Introduction

It is a well-known fact that people are living longer today than ever before. In the early decades of the twentieth century, improvements in life expectancy were driven by falling death rates at younger ages (AIHW 2000a). However, in the last few decades, falling death rates at older ages have led to many more people living to high ages (Kannisto 1994; Vaupel and Jeune 1995; Oeppen and Vaupel 2002). While the debate about the existence or not of a limit on human lifespan continues, more people are living to ages beyond previous lifespan records (Fries 1980; Oeppen and Vaupel 2002). As recently as 50 years ago, the number of centenarians, those who had reached their 100th birthday, was very low (Rau et al. 2008). However, in the last few decades the growth in both the numbers and proportions of people worldwide living for a century or more has picked up speed and in many developed countries this is now the fastest-growing population age group (Kannisto et al. 1994; Rau et al. 2008). Consequently, since the 1990s there has been an increased focus on the growth in centenarian numbers and mortality trends at very high ages, particularly in European countries, the UK, Japan, the US and Canada (Kannisto et al. 1994; Vaupel 1997; Thatcher 1999; Robine and Saito 2003, 2009; Rau et al. 2008). While all developed countries experienced significant growth in very elderly and particularly centenarian numbers, such studies have highlighted large variations in the timing, patterns and rates of change in these numbers and death rates.

In common with other developed countries, Australia’s very elderly population numbers have increased substantially over the last few decades, driven mainly by increases in births and survival, especially survival beyond age 65 (Vaupel and Jeune 1995; Thatcher 1999; Robine and Saito 2009; Terblanche and Wilson 2014a). Little, however, is known about the demographic features and trends in the numbers of centenarians at a sub-national level. This is partly due to a lack of detailed and reliable data. Various problems have been identified with very elderly estimates provided by the Australian Bureau of Statistics (ABS), and centenarian numbers in particular have been found to be very inaccurate (Terblanche and Wilson 2014a). Indirect estimation methods have been widely applied at a national level to derive more accurate estimates of very elderly populations from death counts (Thatcher et al. 2002; Wilmoth et al. 2007). Recent testing of such methods has demonstrated that they can also be successfully applied at a state level (Terblanche and Wilson 2014c). This paper uses indirect estimation methods to estimate centenarian numbers (ages 100+) in Australia’s states, and compare the extent to which growth from 1981 to 2012 was driven by changes in births, survival and net migration.

The next section sets out the data and methods used to estimate numbers of the very elderly, followed by an analysis of the growth in centenarian numbers from 1981 to 2012 in the different states of Australia. The extent to which this growth was driven by changes in births, survival and net migration is then discussed, followed by a summary and conclusion.

Data and methods

The extinct cohort (Vincent 1951) and survivor ratio (Dépoid 1973) methods were used to estimate historical very elderly population numbers (ages 85+) for groups of people born in the same year, referred to as cohorts. These methods allow estimates to be derived from death counts, rather than census counts, and are regarded as more reliable because age is typically verified at death (Coale and Caselli 1990). Death counts for 1971–2012 by single age to 109 and ages 110+ were obtained from the ABS. In line with Terblanche and Wilson (2014c) national estimates were first calculated from total Australian deaths and state-level estimates derived based on their relative proportions of the ABS’ estimated resident populations (ERPs) for ages 85+. The states are New South Wales (NSW), Victoria (Vic), Queensland (Qld), South Australia (SA), Western Australia (WA), with Tasmania and the two territories, the Northern Territory and Australian Capital Territory, combined due to their small numbers (Tas, NT, and ACT).

Historically, churches kept records of births, deaths and marriages in Australia and the responsibility for these registrations was taken over by registrars’ offices in 1838 in Tasmania, 1841 in Western Australia, 1842 in South Australia, 1853 in Victoria, 1856 in New South Wales and Queensland, and 1870 in the Northern Territory. This paper compares birth counts, survival and net migration of 1872–1881 cohorts with that of 1903–1912 cohorts. Given that formal birth and death registration systems were in place across all states and territories by 1872, births and deaths data used for this study can be considered reliable. A number of data quality checks indicated that Australian deaths data for the highest ages after 1971 were reliable (Andreeva 2012; Terblanche and Wilson 2014a; Kannisto 1994; Jdanov et al. 2008).

The extinct cohort method (Vincent 1951) was used for cohorts where all the members have died. The number who survived to each age is estimated by adding up subsequent deaths, starting from deaths at the highest attained age. Say, for example, the last member of the 1881 birth cohort died in 1989, aged 107, it is estimated that at 31 December 1988 there was one person alive, aged 107. If there were three deaths from the 1881 cohort during 1988, then at 31 December 1987 there were four people alive, aged 106. This process is repeated, working backwards to younger ages so that the estimated number of people aged 100 at 31 December 1981 is the sum of deaths occurring from 1982 onwards at ages 100, 101, and so on until the death of the final member of that cohort. Algebraically, the population \(P_{x,t}^{{}}\) of the cohort aged x last birthday on 31st December of year t for cohort c is:

$$P_{x,t} = \mathop \sum \limits_{i = 1}^{{\upomega - {\text{x}}}} {\text{D}}_{t + i}^{c}$$
(1)

where ω is the age of extinction, and \({\text{D}}_{t + i}^{c}\) is the number of deaths in year t + i from cohort c, which are people born in the year t − x. Thatcher et al. (2002) estimated ω as the highest age at which there was expected to be only one survivor.

The survivor ratio method (Dépoid 1973; Thatcher et al. 2002) was used for cohorts with some members still alive at 31 December 2012. The estimated number alive at each age is based on survivor ratios. A survivor ratio is calculated for older cohorts as the number of people who survived to the current age, expressed as a proportion of those who were alive at an earlier age. For example, to estimate the population currently aged 105, it is first determined what proportion of older cohorts reached aged 105 in earlier years from those who were alive at age 100. For an age range of k years this can be expressed as follows:

$$R_{x} = \frac{{P_{x,t} }}{{P_{x - k,t - k} }}$$
(2)

Using Eq. 1, the number of survivors from a particular cohort at time t − k can be derived from that cohort’s population at time t by adding deaths in the interim period:

$$P_{x - k,t - k} = P_{x,t} + \mathop \sum \limits_{i = 0}^{{{\text{k}} - 1}} {\text{D}}_{t - i}^{c}$$
(3)

By combining Eqs. 2 and 3, the survivor ratio for this cohort can be expressed as:

$$R_{x} = \frac{{P_{x,t} }}{{P_{x,t} + \mathop \sum \nolimits_{i = 0}^{{{\text{k}} - 1}} {\text{D}}_{t - i}^{c} }}$$
(4)

By solving for \(P_{x,t}^{{}}\) the population aged x last birthday on 31st December of year t is estimated as:

$$P_{x,t} = \frac{{R_{x} }}{{1 - R_{x} }} \times \mathop \sum \limits_{i = 0}^{{{\text{k}} - 1}} {\text{D}}_{t - i}^{c}$$
(5)

In this study, survivor ratios were averaged over five older cohorts and over 5-year age ranges. The estimated populations at single ages 85 and older were furthermore proportionally adjusted such that the total would equal the ABS’ 85+ ERPs at this date. An earlier paper showed that this method produced accurate results (Terblanche and Wilson 2014b).

In order to understand how changes in births, survival and net migration contributed to growing centenarian numbers, centenarian populations in each state in 1981 and 2012 were expressed as the product of these factors (Vaupel and Jeune 1995; Thatcher 1999). For example, centenarians in 1981 in New South Wales comprised of people born in New South Wales during 1872–1881 who were still alive in 1981 and living in New South Wales, adjusted for net interstate and net overseas migration. Similarly, centenarian numbers in 2012 are a function of births during 1903–1912, their survival and net moves. By expressing centenarian numbers in 1981 and 2012 into the factors of births, survival and net migration, the increases in each of these factors can be separately quantified. This is written in formula terms as follows:

$$P_{x,t} = B_{t - x}\,{}_{x}p_{0}^{c}\,{}_{x}n^{c}$$
(6)

where \(P_{x,t}\) is the population aged x on 31st December of year t; \(B_{t - x}\) is the number of births in year t − x; \({}_{\text{x}}p_{0}^{c}\) is the survival ratio or probability of survival from birth to age x for cohort c. For this study survival ratios were split into the age ranges from birth to age 65, from 65 to 85, from 85 to 100, and beyond age 100; \({}_{x}n^{c}\) is the net migration ratio. This reflects the extent to which net migration supplemented or depleted a cohort and represents the combined impact of overseas and interstate migrants into and out of a state and their survival. The net migration ratio was indirectly derived as a residual:

$${}_{x}n^{c} = \frac{{P_{x,t} }}{{B_{t - x}\,{}_{x}p_{0}^{c} }}$$
(7)

By considering a group of cohorts and expanding Eq. 6, the centenarian population (ages 100+) at 31st December of year t can be written as:

$$\mathop \sum \limits_{i = 0}^{\upomega } P_{x + i,t} = \mathop \sum \limits_{i = 0}^{\upomega } B_{t - x - i} {}_{65}p_{0}^{c - i} {}_{20}p_{65}^{c - i} {}_{x - 85}p_{85}^{c - i} {}_{i}p_{x}^{c - i} {}_{x + i}n^{c - i}$$
(8)

and the centenarian population in year t-h is:

$$\mathop \sum \limits_{i = 0}^{\upomega } P_{x + i,t - h} = \mathop \sum \limits_{i = 0}^{\upomega } B_{t - h - x - i} {}_{65}p_{0}^{c - h - i} {}_{20}p_{65}^{c - h - i} {}_{x - 85}p_{85}^{c - h - i} {}_{i}p_{x}^{c - h - i} {}_{x + i}n^{c - h - i}$$
(9)

The factor increase in centenarian populations from 31st December of year t − h to 31st December of year t is \(\frac{(8)}{(9)}\). This allows the total factor increase to be expressed as the product of factor increases in births, survival ratios and migration ratios:

$$\frac{{\mathop \sum \nolimits_{i = 0}^{\upomega } P_{x + i,t} }}{{\mathop \sum \nolimits_{i = 0}^{\upomega } P_{x + i,t - h} }} = \frac{{\mathop \sum \nolimits_{i = 0}^{\upomega } B_{t - x - i} }}{{\mathop \sum \nolimits_{i = 0}^{\upomega } B_{t - h - x - i} }} \times \frac{{{}_{65}p_{0}^{c - i} }}{{{}_{65}p_{0}^{c - h - i} }} \times \frac{{{}_{20}p_{65}^{c - i} }}{{{}_{20}p_{65}^{c - h - i} }} \times \frac{{{}_{x - 85}p_{85}^{c - i} }}{{{}_{x - 85}p_{85}^{c - h - i} }} \times \frac{{{}_{i}p_{x}^{c - i} }}{{{}_{i}p_{x}^{c - h - i} }} \times \frac{{{}_{x + i}n^{c - i} }}{{{}_{x + i}n^{c - h - i} }}$$
(10)

Historical births data were obtained from the ABS (2008). Survival histories of cohorts were constructed from deaths and population estimates derived from these deaths using the extinct cohort and survivor ratio methods. Survival histories of older cohorts were supplemented at the younger ages with data from ABS’ historic life tables (2008).

Results

Growth in numbers of centenarians

Figure 1 shows how the numbers of centenarians in the states have grown from 1981 to 2012. Across Australia, male and female centenarian numbers increased from 500 in 1981 to 3388 in 2012. Growth rates varied slightly between the states so that the proportions of centenarians in New South Wales, Victoria and South Australia decreased while proportions in Queensland and Western Australia increased. At 31 December 2012, 35 % of Australian centenarians were in New South Wales, 26 % in Victoria, 17 % in Queensland, 9 % in each of South Australia and Western Australia and 4 % in Tasmania, Northern Territory and Australian Capital Territory combined.

Fig. 1
figure 1

Growth in centenarian populations of Australia’s states from 1981 to 2012. Source: Author’s estimates

Full size image

Over the three decades from 1981 to 2012 centenarian numbers in Australia increased at an average rate of 6.4 % per year, compared to an average growth rate of the Australian population as a whole of 1.4 % per year. As a result, the proportion of centenarians relative to the total population also increased. Table 1 shows male and female centenarians per million of the total male and female populations in 1981 and 2012 by state. In 1981 there were only 33 centenarians per million of the total Australian population. By 2012 this rate had increased to 148. In 2012 the proportion of centenarians relative to total population was highest in South Australia and New South Wales, at 192 and 161 respectively, compared to only 115 in Tasmania, Northern Territory and Australian Capital Territory combined. Because these are proportions, they are also affected by demographic factors such as births and migration at all ages. Low birth rates as well as low net interstate and overseas migration for South Australia contributed to the relatively higher proportion of centenarians compared to the other states. In comparison, Queensland’s high net migration over the last 40 years and relatively higher birth rates (ABS 2008) contributed to the comparatively low proportion of centenarians.

Table 1 Centenarians per million of total populations for males, females and persons in 1981 and 2012, by state
Full size table

The greater longevity of women and relative scarcity of male centenarians is also clear from Table 1, which illustrates the significantly greater number of female centenarians relative to total female populations compared to males. This is also evident from examining sex ratios. In 1981 there were on average 18 male centenarians for every 100 females. The numbers of female and male centenarians increased at different rates throughout the three decades but followed a similar trend of accelerating growth in the 1980s, which slowed in the 1990s, to be followed by accelerating growth from the start of the twenty first century. Up until around 1999, female centenarian numbers in New South Wales, Victoria, Queensland and South Australia increased faster than male numbers, so that by the end of the century there were only between 12 and 14 males for every 100 females. From the start of the twenty first century, however, this trend was reversed and by 2012 the ratio was up to 19. During the late 1990s the ratios of males to females in Western Australia and the combined Tasmania, Northern Territory and Australian Capital Territory were significantly higher than in the larger states, but by 2012 the ratios were very similar in all the states.

Not only are more people reaching the milestone of a 100th birthday, but more are also living longer beyond age 100. Figure 2 shows the estimated number of males and females at single ages 100 and older in 1981, 1996 and 2012 for each state. In 1981 there were an estimated 26 semi-supercentenarians (ages 105+), 24 females and 2 males. By 1996 the number of semi-supercentenarians had increased to 63 females and 7 males, a total of 70. Sixteen years later, in 2012, this number had more than doubled again to 150, or 135 females and 15 males. Similar pictures emerge for all the states, albeit at different scales, with higher numbers at all ages above 100.

Fig. 2
figure 2

Estimated numbers by single age in each state in 1981, 1996 and 2012. Source: Author’s estimates

Full size image

What are the demographic drivers of the growth in centenarian numbers?

An understanding of how changes in the demographic drivers of births, survival and net migration contributed to the growth in centenarian numbers in the different states is a vital step towards planning for likely future growth. Table 2 shows estimated numbers of male and female centenarians in each state in 1981 and 2012 and the factor by which the numbers increased. Across Australia centenarian numbers increased almost sevenfold. In New South Wales, South Australia, Western Australia and Tasmania, Northern Territory and Australian Capital Territory combined, numbers of males increased more than numbers of females, albeit from smaller bases. Female centenarians in Queensland increased in number more than in the other states, and male centenarians less.

Table 2 Growth in numbers of male and female centenarians from 1981 and 2012 by state
Full size table

Figure 3 shows the extent to which changes in births, survival and net migration influenced the growth of centenarian populations in each state between 1981 and 2012. The product of the factor increases in births, survival and net migration shown in Fig. 3 make up the total factor increases shown in Table 2. ‘Births’ represents the growth in birth numbers from 1872–1881 to 1903–1912. On average across Australia, births increased by 60 %, but this varied significantly between the states. In Victoria and South Australia births increased by less than 20 %, in Tasmania, Northern Territory and Australian Capital Territory combined by 60 %, in New South Wales by 80 %, while births in Queensland more than doubled. Births in Western Australia, however, increased by a factor of 8.6, from 9000 total births in 1872–1881 to 77,000 in 1903–1912. The 1903–1912 cohorts were born after the discovery of gold in Western Australia in the 1890s, which precipitated a significant influx of people from overseas as well as the other states (Rowland 1979). The discovery of gold in Western Australia followed the much earlier gold rushes of the 1850s and 1860s in New South Wales, Victoria and Queensland and these states were experiencing economic depression and high unemployment when gold was discovered in Western Australia (West 2010).

Fig. 3
figure 3

Factor increases of births, survival and net migration from 1981 to 2012, by state

Full size image

Similar to Queensland’s experience in the 1860s, Western Australia’s net interstate and overseas migration rates spiked in the 1890s to a level never to be reached again (ABS 2008). As a result, the Western Australia cohorts born in 1903–1912 were supplemented to a significantly smaller extent by net migration compared to the 1872–1881 cohorts. This is clear from the low factor increases for net migration in Western Australia for both males and females (Fig. 3). Changes in net interstate and overseas migration varied in the other states. On average across Australia, the impact of net overseas migration on centenarian populations in 1981 and 2012 was very similar, with factor increases of 0.97 and 0.95 for males and females respectively, indicating a slightly smaller contribution to the 2012 population. Net migration for the states, which reflects not only overseas but also interstate migration, supplemented the 2012 centenarian populations in New South Wales and Queensland to a smaller extent than the 1981 centenarian populations, and to a larger extent in Victoria, South Australia and Tasmania, Northern Territory and Australian Capital Territory combined. These factor changes were not significantly different for males and females.

Improvements in survival from age 85 to 100 made a substantial contribution to the growth in centenarian numbers from 1981 to 2012 in all the states, with both males and female survival rates more than doubling. With the exception of Western Australia, where births increased significantly, this was the most significant driver of growth. Survival from age 85 to 100 improved most for males in Western Australia and the least for females in Tasmania, Northern Territory and Australian Capital Territory combined. Survival beyond age 100 improved for males in New South Wales, Victoria, South Australia and the combined Tasmania, Northern Territory and Australian Capital Territory, but decreased for males in Queensland and Western Australia and for females in all the states. Survival improvement at the very elderly ages (85+) exceeded those at elderly (65+) and younger ages. Cohorts born in 1903–1912 had a 30 % greater chance of survival to age 65 compared to the 1872–1881 cohorts, and a 50 % (males) or 60 % (females) higher chance of survival to age 85.

Conclusion

This paper has presented an analysis of the growth, composition and drivers of growth of the centenarian population of Australia’s states. The estimates are based on deaths rather than census counts, because death counts have been shown by earlier research to be more reliable. It was found that both male and female centenarian numbers across the states increased substantially over the three decades to 2012, both in absolute terms and relative to total populations. Numbers at all single ages 105–109 increased. Over the last 10 years, male centenarian numbers have been growing faster than female numbers, although there are still only 19 males for every hundred females. South Australia has the highest proportion of centenarians while Tasmania, Northern Territory and Australian Capital Territory have the lowest. In Western Australia, by far the largest driver of growing centenarian numbers was the significant increase in births following the start of the gold rush in the 1890s, but this was partly offset by lower net migration in later years. The main driver of growing male and female centenarian numbers in the other states was an improvement in survival at the very elderly ages, from 85 to 100. Survival improvement at younger ages also contributed to higher centenarian numbers, but not to the same extent as at the very high ages.

Continued growth in births, especially after World War II, and a continuation of past trends in survival improvement mean that centenarian numbers are likely to continue increasing rapidly in coming decades. Given the high prevalence of disability at the very high age groups and the lack of any recent declines in age-specific prevalence rates (AIHW 2000b), the centenarian population is especially important for health and aged care service planning. The availability of reliable centenarian estimates at a state level should allow the relevant authorities to provide for the needs of this population group.