A generalised life-expectancy model for a population
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A generalised life-expectancy model for a population OA Adekola* The World Bank Country Office, Abuja, Nigeria In a recent paper, it was shown that the life-expectancy behaviour for homogeneous and non-homogeneous population differs markedly for moderately high and low ages. One therefore has two curves for each of these regions and the problem is how to construct a single life-expectancy curve which blends these two curves together in a satisfactory way. This note offers a simple mathematical and analytical model which is useful in estimating an acceptable life expectancy under all severities of life situation. A simple numerical example is given to illustrate the application of the method. Journal of the Operational Research Society (2002) 53, 919–921. doi:10.1057/palgrave.jors.2601394 Keywords: life expectancy; homogeneous and non-homogeneous population; mean survival age; frailty
Introduction At birth, an individual has a certain life expectancy. Life expectancy is the average length of life lived in a population. Life expectancies can be obtained using a numerical integration over the range of age variable (with the upper limit set by a maximum conceivable age) and sometimes, analytically by integrating the survival function over relevant ages. This approach may sometimes have a number of obstacles and drawbacks including the rather tedious numerical procedure and the inability to arrive at a reasonable solution for certain details. The conventional life table assumes that population is homogeneous in which all lives of the same age face equal mortality risks. However, some people are more likely to die than others due to individual frailty (differences in longevity due to biological and behavioural reasons). Whittaker1 has shown how the rate of change in life expectancy can be used as the basis of calculating acceptable risk. Wajiga and Adekola2 gave the effect of additional mortality risks on life expectancy but do not consider individual risks. Congdon3 stated that life expectancy based on homogeneous assumption will be overstated for all ages due to the unobserved risk factors. In a recent paper, Wajiga and Adekola,4 showed empirically that life expectancies computed for homogeneous population models are overstated for ages less that the mean survival age and understated for higher ages. It was also observed that the life-expectancy curves for homogeneous and non-homogeneous populations intersect at the mean survival age (when the most frail would have died off) and the maximum age which all members of the cohort can live. For definition of homogeneous and non-homogeneous
*Correspondence: OA Adekola, The World Bank Country Office, Plot 433, Yakubu Gowon Crescent, Asokoro District, PO Box 2826, Abuja, Nigeria. E-mail: [email protected]
population, see Congdon.3 One therefore has separate curves for the two regions corresponding to moderately high ages and low ages. The problem is to produce
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