The rapid growth of very elderly populations requires accurate population estimates up to the highest ages. However, it is recognised that estimates derived from census counts are often unreliable. Methods that make use of death data have not previously been evaluated for Australia and New Zealand. The aim was to evaluate a number of nearly-extinct cohort methods for producing very elderly population estimates by age and sex for Australia and New Zealand. The accuracy of official estimates was also assessed. Variants of three nearly-extinct cohort methods, the Survivor Ratio method, the Das Gupta method and a new method explicitly allowing for falling mortality over time, were evaluated by retrospective application over the period 1976-1996. Estimates by sex and single years of age were compared against numbers derived from the extinct cohort method. Errors were measured by the Weighted Mean Absolute Percentage Error. It is confirmed that for Australian females the Survivor Ratio method constrained to official estimates for ages 90+ performed well. However, for Australian males and both sexes in New Zealand, more accurate estimates were obtained by constraining the Survivor Ratio method to official estimates for ages 85+. Official estimates in Australia proved reasonably accurate for ages 90+ but at 100+ they varied significantly in accuracy from year to year. Estimates produced by Statistics New Zealand in aggregate for ages 90+ proved very accurate. We recommend the use of the Survivor Ratio method constrained to official estimates for ages 85+ to create very elderly population estimates for Australia and New Zealand.

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,...

Increasing very elderly populations (ages 85+) have potentially major implications for the cost of income support, aged care, and healthcare. The availability of accurate estimates for this population age group, not only at a national level but also at a state or regional scale, is vital for policy development, budgeting, and planning for services. At the highest ages census-based population estimates are well known to be problematic and previous studies have demonstrated that more accurate estimates can be obtained indirectly from death data. This paper assesses indirect estimation methods for estimating state-level very elderly populations from death counts. A method for incorporating internal migration is also proposed. The results confirm that the accuracy of official estimates deteriorates rapidly with increasing age from 95 and that the survivor ratio method can be successfully applied at subnational level and internal migration is minor. It is shown that the simpler alternative of applying the survivor ratio method at a national level and apportioning the estimates between the states produces very accurate estimates for most states and years. This is the recommended method. While the methods are applied at a state level in Australia, the principles are generic and are applicable to other subnational geographies.

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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