shows how “age dynamics” of chronic conditions – the probabilities of contracting conditions at different ages, of moving from one chronic condition state to another, and of dying – can be inferred from prevalence data for those conditions that can be viewed as irreversible. Transition probability matrices are constructed for successive age groups, with the sequence representing the age dynamics of the health conditions for a stationary population. We simulate the life path of a cohort under the initial probabilities, and again under altered probabilities, to explore the effects of reducing the incidence or mortality rate associated with a particular condition. We show that such surveys of chronic conditions can be made even more valuable by allowing the calculation of the transition probabilities that define the chronic conditions aging process

Les sondages sur les conditions de santé chroniques fournissent des informations sur la prédominance mais pas l'incidence et le processus de changement au sein de la population. Notre étude a révelé comment "les dynamiques d'âge" des conditions chroniques—les probabilités de contracter des conditions aux âges divers, de passer d'un état d'une maladie chronique à l'autre, et de mourir—peuvent être déduites des données sur la prédominance de ces conditions, qui peuvent être considerées comme irreversibles. Les matrices de transition de probabilité ont été construites pour les groupes d'âge successifs, la séquence représentant la dynamique d'âge des conditions de santé pour une population sédentaire. Nous avons simulé la trajectoire de vie d'une cohorte sous les probabilités initiales, et encore sous les probabilités altérées, afin d'explorer les effets de la réduction du taux d'incidence ou de la mortalité associée à une condition particulière. Nous avons démontré que ces enquêtes sur les conditions chroniques peuvent être rendues encore plus valables en permettant le calcul des probabilités de transition qui définissent le processus de vieillissement pour des conditions chroniques.


Corresponding author

La correspondance et les demandes de tirés-à-part doivent être adressées à: / Correspondence and requests for offprints should be sent to: Byron G. Spencer, Ph.D. Department of Economics McMaster University 1280 Main Street West Hamilton, ON L8S 4M4 (


Hide All

The authors are grateful to two referees for helpful comments on earlier drafts of the article, and to the Social Science and Humanities Research Council of Canada which provided support through its Major Research Collaborative Initiative to the Research Program on the Social and Economic Dimensions of an Aging Population (SEDAP).



Hide All
Bacharach, M. (1965). Estimating nonnegative matrices from marginal data. International Economic Review, 6, 294310.
Bacharach, M. (1970). Biproportional matrices and input-output change. Cambridge, MA: Cambridge University Press.
Beltrán-Sánchez, H., Preston, S. H., & Canudas-Romo, V. (2008). An integrated approach to cause-of-death analysis: Cause-deleted life tables and decompositions of life expectancy. Demographic Research, 19, 13231350.
Comino, E. J., Tran, D. T., Haas, M., Flack, J., Jalaludin, B., Jorm, L., et al. (2013). Validating self-report of diabetes use by participants in the 45 and up study: A records linkage study. BMC Health Services Research, 13, 481,
de Groot, V., Beckerman, H., Lankhorst, G. J., & Bouter, L. M. (2003). How to measure comorbidity: A critical review of available methods. Journal of Clinical Epidemiology, 56, 221229.
Deming, W. E., & Stephan, F. F. (1940). On a least squares adjustment of a sampled frequency table when the expected marginal totals are known. Annals of Mathematical Statistics, 11, 427444.
Denton, F. T., & Spencer, B. G. (2010). Chronic health conditions: Changing prevalence in an aging population and some implications for the delivery of health care services. Canadian Journal on Aging, 29, 1121.
Keyfitz, N. (1977). What difference would it make if cancer were eradicated? An examination of the Taeuber Paradox. Demography, 4, 411418.
Keyfitz, N., & Carswell, H. (2005). Applied mathematical demography (3rd ed.). New York, NY: Springer.
Kim, A. A., Hallett, T., Stover, J., Gouws, E., Musinguzi, J., Mureithi, P. K., et al. (2011). Estimating HIV incidence among adults in Kenya and Uganda: A systematic comparison of multiple methods. PLoS One, 6(3), e17535. doi:10.1371/journal.pone.0017535.
Kintner, H. J. (2004). The life table. In Siegel, J. S., & Swanson, D. A. (Eds.), The methods and materials of demography (2nd ed.) (pp. 301340). London, UK: Elsevier Academic Press.
Mackenbach, J. P., Kunst, A. E., Lautenbach, H., Oei, Y. B., & Bijlsma, F. (1999). Gains in life expectancy after elimination of major causes of death: Revised estimates taking into account the effect of competing causes. Journal of Epidemiology and Community Health, 53, 3237.
Manuel, D. G., Luo, W., Ugnat, A.-M., & Mao, Y. (2003). Cause-deleted health-adjusted life expectancy of Canadians with selected chronic conditions. Chronic Diseases in Canada, 24, 108115. Ottawa, ON: Public Health Agency of Canada: 1–13.
Mariotto, A. B., Wang, Z., Klabunde, C. N., Cho, H., Das, B., & Feuer, E. J. (2013). Life tables adjusted for comorbidity more accurately estimate noncancer survival for recently diagnosed cancer patients. Journal of Clinical Epidemiology, 66, 13761385.
Nusselder, W. J., van der Velden, K., van Sonsbeek, J. L. A., Lenior, M. E., & van den Bos, G. A. M. (1996). The elimination of selected chronic diseases in a population: The compression and expansion of morbidity. American Journal of Public Health, 86, 187194.
Oksanen, T., Kivimäki, M., Pentti, J., Virtanen, M., Klaukka, T., & Vahtera, J. (2010). Self-report as an indicator of incident disease. Annals of Epidemiology, 20(7), 547554.
Owen, C. G., Jarrar, Z., Wormald, R., Cook, D. G., Fletcher, A. E., & Rudnicka, A. R. (2012). The estimated prevalence and incidence of late stage age related macular degeneration in the UK. British Journal of Ophthalmology, 96(5), 752756. doi:10.1136/bjophthalmol-2011-301109.
Sarfati, D. (2012). Review of methods used to measure comorbidity in cancer populations: No gold standard exists. Journal of Clinical Epidemiology, 65, 924933.
Somerville, K., & Francombe, P. (2005). Modeling disease elimination. Journal of Insurance Medicine, 37, 1319.
Statistics Canada. (2006a). Life tables, Canada, provinces and territories, 2000 to 2002. Ottawa, ON: Statistics Canada.
Statistics Canada. (2006b). Canadian community health survey, cycle 3.1. Ottawa, ON: Statistics Canada.
Statistics Canada. (2009). Canadian community health survey, 2007–2008. Ottawa, ON: Statistics Canada.
Stone, R. (1961). Input-output and national accounts. Paris: Organization for European Economic Cooperation.
Stone, R. (1962). Multiple classifications in social accounting. Bulletin de l’Institut International de Statistique, 39, 215233.


Modelling the Age Dynamics of Chronic Health Conditions: Life-Table-Consistent Transition Probabilities and their Application*

  • Frank T. Denton (a1) and Byron G. Spencer (a1)


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed