Forecasting disability: application of a frailty model

Abstract

Random changes in individual frailty occur due to the stochastic processes of physical deterioration or environmental influences. This paper implements a stochastic ageing model using maximum likelihood methods and calibrates the model to more than 30 years of historical Australian mortality data in order to examine cohort and gender differences in health-state distributions among older adults. We find that frailty levels have declined over time for both male and female cohorts. Nonetheless, patterns of frailty are different between genders. Older females experience a faster pace of health deterioration than their male counterparts causing them to move quicker into worse states of health. Health states are also more heterogeneous among women than men. Population-level estimates suggest that the number of elderly Australians requiring aged care services will exceed that projected under governmental assumptions by 2050.

Keywords:

• population ageing
• morbidity
• disability risk
• health-state distributions

Acknowledgements

We would like to thank an anonymous referee for many valuable suggestions which helped improve the paper. This work was supported by the SIM University under the Centre for Applied Research Grant RF15UC03. An earlier version was supported by the ARC Centre of Excellence in Population Ageing Research under grant CE110001029. Opinions and errors are solely those of the authors and not of the institutions providing funding for this study or with which the authors are affiliated.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

¹ There may be cases that deviate from this general assumption, for example, when a newborn is born impaired with an initial damage load.

² More formally, the likelihood function in Equation (5) is proportional to the expression given, rather than equal to it.

³ Theoretically, the model does not impose an upper limit to the maximum age which might be attained. For the cohorts examined in this paper, we find that the limiting age is approximately 219 on average. See also Appendix 1 for a mathematical derivation of the limiting average physiological age (). represents the average level of frailty among survivors at very advanced ages within a given cohort.

⁴ The Intergenerational Report is commissioned by the Commonwealth Government every 5 years and is prepared by The Treasury Department. It assesses the fiscal and economic challenges of an ageing population, implications of demographic change for economic growth and financial implications of continuing current policies and trends over the next four decades. Core activities comprise self-care tasks such as bathing or toileting, mobility tasks such as moving around at home or using public transport as well as communication with family and friends. The SDAC surveys specify four levels of severity (profound, severe, moderate and mild) based on the person’s ability to perform tasks relevant to these areas and on the amount of help required. Specifically, individuals who are classified as having ‘profound’ or ‘severe’ core activity limitations require personal help or supervision constantly or sometimes, and are unable to perform tasks without help or supervision.

⁵ Older SDAC survey waves in 1981, 1988 and 1993 are not used in our analysis because the final age group for those earlier waves terminated at age 75+ instead of age 90+.

⁶ This transformation stabilizes the variances and sets a lower bound of zero on parameter forecasts.

⁷ Appendix 2 provides details about the population data used.

⁸ Page 145 of the Intergenerational Report 2010 states: ‘The Australian Bureau of Statistics surveys and Australian Institute of Health and Welfare analyses continue to suggest a relatively stable prevalence rate of severe disability among older Australians. Accordingly, the base projections presented here do not assume any change in severe disability rates.’