On the Statistical Dependence of Life Expectancy and Mortality Rate at a Given Age

The article examines the problems of estimating the life expectancy in the older age group under the conditions of incomplete and inac­curate mortality statistics.  In the introductory part of the article, the author addresses the need to improve statistics methodology, that focuses on increasing the ac­curacy of data on mortality and life expectancy for older age groups of the population.  In the main part of the article, the author proposes to use the regression dependence between life expectancy and mortality rate at the be­ginning of the open-ended age interval in addition to the traditional methods (standard life tables, methods of Horiuchi-Coale and Mitra).  The proposed two regression models show good accuracy on both cohort and calendar data. They were tested on the Human Mortality Database (HMD) international mortality database and showed a higher accuracy of the proposed method compared with the life tables and the extrapolation method. At the same time, the regression method is slightly inferior in accuracy to the methods of Horiuchi-Coale, and Mitra but is not as unstable as the Mitra method. Furthermore, the proposed method showed greater accuracy, in comparison with the known alternative methods, on high life expectancy data. The recommended method is appropriate when traditional methods cannot be applied due to the lack of necessary data (for example, population growth rate or average age of the population in the open-ended age group) or violation of the assumption of a stable age structure of the population that was used in developing methods Coale and Mitra.  Life expectancy estimates for the elderly using regression models are weakly correlated with alternative estimates using Horiuchi-Coale, and Mitra approaches. It indicates that the recommended in this article models can be used together with the known models in developing methods for reducing the variance of life expectancy estimates.  

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