Abstract
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.
Highlights
Due mostly to substantial declines in older age mortality over the last few decades, Australia and New Zealand’s very elderly populations—defined here as those aged 85+—are growing faster than all younger age groups [1,2]
Estimated Resident Populations (ERPs) are not included in Fig 2 because only an aggregate 100+ ERP is available, which means Weighted Mean Absolute Percentage Error (WMAPE) cannot be determined
Previous studies have evaluated alternative methods for estimating very elderly populations for a number of European countries, Japan and the US, but no evaluations had been undertaken for Australia or New Zealand
Summary
Due mostly to substantial declines in older age mortality over the last few decades, Australia and New Zealand’s very elderly populations—defined here as those aged 85+—are growing faster than all younger age groups [1,2]. Based on average rankings of absolute deviations of estimated numbers from observed numbers at ages 95+ and ages 100+, they concluded that the Survivor Ratio method constrained to official 90+ population estimates produced the most accurate results This method is used for producing estimates in the Human Mortality Database (HMD) at ages 80 to 110+ for 37 countries, including Australia and New Zealand [26], and is applied by the UK’s Office for National Statistics [27]. The notation is Method (age range, number of cohorts for averaging survivor ratio or death ratio, official population estimate used as a constraint). This measure of accuracy is referred to as the Weighted Mean Absolute Percentage Error (WMAPE) [32] and is calculated as follows: WMAPEt
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