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Life table functions
Calculation of infant mortality
Calculation of mortality at ages 1-74
Calculation of mortality at ages 75+
Calculation of lx, nLx, Tx and e0x
Australia has a very good system of population measurement by international standards. There are accurate censuses of population and housing every five years, birth and death registration has high coverage, and movements into and out of Australia are comprehensively monitored. Therefore it is possible to maintain high quality estimates of the total Australian population. However, there are a range of data quality issues associated with estimating the Aboriginal and Torres Strait Islander (Indigenous) population. These issues impact on the estimation of the size and age structure of the Indigenous population and thus on the production of Indigenous age-specific death rates and life tables.
This paper describes how the registered Indigenous deaths are adjusted to calculate death rates for Indigenous populations. It then shows how these rates are used to produce experimental Indigenous life tables for selected States and Territory for the periods 1990-92, 1995-97 and 1997-99.
The life expectancy estimates presented in this paper are described as experimental because of deficiencies in deaths (and births) registration data. The intercensal volatility in the counts of the Indigenous population further adds to the problem of estimating the 'true' Indigenous population. Consequently, there is uncertainty about the accuracy of death rates which use census counts or census-based population estimates as their denominator. The life expectancy estimates are therefore sensitive to the inputs used and over-precise analysis is cautioned. They should be used only as an indicative summary measure of the level of mortality of the Indigenous population.
Before attempting to construct life tables for Indigenous Australians, it is important to recognise the major data quality issues relating to the Indigenous population.
2. How accurate are the coverage estimates?
The ABS calculates, for each State and Territory and Australia, the coverage of Indigenous deaths by dividing the number of deaths registered by the number of deaths estimated from the 1991 and 1996 Census-based experimental estimates and projections. There is some uncertainty about the accuracy of the coverage estimates. This uncertainty stems from the intercensal volatility in the counts of the Indigenous population and deficiencies in births and deaths registration data. There is also uncertainty relating to the method used to estimate the expected deaths and the death coverage (described below).
In constructing the 1991-96 experimental Indigenous life tables, a demographic technique outlined by Preston and Hill (1980) was used to estimate the completeness of Indigenous deaths registered during the 1991-96 intercensal period. The estimate derived from the Preston-Hill analysis was applied across all age groups to obtain an adjusted number of Indigenous deaths. The estimated death numbers were then used in the construction of the experimental Indigenous life tables for the period 1991-96. The use of the Preston-Hill method in constructing the 1991-96 experimental Indigenous life tables was a weakness of these life tables.
In an earlier attempt to produce Indigenous life tables for 1995-97, the Preston-Hill Method was applied again to estimate the completeness of registered deaths of Indigenous Australians (see Demography Working Paper 2000/2 - Draft Experimental Aboriginal and Torres Strait Islander Life Tables, Australia and States/Territories, 1995-97). In that paper the Preston-Hill Method was applied to Indigenous data assuming that there was no migration of Indigenous people into and out of the Australian population. It is a valid assumption as both in- and out-migration for Indigenous people are negligible. But the changes in the propensity of an individual to identify as being of Indigenous origin has resulted in the 1991-96 intercensal growth of the population which cannot be fully explained by demographic factors such as births, deaths and migration. All the five-yearly survivorship ratios (ratios of the 1991 Census counts to the 1996 Census counts of each age-sex cohort) exceeded one, meaning that there were more survivors in the age cohorts in 1996 than in 1991.
The issue of changes over time in the propensity of people to identify as Indigenous on census forms could be considered as migration into the population. This raises the concern that the Preston-Hill method cannot possibly be used to estimate the completeness of Indigenous deaths registration. Prof Preston was contacted and asked "Can the Preston-Hill method be applied to Australian Indigenous data". He responded "Probably not, certainly not if the extent of migration is high". As the Preston-Hill method is not an appropriate method to assess the completeness of Indigenous deaths registration, its use introduces a degree of uncertainty to the 1991-96 life expectancy estimates. The ABS coverage estimates were based on experimental estimates and projections of the population which in turn used 1991-96 experimental Indigenous life tables. This circularity introduces uncertainties to the coverage estimates as well.
To add to uncertainties about mortality rates due to the use of the Preston-Hill method, there are additional difficulties relating to the use of a single national experimental Indigenous life table. The expected Indigenous deaths for individual State/Territory were obtained using a single national experimental Indigenous life table for the period 1991-96. The use of a single national life table for all States/Territories implies that the same age-specific mortality rates apply for Indigenous people throughout Australia; that is, they equally apply to Indigenous people in New South Wales and the Northern Territory, for example. While this may or may not be the case, it is impossible to know for certain in the absence of complete coverage of Indigenous deaths and/or more predictable census counts. However, if such data were available, there would be no need to use experimental methods in the first place. If there are underlying differences in mortality among the States/Territories, then the use of a single national life table would result in an over-estimation of expected deaths for some States/Territories and an under-estimation for others. As a result, the results of any assessment of the completeness of coverage of Indigenous deaths should be interpreted with caution. They should be used only as indicative guides to the completeness with which Indigenous deaths are correctly registered.
3. Registered Indigenous Deaths and Estimated coverage of Indigenous Deaths
Indigenous deaths registered in Australia during 1990-92, 1995-97 and 1997-99 formed the basis of this analysis. The number of deaths registered as Indigenous has increased from 3,364 in 1990-92 to 4,150 in 1995-97 and to 5,752 in 1997-99. During 1997-99, the number ranged from an average of about 550 per year in Queensland to less than 10 per year in Tasmania and Australian Capital Territory. These figures underestimate the actual number of deaths of Indigenous people, as not all Indigenous people who died were identified as Indigenous on their death notification forms. An estimate of the level of such under-reporting can be made by comparing the proportions of registered to estimated deaths (See Section 2 for details on calculations of proportions).
As well as the differences in number, there is a high degree of variability in the deaths coverage among States/Territories (Table 1). While overall there was considerably better coverage in 1997 than in the past, there is a high degree of variability in the coverage among the States/Territories. Prior to 1997, only South Australia, Western Australia and the Northern Territory had a relatively high level of coverage. A relatively high coverage of Northern Territory registered Indigenous deaths in 1997, followed a relatively low coverage in 1996. This reflects the clearing of a backlog of death registrations in 1997. Queensland coverage of Indigenous deaths in 1997 approached the level of coverage in the States/Territories with traditionally high coverage, following the introduction of a new Death Information Form in 1996-97 which included an Indigenous question. Penetration of the new forms only reached reasonable levels late in that year making 1997 the first full year of Indigenous deaths data for that state. The decline in the New South Wales coverage in 1997 was the result of a technical problem with the State's death database. Victorian coverage improved markedly during the later years and was higher than New South Wales, South Australia, Queensland and the national coverage in 1999. While Tasmania has not provided adequate deaths data to date, it is expected that a new Notice of Death form will help address this problem when it is introduced in 2000. The ongoing efforts to improve the level of identification on death certificates (such as improved form design and awareness raising) should see further improvement in the coverage of Indigenous death registrations.
Table 1: Registered and Expected Indigenous Deaths and Estimated Coverage of Indigenous Deaths
- Nil or rounded to zero (including null cells).
(a) includes 'Other Territories' from 1993.
(b) Source: Experimental Projections of the Aboriginal and Torres Strait Islander Population, 1996-2006, (ABS Cat. No. 3231.0), Low Series.
Source: Deaths, Australia 1999 (ABS, 2000b).
4. Processes of constructing experimental life tables for 1990-92, 1995-97 and 1997-99
The method of constructing experimental life tables presented in this paper was a four stage process. Firstly, the Preston-Hill method was applied to estimate the completeness of Indigenous deaths registration. The estimate derived from the Preston-Hill analysis was used to obtain an adjusted number of Indigenous deaths. The estimated death numbers were then used in the construction of the experimental Indigenous life tables for the period 1995-97. The details of the method used and results obtained were put together in a Demographic Working Paper, which was made available on the ABS web site for comments. Secondly, the working paper was presented in two seminars, one at an ABS seminar series and the other at the ANU Demography Department seminar series. Many useful issues were raised at the seminars, but some were more critical than others. One particular issue raised at the ABS seminar was that of the appropriateness of the Preston-Hill method to assess the completeness of Indigenous deaths registration (See Section 2 for details). Thirdly, the major issues raised at the seminars were discussed in-house and advice was sought from different academics including Prof. Preston. Finally, on the basis of the response obtained from Prof. Preston and the results of in-house discussion, the Preston-Hill method was not applied to adjust deaths used in the construction of life tables for the periods 1990-92, 1995-97 and 1997-99. Instead, deaths were adjusted using the ABS estimates of expected deaths, which were themselves derived using the 1991-96 experimental Indigenous life tables. A dilemma faced by the ABS is that, without additional data, there are no satisfactory alternatives for producing Indigenous population estimates and projections, and in turn, the number of expected deaths, especially in the face of the volatility of census counts of Indigenous people over time.
Experimental Indigenous abridged life tables were produced for the periods 1990-92, 1995-97 and 1997-99. During these periods, only South Australia, Western Australia and the Northern Territory had a relatively high coverage of Indigenous deaths. For this reason experimental Indigenous life tables for these three States/Territories were produced for all these periods. Experimental life tables were also produced for New South Wales, Victoria and Queensland but only for 1997-99 as the coverage of Indigenous deaths has improved considerably for Victoria and Queensland in 1997-99 and for New South Wales in 1998-99. Because of the small number of registered Indigenous deaths and/or very low coverage, Indigenous life tables were not produced for Tasmania and the Australian Capital Territory. Experimental Indigenous life tables for all of Australia were produced only for the period 1997-99. Indigenous deaths registered in Tasmania and the Australian Capital Territory were excluded from the Australian tables. This exclusion would have only a minimal effect on the Australia level life expectancy.
The 1990-92, 1995-97 and 1997-99 life tables used mortality rates based on an average annual number of Indigenous deaths registered in 1990-92, 1995-97 and 1997-99 respectively. Deaths were averaged over the three-year periods to smooth out the irregularities from year to year in the number of deaths, bearing in mind the relatively small number of Indigenous deaths in many areas and age groups. The only exception was the New South Wales life tables which were based on the average deaths registered only in 1998-99.
Experimental estimated resident Indigenous population at June 1991 (both 1991 and 1996 Census based estimates), experimental estimated resident Indigenous population at June 1996 and experimental projected resident Indigenous population at June 1998 (low series) were used as mid-year populations to calculate mortality rates for 1990-92, 1995-97 and 1997-99 respectively.
Two sets of experimental Indigenous life tables were produced. One set was based on the actual number of registered deaths which were not adjusted for under-coverage. There is under-coverage based on the projections of Indigenous deaths to some degree in all States/Territories. To compensate for under-coverage, the other set was produced after inflating the number of registered deaths in a State/Territory by the respective adjustment factor. The coverage estimates presented in Table 1 were used to obtain an average coverage of Indigenous deaths for the periods 1990-92, 1995-97 and 1997-99. The average coverage estimates used in calculating life tables are presented in Table 2. The reciprocal of the average coverage was then used as an adjustment factor to obtain the adjusted deaths. No separate adjustment factor was derived for Australia, instead the number of adjusted deaths in New South Wales, Victoria, Queensland, South Australia, Western Australia and the Northern Territory were combined to construct life tables for Australia. The 1997-99 life tables for New South Wales, Victoria, Queensland, South Australia, Western Australia, the Northern Territory and all of Australia based on adjusted number of deaths were published in Deaths, Australia 1999 (ABS, 2000b).
Table 2: Estimated Average Coverage of Indigenous Deaths (%) used in Life Tables Calculations
Source: Calculated from coverage estimates published in Deaths, Australia 1999 (ABS, 2000b)
The observed life expectancies are higher than the expected life expectancies in all the three States and Territory for both sexes. The observed life expectancies are based on the actual number of registered deaths. As Indigenous deaths are under-registered to some extent in all States/Territories, the observed life expectancies are over-estimates of the true life expectancies. The expected life expectancies (hereafter refer to as life expectancies), on the other hand, are based on the number of deaths which are obtained after inflating the observed number of deaths by an adjustment factor and hence are expected to be closer to reality than the observed life expectancies.
At the national level, the life expectancy at birth in the period 1997-99 was estimated to be about 55.6 years for Indigenous males and 63.0 years for Indigenous females. Life expectancy at birth for Indigenous males in 1997-99 ranged from 54 years in South Australia to 56 years in most States. For Indigenous females, life expectancy at birth ranged from 61 years in the Northern Territory to 65 years in Victoria.
The 1990-92 life tables based on the June 1991 experimental estimated resident Indigenous population (1991 Census-based) produced somewhat lower life expectancy than those based on the June 1991 experimental estimated resident Indigenous population (1996 Census-based). These life tables are included to indicate the uncertainty involve with the population estimates.
Table 3: Observed and Adjusted Life Expectancies at Birth, 1990-92, 1995-97 and 1997-99
n.a. Not available
(a) Based on 1998-99 deaths.
(b) Excludes Tasmania and the Australian Capital Territory.
(c) Experimental Indigenous ERP at June 1991 (1991 Census based) used as mid-year population.
(d) Experimental Indigenous ERP at June 1991 (1996 Census based) used as mid-year population.
8. Comparison with figures from other sources
The life expectancy at birth for all of Australia in the period 1997-99 was estimated to 55.6 years for Indigenous males This compares to the life expectancy of Indigenous males of 56.9 years previously estimated for 1991-96, a decrease of 1.3 years. The life expectancy at birth of Indigenous females in the 1997-99 period was estimated to be 63.0 years, 1.3 years more than that in 1991-96. There are several possible reasons for the apparent decrease in Indigenous male life expectancy. It could be due to improved recording of Indigenous deaths, particularly male deaths, including the introduction of a question on Indigenous status on Queensland death registration forms in 1996. It could also be due to the differences in method used. The previous Indigenous life tables used Preston-Hill method to estimate the coverage of Indigenous deaths registered in the 1991-96 intercensal period. The present analysis used coverage estimates which were derived by dividing the number of deaths registered by the number of deaths estimated from the 1996 Census-based experimental projections. For these reasons, comparison of life expectancy estimates presented in this publication with estimates from other sources should only be undertaken with extreme caution. The lower male life expectancy in 1997-99 than in 1991-96 does not necessarily mean that the Indigenous male mortality has increased during this period.
Gray and Tesfaghiorghis (1993) also produced state-specific life expectancy estimates using the Preston-Hill method. Their estimates are higher than those presented in this paper. This could also be due to the reasons mentioned above.
9. Evaluation of the 1990-92, 1995-97 and 1997-99 experimental Indigenous life tables
The assessment in Deaths, Australia 1999 (ABS, 2000b) that from 1990-92 to 1997-99 there appears to be some improvement in the life expectancy of Indigenous people in South Australia, Western Australia and the Northern Territory may not be correct.
As outlined in appendix 1 of the publication, two sets of experimental Indigenous life tables were produced. One set was based on the actual number of registered deaths and the other set was based on adjusted deaths. The adjusted deaths took into account the estimated under-coverage of Indigenous deaths in each State/Territory. These undercoverage estimates were based on experimental estimates and projections of the populations which in turn used 1991-96 experimental Indigenous life tables.
The application of the age-specific death rates based on the 1991-96 life tables to the estimated/projected population for determining "expected deaths" may not be right for two reasons: (1) the accuracy of the 1991-96 life tables, and (ii) its applicability to the post-1996 period.
The 1991-96 experimental life tables have a methodological weakness. In constructing these life tables, a demographic technique outlined by Preston and Hill was used to estimate the completeness of Indigenous deaths registered during the 1991-96 intercensal period. The estimate derived from the Preston-Hill analysis was applied across all age groups to obtain an adjusted number of Indigenous deaths. The adjusted deaths were then used in the construction of the experimental Indigenous life tables for the period 1991-96. The use of the Preston-Hill method introduces some uncertainties to the 1991-96 life expectancy estimates tables (see Section 2 for details).
The application of the 1991-96 life tables for the post-1996 period assumes constancy of Indigenous mortality over time. It is not known whether the Indigenous mortality has declined in the recent years. It is possible that, in response to various measures taken to improve health status of Indigenous Australians, their mortality has declined in the recent past. Then all other things being equal, a decline in mortality would result in a lower number of expected deaths than those based on the 1991-96 mortality. This in turn would mean that coverage of deaths is actually higher that originally estimated. As a consequence, the coverage factor (reciprocal of death coverage) used in post-1996 life tables to inflate the observed (registered) number of Indigenous deaths will be lower. Therefore the adjusted number of deaths will also be lower. The use of these adjusted numbers will result in higher life expectancy estimates. In short, under a declining mortality condition, the life expectancy estimates will be higher than the experimental estimates presented in Deaths, Australia 1999 (ABS, 2000b).
In evaluation of the experimental life tables, it was realised that the 1990-92 to 1997-99 life expectancy calculations replicated the 1991-96 life expectancy values with slight modification which was due to the varying age distribution of registered deaths in the time periods in question. Hence, the adjusted life expectancy estimates cannot be validly interpreted as reduction in Indigenous mortality over time. On the other hand, there is an apparent improvement in the experimental observed life expectancy estimates although much uncertainty applies to them.
10. Where to from here?
In the absence of adequate information on Indigenous births, deaths and migration, it remains necessary to use non-standard methods to estimate the size and composition of the Indigenous population. These non-standard methods will never be as good as standard methods, but the latter continue to involve difficulties when used for the Indigenous population.
It would be ideal to describe trends in mortality by only those measures of mortality which do not require the use of experimental population estimates and projections as base populations and hence would not be affected by the uncertainties associated with these estimates and projections. One such measure is the median age at death. It can be calculated using registered Indigenous deaths only. Median age at death in the population refers to the age which divides the deaths registered in a year (or period) into two equal parts, that is, the age by which half of all deaths have occurred. Unfortunately, the median age at death does not take into account the size of the population or under-recording of Indigenous status on registration forms and therefore is a crude measure of mortality.
To improve the identification of Indigenous status in birth and death registrations, the ABS continues to support State and Territory registrars of birth and death. In some States cross-agency working parties have been established to progress this issue. As the identification of Indigenous status in birth and death registration improves, so too do the prospects of being able to use birth and death registration data directly in Indigenous population estimates and projections and to calculate rates and ratio statistics based on these population figures.
There is the possibility of data collection which would enable indirect techniques to used in assessing mortality. This possibility is being considered by ABS for the 2002 Indigenous Social Survey although much sensitivity exists about this issue.
There are still options to producing life tables for the Indigenous population using registration data. Life tables are required to produce experimental estimates and projections of the Indigenous population. Fortunately, the use of experimental life tables for this purpose has minimal impact on projected total Indigenous population as population projections are not only insensitive to small variations in future mortality rates, but also to larger variations (ABS, 1998). One option is to produce life tables for States/Territories with apparent high coverage of Indigenous deaths (SA, WA and the NT for 1995-97) by using the actual number of registered deaths for the three year period centred on the census year and census year experimental estimated resident Indigenous populations. This has been done for 1995-97 as reflected in Appendix 1 of Deaths, Australia 1999 (ABS, 2000). It is proposed to do this for relevant States/Territories for 2000-02 using the appropriate census year population. The other option is to assess the error of closure defined as the difference between the expected population growth due to births and deaths and that would be observed from the 2001 Census counts of Indigenous population. In 1996, the error of closure as a percentage of 1996 Indigenous population was around 7% for South Australia, 5% for Victoria, and 3% for Western Australia and the Northern Territory (Ross, 1999, p. 52). If the error of closure in 2001 remains at a low level then the Preston-Hill method could be used for relevant States/Territories to produce experimental 1996-2001 life tables complemented where appropriate by 1991-1996 tables. For States/Territories not covered by these two options, subjective life tables will need to be produced based on some assumed rates of mortality and mortality change.
ABS, 1998, Experimental Estimates of the Aboriginal and Torres Strait Islander Population, 1998, ABS Cat. No. 3230.0, Canberra.
ABS, 2000a, Births, Australia 1999, ABS Cat. No. 3301.0, Canberra.
ABS, 2000b, Deaths, Australia 1999, ABS Cat. No. 3302.0, Canberra.
Gray A and Habtemariam Tesfaghiorghis, 1993, "Aboriginal Population Prospects", Journal of the Australian Population Association, Vol. 10, No. 2.
Preston S H and Hill K J, 1980, "Estimating the Completeness of Death Registration", Population Studies, Vol. 34, pp. 349-66.
Ross K, 1999, Occasional Paper, Population Issues, Indigenous Australians, 1996, ABS Cat. No. 4708.0, Canberra.
Shahidullah and Kim Dunstan, 2000, "Draft Experimental Aboriginal and Torres Strait Islander Abridged Life Tables, Australia and States/Territories, 1995-1997", ABS Demography Working Paper 2000/2.
Abridged Life tables
Abridged life tables are generally constructed in preference to complete life tables when reliable age-specific death rates are not available by single years of age. Reliable single year age-specific deaths rates are not available for the Indigenous population. However, abridged life tables are generally sufficient for most purposes of demographic analysis.
Life Table Functions
Abridged life tables for the Indigenous population contain the following life table functions:
nqx = Proportion of persons dying between exact age x and exact age x + n;
lx = Number of persons surviving at exact age x;
ndx = Number of deaths between exact age x and exact age x + n;
nLx = Number of persons-years lived during the interval age x to age x + n;
Tx = Total number of person-years that would be lived after exact age x; and
ex = Complete expectation of life at exact age x.
The principal step in life table construction is one of calculating age-specific mortality rates or probability of dying. Below is a discussion of how mortality rates at different ages are calculated.
Calculation of Infant Mortality rate (1q0)
Infant mortality rates (1q0) for Indigenous males and females were calculated in the following two ways:
where d0 = registered infant deaths in a year and B = registered births in the same year.
where m0 = death rate at age 0 = infant deaths/mid-year population at age 0 and f is the proportion of infant deaths occurring in the reference year to births in that year. This factor was taken as 0.75 for Indigenous population (and 0.88 for total Australian population). The proportion of infant deaths occurring in the year they are born is higher in total Australian population than in Indigenous population. This is because in the total Australian population, the majority of infant deaths occur during the first four weeks of life whereas Indigenous babies continue to die after that period.
Indigenous male and female infant mortality rates calculated using equations (1) and (2) fluctuate considerably among the States/Territories. The small number of infant deaths registered in the States/Territories could be the main reason for this fluctuation. Because of this fluctuation, State/Territory-specific infant mortality rate was not used in constructing Indigenous life tables. Instead, the average of infant mortality rates obtained from equations (1) and (2) was derived for Australia (excluding Tasmania and the Australian Capital Territory). This average rate was estimated to be 24 per 1,000 live births for Indigenous males and 20 per 1,000 live births for Indigenous females for the period 1997-99. These rates were then used in the construction of the 1997-99 experimental Indigenous life tables for New South Wales, Victoria, Queensland, South Australia, Western Australia, the Northern Territory and all of Australia. The same procedure was used to producing experimental Indigenous life tables for the periods 1990-92 and 1995-97.
Calculation of Mortality at Ages 1-74
Mortality rates (nqx values) for persons aged 1-74 were derived from central death rates (nmx values). These nmx values were calculated for the period 1997-99 using the following equation:
The nmx values were then inflated by the adjustment factor to derive the adjusted nmx values. The follow formula given by Greville was used to convert the adjusted age-specific death rates into their corresponding mortality rates, or probability of dying.
nqx = nmx /(1/n) + nmx (1/2 + n/12 (nmx - loge c))) (4)
Empirically, the value of c has been found to be between 1.08 and 1.10. Loge c could be assumed to be about 0.95 as an intermediate value.
Calculation of Mortality at Ages 75+
Since all persons aged 75 and over will die while still within this age group, the probability of dying after age 75 is 1.
Calculation of lx, nLx, Tx and e0x
The value for l0 (the radix) is set at 100,000. Remaining values of lx are calculated as:
nLx, Tx and ex are calculated using the following equations:
L0 = .25*l0 + .75*l1 for age 0
4L1 = .034*l0 + 1.184*l1 + 2.782*l5 for ages 1-4
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