A Relational Model of Mortality at Older Ages in Low Mortality Countries

Himes, Christine L.; Preston, Samuel H.; Condran, Gretchen A.

doi:10.1080/0032472031000147796

Cited by 61 publications

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“…This makes it impossible to produce complete net and overall survival functions and to estimate life expectancy and other actuarial functions, under the dependent competing risk model, and to investigate the complete or partial elimination of one or more causes of death. There have been several approaches to extending life tables beyond an upper age limit, such as the old-age mortality standard, developed by Himes, Preston and Condran (1994), the old age part of the Heligman-Pollard mortality model (see Heligman-Pollard, 1980) and also the Coale-Kisker method of closure of mortality tables (see Coale and Kisker, 1990, developed from a previous paper by Coale and Guo, 1989, and a recent investigation by . For a more detailed account on these methods and their application we refer to Buettner (2004).…”

Section: Estimating and Extrapolating The Crude Survival Functionsmentioning

confidence: 99%

Modelling the joint distribution of competing risks survival times using copula functions

Kaishev

Dimitrova

Haberman

2007

Insurance: Mathematics and Economics

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The problem of modelling the joint distribution of survival times in a competing risks model, using copula functions is considered. In order to evaluate this joint distribution and the related overall survival function, a system of non-linear differential equations is solved, which relates the crude and net survival functions of the modelled competing risks, through the copula. A similar approach to modelling dependent multiple decrements was applied by Carriere (1994) who used a Gaussian copula applied to an incomplete double decrement model which makes it difficult to calculate any actuarial functions and draw relevant conclusions. Here, we extend this methodology by studying the effect of complete and partial elimination of up to four competing risks on the overall survival function, the life expectancy and life annuity values. We further investigate how different choices of the copula function affect the resulting joint distribution of survival times and in particular the actuarial functions which are of importance in pricing life insurance and annuity products. For illustrative purposes, we have used a real data set and used extrapolation to prepare a complete multiple decrement model up to age 120. Extensive numerical results illustrate the sensitivity of the model with respect to the choice of copula and its parameter(s).

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Section: Estimating and Extrapolating The Crude Survival Functionsmentioning

confidence: 99%

Modelling the joint distribution of competing risks survival times using copula functions

Kaishev

Dimitrova

Haberman

2007

Insurance: Mathematics and Economics

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“…Alternative direct mortality extrapolation methods include, for example, the Geometric method (Pollard, 1987), Ediev's adjusted version of the Geometric method (Ediev, 2008) and a Relational model (Brass, 1974;Himes, Preston, & Condran, 1994). Mortality can also be forecast indirectly by extrapolating the parameters of functions fitted to the age profile of death rates (Keyfitz, 1982;McNown & Rogers, 1989).…”

Section: Projected Very Elderly Population Numbersmentioning

confidence: 99%

“…Given the approximate relationship, , this function may also be applied to the central death rate (Himes et al, 1994): will result in the probability of death approaching an asymptote of less than 1 (around 0.632) with increasing age. Under equation 2.21, however, the probability of death approaches an asymptote of 1 with increasing age.…”

Section: Exponential Functionsmentioning

confidence: 99%

“…A logit transformation of the force of mortality ( ) modelled by this two-parameter logistic function is a two-parameter linear function of age (Himes et al, 1994;Thatcher, 1999b;Thatcher et al, 1998): which simplifies to:…”

Section: Exponential Functionsmentioning

confidence: 99%

“…Himes et al (1994) employed a combination of methods by fitting a logistic curve on a standard set of mortality rates at ages 45 to 99 derived from the smoothed observed rates based on pooled data for 16 low-mortality countries over the period 1948 to 1985, and extrapolating to age 115.…”

Section: Volatility Of Rates At the Highest Agesmentioning

confidence: 99%

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Population estimates and projections for Australia’s very elderly population at state and national level

Terblanche¹

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As in many developed countries, the very elderly population (ages 85+) is the fastest growing age group in Australia, with far-reaching economic and social consequences. To effectively plan and budget for the income, aged care and health care needs of the very elderly, accurate estimates and projections are required. There are, however, several obstacles relating to the availability and accuracy of very elderly data. Official population estimates at very high ages in Australia have been found to be too high and fluctuate implausibly over time. International and local studies have found large errors in projected very elderly populations, stemming from inaccurate mortality rate forecasts.This thesis aims to create accurate estimates and projections for Australia's very elderly population at a state and national level. Various methods for estimating very elderly populations from death counts were assessed for accuracy at both a national and state level.While the Human Mortality Database uses such methods to create estimates for many countries, their accuracy has never been assessed for Australia. Furthermore, little is known, locally or internationally, about their performance at a sub-national scale. In this study, the accuracy of various nearly-extinct-cohort methods were assessed at the Australian national and state level by retrospectively applying them to extinct cohorts and comparing the results against those obtained from applying the Extinct Cohort method. Suitable methods were applied to create very elderly population estimates and death rates for Australia from 1972-2012 by sex, state and at single ages 85-110+. The growth, changes in the age-sex composition and the demographic drivers of growth of Australia's very elderly population were analysed. Based on these estimates, more reliable death rates were calculated, allowing a detailed study of the changing patterns and trends in Australian adult mortality. Finally, a number of mortality forecasting methods were retrospectively evaluated for their accuracy in projecting adult death rates for Australia over 10 and 20 years ending in 2012. An appropriate method was applied to create projections for the next three decades.It was found that, compared to the official census-based estimates, more plausible and accurate estimates, especially for ages 95+, could be derived from death counts. The Survivor Ratio (SR) method with results constrained to official estimates for ages 85+ produced accurate very elderly population estimates for Australia across the sexes and ages at both a national and state level. Internal migration is sufficiently minor to be ignored. Very accurate state-level estimates could also be derived using a simpler method of apportioning national single-age estimates between the states. Adult death rates in Australia were found to show consistent and regular patterns of decline since the 1970s, with rates of decline decreasing with age. These patterns support the use of simple direct extrapolation methods for forecasting. The Geometric,...

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Retrospective Testing of Mortality Forecasting Methods for the Projection of Very Elderly Populations in Australia

Terblanche

2016

Journal of Forecasting

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The purpose of this paper is to present the results of retrospective tests of various extrapolative methods to forecast adult mortality and very elderly populations for Australia. Direct extrapolation methods tested include the Geometric method, Ediev variant, Lee-Carter method, BMS variant and a relational model. Indirect methods include the extrapolation of parameters of models fitted to the age profile of death rates and a new method involving the extrapolation of features of death frequency distributions namely the modal age and concentration. The geometric, Ediev and LeeCarter BMS methods were very successful in projecting death rates and very elderly populations. Differences between these methods were small. The extrapolation of parametric functions proved successful for males but less so for females. Very elderly populations can be viably projected by directly extrapolating death rates by age when rates of decline in death rates show consistent relationships between ages and are stable over time.

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A Relational Model of Mortality at Older Ages in Low Mortality Countries

Cited by 61 publications

References 0 publications

Modelling the joint distribution of competing risks survival times using copula functions

Modelling the joint distribution of competing risks survival times using copula functions

Population estimates and projections for Australia’s very elderly population at state and national level

Retrospective Testing of Mortality Forecasting Methods for the Projection of Very Elderly Populations in Australia

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