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3106.0.55.003 - Demography Working Paper 2004/3 - Calculating Experimental Life Tables for Use in Population Estimates and Projections of Aboriginal and Torres Strait Islander Australians, 1991 to 2001  
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ABSTRACT

Estimates and projections of the Australian Aboriginal and Torres Strait Islander (Indigenous) population are required for a wide range of planning, policy development, evaluation, research and analysis purposes. A key component of the estimation/projection process is the construction of experimental Indigenous life tables. This paper therefore focuses on the life table construction process, and its associated assumptions. The ABS assesses that these life tables allow the best experimental Indigenous population estimates and projections using currently available data.

The Indigenous life expectancy estimates presented in this paper are experimental because of the nature of the base population estimates, which are affected by both intercensal volatility in the counts of the Indigenous population and deficiencies in Indigenous identification in birth and death registration data. Consequently, there is uncertainty about the accuracy of death rates which can be derived from these inputs and used in life table construction. While the life expectancy estimates are the best that can be compiled with currently available data, and are assessed to be suitable for experimental population estimates and projections, over-precise analysis of the life expectancy estimates as measures of Indigenous health outcomes should be avoided. In particular, the differences between the life expectancy estimates in this paper and those previously published by the ABS, which were based on analysis of data for the intercensal period 1991 to 1996, represent improvements in methods and data quality and do not necessarily represent any change over time in the life expectancy of the Indigenous population.

The standard approach to calculating death rates used in life tables is to divide the number of deaths in a given population by the population 'exposed to risk' during that period. Precisely estimating the population at risk between census years and in the projection period requires accurate information on births. Although it is considered likely that most Indigenous births and deaths are registered, a proportion of Indigenous births and deaths are not identified as ‘Indigenous’. There have also been intercensal increases in the Indigenous population that cannot be explained solely by demographic factors, i.e. by biological natural increase (the excess of births over deaths), or by migration to/from Australia. Without complete and accurate data on Indigenous births and deaths, and accurate data on the size and structure of the Indigenous population, the standard method for calculating death rates cannot be used for the Indigenous population.

This paper describes a new demographic method for determining consistency factors to make registered intercensal deaths data consistent with two-end census date population estimates. This method was developed by Bhat (2002) and offers improvement over other indirect methods available for estimating mortality from incomplete data. The main advantage of the Bhat method over other methods is that it explicitly allows for an adjustment for 'migration' to be taken into account. The migration component in the Bhat method is being used in this paper to allow for the non-biological, or unexplained, change in the measured Indigenous population. Using the Bhat method, this paper calculates the consistency of Indigenous death registrations for the 1991-1996 and 1996-2001 intercensal periods relative to population estimates at the beginning and end of each five year period. A consistency factor, assumed to be constant at each age group, is applied to the observed age-specific death rates, which are then used for the calculation of the Indigenous life tables.

While life table construction based on the Bhat method provides an essential component for preparing experimental population estimates and projections for Aboriginal and Torres Strait Islander Australians, the use of the life tables for other purposes should be undertaken with caution and an understanding of the assumptions used in their construction. This paper assesses the sensitivities of the method to assumptions about the level and age distribution of unexplained growth in the Indigenous population. The sensitivity analysis is restricted to the 1996-2001 period only. Results obtained from the sensitivity analysis show that life expectancy estimates derived under various assumptions vary widely, suggesting that the life expectancy estimates in the life tables will not be robust for some forms of analysis. While the Bhat method overcomes one of the deficiencies inherent in previous methods used to construct experimental Indigenous life tables published by the ABS, it cannot overcome the underlying issues of quality in the input data.

For more information please contact Shahidullah on (02) 6252 5129 or client.services@abs.gov.au.


TABLE OF CONTENTS

1. Introduction

2. Issues in calculating the Indigenous population

    2.1 Census editing procedures
    2.2 Undercount

    2.3 System created records
    2.4 Non-response to the Indigenous status census question
    2.5 Unexplained growth in Indigenous census counts
    2.6 Administrative data for components of Indigenous population growth

3. Life tables and the production of Indigenous estimates

4. Deriving life expectancy estimates from incomplete data - the Bhat method

    4.1 Data requirements

    4.2 Results

5. Sensitivity analysis

6. Recommendations

7. Cautionary remarks

8. Future directions

9. Further information

10. References

Appendix. Application of the Bhat Method


1. INTRODUCTION

Population statistics are measures of the size, growth, composition and geographic distribution of the population as well as the components that shape population change, that is births, deaths and migration. Population statistics underpin the discussion of a wide range of issues of concern to the community, including immigration, cultural diversity, ageing and provision of services. Changes in Australia's population affect policy areas such as health, education, housing, the labour market and the environment.

The size and geographic distribution of the Australian Aboriginal and Torres Strait Islander (Indigenous) population are significant determinants of the distribution of government resources and the provision of services. Population estimates and projections are also essential components to the calculation of key Indigenous social statistics needed to monitor progress in addressing changes in health status or social and economic disadvantage over time. However, calculation of accurate estimates and projections for the Indigenous population is difficult due to the lack of sufficiently reliable data on components of population growth.

This working paper introduces various issues relevant to calculating the Indigenous population (Section 2) and the reasons why life tables are required for the production of Indigenous estimates and projections (Section 3). A new method (the Bhat method) is described for determining consistency factors to make registered intercensal deaths data consistent with population data (Section 4). This method has been used to produce adjusted life expectancy at birth estimates suitable for compiling experimental Indigenous life tables. The paper evaluates the outcomes of using the Bhat method for the 1991-1996 and 1996-2001 intercensal periods at the state/territory level and for both males and females. It also assesses the sensitivity of this method to assumptions about the level of unexplained growth and its age distribution (Section 5). The resulting experimental life tables will be applied in the production of the most recent set of experimental population estimates and projections for the Aboriginal and Torres Strait Islander population of Australia.

The previous method used by the ABS to derive experimental Indigenous life tables for an intercensal period relied on the assumption that the intercensal population growth based on the two consecutive population census counts was entirely accounted for by the excess of births over deaths during the period (ie the population has been closed to migration). However, this is known to not be the case, with some of the growth between the two census year population counts remaining unexplained. The application of the Bhat method allows for an assumption of unexplained growth of population (that which cannot be explained by births and deaths) to be included in the analysis.

Bhat technique determines an adjustment factor for the two-end census date population estimates and the registered deaths during the intercensal period to be consistent with one another. The observed age-specific death rates are multiplied by the inverse of the consistency factor and adjusted life table is calculated. This factor, assumed invariant by age, is the slope (beta coefficient) of a fitted linear regression line between a 'birth' function by age as Y variable and observed age-specific death rates as X variable. The calculation of the 'birth' function is based on the stable population theory and allows for the lack of stability of the population and the unexplained growth of the population. The unexplained growth of the population can only be deduced by a subjective judgement about the level of natural increase of population and subtracting it from the observed growth rate of the population. In addition, a proportionate age structure of the population involved in unexplained growth is required, which can only be approximated. A sensitivity analysis has shown that the assumed different levels of unexplained population growth and a fixed age distribution of this population has little impact on the calculated consistency factor (and thus on the adjusted life tables). Large variation in the values of the consistency factor results from using different proportionate age structures of the unexplained growth of population with a fixed level of unexplained growth (Tables 3 and 4).

Combined with an estimated age distribution of unexplained growth of the population for the 1996-2001 period and different levels of unexplained growth, the consistency factors and adjusted life tables for 1996-2001 were calculated for Australia and the states and territories (Table 6). A final selection of the life tables for 1996-2001 was made which required the grouping of some states with small numbers of deaths. The resulting life expectancies at birth are given in Table 7. These life tables are experimental and are being used in the next series of the ABS Indigenous population estimates and projections to be released on 27 September 2004 (ABS Catalogue number 3238.0). The paper concludes with cautionary remarks and an outline of future analytical directions.


2. ISSUES IN CALCULATING THE INDIGENOUS POPULATION

The Census of Population and Housing is the principal source of information about Australia's population. It has been held every five years since 1961 with the most recent census conducted in August 2001.

The census provides a base from which Australia's estimated resident population is calculated. The census count of the population is adjusted for:
  • visitors from overseas;
  • Australian residents temporarily overseas on census night;
  • estimates of the numbers of people missed in the census; and
  • estimates of those counted more than once in the census.

To obtain estimated resident population figures for dates between censuses, births and net overseas migration are added and deaths are subtracted. This method of calculating population estimates is known as the cohort component method and can be expressed in the following balancing equation:

Image - demographic growth balancing equation P(t+1) = P(t) + B - D + NOM
(1)

Where:
    Pt = the estimated resident population at time point t;
    Pt+1 = the estimated resident population at time point t+1;
    B = the number of births occurring between t and t+1;
    D = the number of deaths occurring between t and t+1; and
    NOM = net overseas migration occurring between t and t+1.
For state and territory population estimates, an additional term is added to the equation representing net interstate migration occurring between t and t+1.
    However, calculation of the Indigenous population is more complicated. The above standard approach to population estimation cannot be used due to the lack of sufficiently reliable data on births, deaths and migration, as well as volatility in census counts of the Indigenous population.

    More specifically, in estimating the Indigenous population there are issues relating to:
    • census editing procedures, undercount and non-response to the Indigenous origin question;
    • changes in the extent to which persons of Indigenous origin are identified as Indigenous in the census; and
    • Indigenous identification in administrative data sources relating to components of post-censal population growth (i.e. births, deaths and migration).

    2.1 Census editing procedures

    During census processing, a series of edits are applied to remove certain inconsistencies and errors from the collected data. The Indigenous status variable is edited to change responses of 'Aboriginal' or 'Torres Strait Islander' to 'non-Indigenous' for persons who are unlikely to be Indigenous. These edits are based on the birthplaces of individual respondents and their parents.

    Changes in editing practice resulted in the 1996 census Indigenous count including an additional 6,000 records that would have been coded to non-Indigenous using 1991 editing rules, of which about 4,000 would have been excluded from Indigenous counts using 2001 editing rules. In other words, about 6,000 of the unexplained growth in the 1991-1996 intercensal period was accounted for by editing changes, while unexplained growth in the 1996-2001 period is understated by about 4,000 records.

    2.2 Undercount

    In any population census, some people are missed and some are counted more than once. The difference between the census count and the true population is called the net undercount of the census. In the 2001 census, the net undercount was estimated to be 1.8% for the total Australian population and 6.1% for the Indigenous population.

    The Indigenous undercount should be used with caution as there are high sampling errors associated with the estimates in both censuses. This measure of undercount provides direct information only on the quality of counts of Indigenous Australians who live in non-sparsely settled areas of Australia. Quantitative measures of the quality of census counts of Indigenous Australians living in sparsely settled areas are not currently available, but are assumed for estimation purposes to be the same as in non-sparsely settled areas. For more information, see Appendix 2: Estimated resident Indigenous population - Method of calculation in Population Distribution, Aboriginal and Torres Strait Islander Australians (ABS cat. no. 4705.0).

    2.3 System created records

    System created records (SCRs) are created during census processing for people for whom a census record has not been received, or people whom the census collector believes have been missed from the census counts. The proportion of SCRs has increased from 1.4% in the 1996 census to 2.2% in 2001. Almost 95% of SCRs in 2001 were created for non-contact dwellings. However, subsequent analysis of the 2001 census results showed that there had been a significant level of over-imputation of SCRs (about 87,100 too many people were imputed) such that the increase in SCRs should have been much lower. More information on the factors that might have contributed to the increase in SCRs and the implications for non-response rates can be found in Fact Sheet: Effect of Census Processes on Non-response Rates and Person Counts. For information on how population estimates are adjusted for census over-imputation of system created records in non-contact dwellings, see Demography Working Paper 2002/2 - Estimated Resident Population and Effects of Census System Created Records and Information Paper: Census of Population and Housing, Data Quality-Undercount, 2001 (ABS cat. no. 2940.0).

    Some of the records imputed during census processing will represent Indigenous people. It is not known what proportion were actually Indigenous, or what proportion would have been identified as Indigenous if they had been included on an census form.

    2.4 Non-response to the Indigenous status census question

    In addition to those people who are not enumerated by the census, for some people who are enumerated, not all questions are answered. While some people coded as 'not stated' for the Indigenous origin question are likely to be of Indigenous origin, the proportion of Indigenous persons for whom a response to the Indigenous status question is not obtained is not known. The non-response rate for the Indigenous status question has increased slightly from 1.7% in the 1996 census to 2.0% in 2001.

    Among records on returned census forms for which no answer to Indigenous status was provided (representing 365,568 persons), there was a consistent pattern of non-response to other variables such as place of birth, ancestry, language and religion. The proportion of not stated responses for this group was in excess of 40% for each of these variables. Some 115,674 people did not answer any of the questions on Birthplace, Language spoken at home, Indigenous status, Ancestry and Religious affiliation.

    About one-fifth (21%) of non-respondents were people aged 75 years and over, although this age group represented only 6% of the total population. Those aged between 55 and 74 years were also slightly over-represented in the non-respondent population (20% compared with 16% of the total population). Older people are more likely to have their census forms completed by someone else.

    A very small number of non-respondents may be assumed to be Indigenous, based on responses to other census questions. Some 328 persons without Indigenous status recorded had Australian Indigenous ancestry recorded (in some cases together with an Indigenous language and/or religious affiliation), while an additional 116 non-respondents to the Indigenous status question were recorded with an Indigenous language and/or religion, but without Indigenous ancestry. These numbers are too small to have any significant impact on population counts.

    The question non-response for Indigenous status where special Indigenous forms were administered by interviewers is lower than the overall non-response rate (1.0% compared with 2.0%). The absence of some Indigenous status responses may reflect a relative lack of training and experience in census procedures for some people recruited as temporary census interviewers. The Indigenous status question may not have been asked by interviewers using the special form because in some cases the response to Indigenous status may have seemed obvious to them.

    When compiling Indigenous population estimates, census records with the Indigenous status question unanswered are adjusted:
    • directly for discrete Indigenous communities where special Indigenous forms have been administered by interviewers who have omitted to mark the appropriate box on the form;
    • directly for records relating to immigration detention centres where Indigenous status is neither asked nor required;
    • directly where other information supports a determination on Indigenous status; or
    • indirectly according to the ratio of the Indigenous response to the total stated responses of the population, separately applied for males and females in each SLA by census form type and age.

    2.5 Unexplained growth in Indigenous census counts

    The way in which the Indigenous status of a person is recorded in the census can change over time and in different situations. The recorded status of an individual may move between any of the categories of Indigenous status, including between Indigenous and non-Indigenous.

    Over the past 35 years, large increases in Indigenous census counts have occurred on several occasions. The excess of births over deaths account for a proportion, but not all of these increases, while overseas migration has had an insignificant impact on the size of the Indigenous population. Between the 1996 and 2001 censuses, the census counts of Indigenous people increased by 57,000 (16%). The components of the Indigenous census count increase between 1996 and 2001 were initially estimated to be 12% due to births and deaths, and a further 4% due to other factors, including changes in census procedures and a difference in the identification of people in the census as being of Indigenous origin. Comparable figures for the 1991-1996 increase were: 33% total increase, 14% due to births and deaths, and a further 19% due to other factors.

    2.6 Administrative data on components of population growth

    Post-censal population estimation processes incorporate administrative data relating to births, deaths and migration. Estimates of births and deaths are based on registrations (i.e. data provided by state and territory Registrars of Births, Deaths and Marriages).

    While Indigenous identification in birth registration data is considered to be reasonably accurate for many purposes, less than complete Indigenous identification in deaths records remains a limitation in estimating the Indigenous population between census years and in developing Indigenous population projections. Tables 1 and 2 below show Indigenous births and deaths registered from 1991 to 2001. Table 2 highlights the variability that has occurred in Indigenous death registration data over time.

    TABLE 1. REGISTERED BIRTHS, Indigenous population, 1991-2001
    NSW
    Vic.
    Qld
    SA
    WA
    Tas.
    NT
    ACT
    Period
    no.
    no.
    no.
    no.
    no.
    no.
    no.
    no.

    1991-1992
    43
    538
    5
    577
    454
    202
    1303
    26
    1992-1993
    483
    459
    15
    572
    1535
    237
    1374
    34
    1993-1994
    1790
    511
    31
    500
    1635
    256
    1356
    41
    1994-1995
    2121
    575
    33
    545
    1465
    251
    1278
    65
    1995-1996
    2468
    463
    1070
    555
    1561
    250
    1386
    58
    1996-1997
    2590
    482
    3069
    576
    1504
    292
    1397
    65
    1997-1998
    2870
    508
    3054
    623
    1451
    290
    1216
    39
    1998-1999
    3012
    566
    3106
    638
    1447
    325
    1385
    67
    1999-2000
    3036
    470
    3033
    669
    1669
    325
    1482
    59
    2000-2001
    3081
    491
    3186
    619
    1697
    443
    1543
    71


    TABLE 2. REGISTERED DEATHS, Indigenous population, 1991-2001
    NSW
    Vic.
    Qld
    SA
    WA
    Tas.
    NT
    ACT
    Period
    no.
    no.
    no.
    no.
    no.
    no.
    no.
    no.

    1991-1992
    180
    62
    -
    128
    392
    3
    393
    -
    1992-1993
    187
    51
    -
    100
    356
    5
    384
    5
    1993-1994
    212
    49
    -
    120
    380
    4
    357
    8
    1994-1995
    169
    44
    3
    122
    379
    -
    398
    9
    1995-1996
    266
    57
    95
    110
    371
    4
    412
    7
    1996-1997
    102
    45
    408
    120
    389
    -
    330
    8
    1997-1998
    264
    137
    575
    139
    346
    8
    458
    -
    1998-1999
    449
    112
    572
    126
    376
    14
    378
    6
    1999-2000
    443
    113
    518
    138
    371
    6
    460
    -
    2000-2001
    479
    109
    576
    129
    362
    26
    446
    -



    Estimates of net overseas migration are calculated for the total population from data provided on incoming and outgoing passenger cards as well as some information provided in visa applications. Since there is no direct measure of interstate migration for post-censal periods, estimates for the total population are modelled using Medicare data on changes of address. Data collected relating to net overseas migration do not include an Indigenous identifier, and while an Indigenous identifier was introduced to Medicare registrations in 2002, this data item is voluntary and coverage is not complete. It is therefore assumed in ABS experimental Indigenous population estimates backcast from 2001 that there is nil net migration of Indigenous people between states and territories and between Australia and overseas.


    3. LIFE TABLES AND THE PRODUCTION OF INDIGENOUS ESTIMATES

    The limitations of the Indigenous births, deaths and migration data make it impractical to use the cohort component method to estimate the Indigenous population. Previous experimental estimates of the Indigenous population have been produced from adjusted census counts by surviving the population back in time (the reverse survival method) using Preston-Hill life tables. For more information on this method see
    Demography Working Paper 2001/4 - Issues in Estimating the Indigenous Population. In that Working Paper, not only were net internal migration (by age, sex and state/territory) and net overseas migration (by age and sex) assumed to be nil, but also no attempt was made to adjust for any change in the extent to which people were identified as Indigenous in the census.

    Since 1998 the ABS has used the Preston-Hill method (1980) as the basis for determining the extent to which Indigenous deaths counted in the death registration system have been incomplete. The Preston-Hill method yields correction factors which adjust the counts of deaths recorded during intercensal periods such that the census date population estimates at each end of the period are consistent with corrected intercensal death registrations. It was first applied by ABS to data relating to the 1991-1996 intercensal period, with the adjusted numbers of deaths used to produce more plausible estimates of Indigenous mortality than those produced from raw counts.

    However, recent scrutiny of the underlying data used to calculate the Preston-Hill correction factors has confirmed that it was inappropriate to use this method for Indigenous population estimates. Preston-Hill relies on an assumption that the two census year population counts used as inputs are demographically consistent. However, the increase in the size of the Indigenous population observed between the 1991 and 1996 censuses (and since then to a much lesser extent between the 1996 and 2001 censuses) cannot be fully explained by demographic events (namely births and deaths occurring during the intercensal period). Instead, the intercensal increases suggest that the population has grown as if there had been very significant net migration gains for the Indigenous population. As this ongoing net inward migration is not plausible, the increase remains unexplained. The Preston-Hill assumption of demographic consistency is therefore invalid when applied to the Indigenous population.


    4. DERIVING LIFE EXPECTANCY ESTIMATES FROM INCOMPLETE DATA - THE BHAT METHOD
    There are several demographic methods which can be used to combine less than comprehensive death registrations and reasonably good population estimates to produce an undercoverage factor by which registered deaths are adjusted to provide plausible measures of mortality, including the life table. Each of these methods contains assumptions, the major one being that the population being studied is stable, i.e. a population which is constant in its proportionate age structure over time and is closed to migration. The other assumption is that the undercoverage factor of registered deaths does not vary by age. Divergence from the stability assumption has been tested in many applications and the techniques developed have been found to be robust to the violation of this assumption. A review of the techniques is given by Gray (1986).

    The Brass Growth Balance Equation (Brass, 1975) was the first innovation which gave a method of 'balancing' population growth and death registrations during an intercensal period using the stable population theory and deriving an adjustment factor for the under-registration of deaths. The method required population data classified by age and sex and the distribution of the registered deaths by age and sex. The Brass method has been modified over time, mainly in terms of its application to non-stable populations. Until recently, these newly developed methods were applied to closed populations, i.e. to populations not exposed to migration. A recent paper by Bhat (2002) lifted this restriction and introduced interstate migration to study mortality differentials across the States in India. A description of the method is given in the appendix to this Working Paper.

    The Bhat method (2002), like the Preston-Hill method (1980), is a demographic technique for estimating the completeness of death registration data and represents a definite improvement over other indirect methods available for estimating mortality from defective data. The main advantage of Bhat over other methods is that it explicitly allows for an adjustment for migration to be taken into account. The Bhat method uses data on the age distribution of Indigenous population from two successive censuses and registered Indigenous deaths by age during the intervening period to calculate partial birth rates and partial death rates for the Indigenous population. Partial birth rates are then adjusted for unexplained growth (growth which is unexplainable by demographic factors) in the Indigenous population during the intercensal period. The adjusted partial birth rates are regressed on partial death rates to estimate consistency factors. The reciprocal of the consistency factor is then used as a correction factor for registered Indigenous deaths so that the age distribution of the two census date estimates and the reported intercensal deaths are consistent with one another.

    In this paper, Bhat's improvement on the Brass growth balance method has been applied in three steps in the development of Indigenous life tables. First, the method is applied to calculate consistency factors for Indigenous death registrations for the 1991-1996 and 1996-2001 intercensal periods relative to the population at the beginning and end of each five year period. The observed age-specific death rates are multiplied by the reciprocal of the consistency factor (constant at each age group) to calculate adjusted age-specific death rates. The adjusted age-specific death rates are then used to calculate Indigenous life tables. This analysis assumes no unexplained growth in the Indigenous population (i.e. all growth is a result of births minus deaths). Results are presented in Table 3.

    Secondly, a sensitivity analysis is carried out by introducing a term for unexplained growth in the Indigenous population to replace interstate migration in Bhat's modification of the technique. Interstate migration for the Indigenous population is small and can be ignored for the present analysis. Various levels of unexplained growth have been subjectively tested. This analysis is restricted to the 1996-2001 period only and assumes that the age distribution of unexplained growth is the same as that of the estimated population at the second census date (see Section 5 for more information). Results are shown in Table 4.

    Finally, to further the sensitivity analysis, the proportionate age distribution of unexplained growth itself based on 1996-2001 data is used along with same levels of unexplained growth as used in the second step. Detailed information is given in Section 5.

    The Bhat technique has been applied to Indigenous death registration data for 1991-1996 and 1996-2001 for all states and territories. The results show that registered intercensal deaths and two-end census date population estimates are less consistent in 1991-1996 than in 1996-2001.

    4.1 Data requirements

    The Bhat method is applied to calculate consistency factors for Indigenous death registrations for the 1991-1996 and 1996-2001 intercensal periods relative to the population at the beginning and end of each five year period. The data needed for each set of calculations comprise: (i) population estimates at the beginning and end of each five year period (rather than actual census counts, 30 June population estimates based on the respective census counts have been used), and (ii) intercensal deaths. Both the population and deaths data were disaggregated by age (five year age groups), sex and state and territory.

    The percentage age distribution of the Indigenous estimated resident population at 30 June 1991 and 2001, based on respective censuses, has remained more or less the same. In regard to the quality of the Indigenous deaths data, some observations may be made by analysing the annual series of counts available for each state and territory (Tables 1 and 2). These series look fairly reasonable for South Australia, Western Australia and the Northern Territory for the entire period since 1991. Year to year counts are consistently much the same in terms of numbers and appear to stand at a reasonable level. However, in the other jurisdictions, especially New South Wales and Queensland, the data for the first half of the 1990s are clearly incomplete and show that relatively few, if any, Indigenous deaths were recognised as such. Since about 1996-97 the counts in these states have begun to look more reasonable and are more consistent on a year to year basis as well.

    For the analysis of the 1996-2001 deaths, adjustments were made to deaths in New South Wales, Victoria and Queensland to account for observed deficiencies. The adjustments to the New South Wales counts of Indigenous deaths were made to allow for the deficit in counts in the first two years of the five year reference period. In practice, and so as not to overinflate the deaths counts, it was assumed that the numbers of Indigenous deaths recorded in 1996-97 and 1997-98 were the same by age and sex as those recorded in 1998-99. These were then added to the deaths recorded in 1998-1999, 1999-2000 and 2000-2001 to provide the total number of deaths for the five year period. Similar adjustments were also made to the counts of Indigenous deaths recorded in Victoria and Queensland. In these latter two states, all deaths recorded over the five year calendar year period 1 January 1997 to 30 December 2001 were used instead of those recorded between 1 July 1996 and 30 June 2001. This effectively allowed for the readily apparent data improvements which occurred at the very beginning of the reference period. As might be expected, these adjustments much better reflect the coverage rate experienced in these states (and Australia) in more recent years.

    4.2 Results

    Table 3 provides estimates of life expectancy at birth for the Indigenous population, based on observed deaths, and adjusted deaths using the consistency factor estimates as determined by Bhat's procedure for each state and territory during 1991-1996 and 1996-2001. The consistency factors presented in the table are used to calculate adjustment factors applied to age-specific death rates so that two end census date population estimates are consistent with the number of deaths registered during the intercensal period.

    Adjustment factors are calculated by taking the reciprocal of the consistency factors. For example, the consistency factor was 0.872 for Indigenous males for Australia in 1996-2001 (Table 3). Therefore, the male age-specific death rates were inflated by an adjustment factor of 1.15 (=1/0.872) to make registered Indigenous male deaths data consistent with the census year population estimates. The consistency factor estimates suggest that registered Indigenous deaths and two-end census date experimental Indigenous population estimates were less consistent in 1991-1996 than in 1996-2001.

    For the period 1991-1996, with the exception of Western Australia, the consistency factors for individual states and territories show poor consistency between registered deaths and two end census date population estimates (i.e. more than 20% below, or above, full consistency). However, in Western Australia the consistency factor was close to 1.0 (fully consistent). This implies that the two end point population estimates and the intercensal death registrations were largely consistent with one another for this state. The very high consistency factors for 1991-1996 for the Northern Territory, which has generally been found to have close to complete records of Indigenous deaths, are especially noteworthy. While the results presented in Table 3 do not provide a basis for disputing the high level of completeness in the deaths data, they do inform that the registered intercensal deaths and two census date population estimates do not accord well with each other. However, the consistency factors for the Northern Territory for the 1996-2001 period are close to unity, therefore a small adjustment was made to make deaths data consistent with the population data. This means that the application of the method to the 1996-2001 intercensal period is likely to give more robust estimates of life expectancy for the Northern Territory. For the 1996-2001 period, the consistency factors were in the range of between 0.8 to 1.2 for Queensland, South Australia, Western Australia and the Northern Territory. On the other hand, consistency factors for New South Wales, Victoria, Tasmania and the Australian Capital Territory were outside that range.

    TABLE 3. CONSISTENCY FACTORS, OBSERVED AND ADJUSTED LIFE EXPECTANCY AT BIRTH(a), Indigenous population, 1991-1996 and 1996-2001
    Consistency factors
    1991-1996
    Consistency factors
    1996-2001
    Observed
    e(0)
    1991-1996
    Observed
    e(0)
    1996-2001
    Adjusted
    e(0)
    1991-1996
    Adjusted
    e(0)
    1996-2001
    Change in adjusted e(0) over the period
    StateSex
    proportion
    proportion
    years
    years
    years
    years
    years

    NSW (b)Males
    0.556
    0.709
    70.99
    69.64
    65.51
    66.37
    0.86
    Females
    0.483
    0.651
    74.38
    73.49
    69.47
    70.56
    1.09
    Persons
    0.534
    0.679
    72.71
    71.58
    67.67
    68.38
    0.71
    Vic (b)Males
    0.523
    0.734
    70.13
    66.92
    63.39
    63.46
    0.07
    Females
    0.676
    0.594
    73.21
    72.22
    70.51
    68.04
    -2.47
    Persons
    0.677
    0.654
    71.66
    69.53
    68.42
    65.34
    -3.08
    Qld (b)Males
    0.044
    0.822
    78.86
    64.40
    61.71
    62.04
    0.32
    Females
    0.030
    0.841
    79.27
    69.14
    63.05
    67.56
    4.51
    Persons
    0.036
    0.841
    79.08
    66.79
    62.00
    64.94
    2.94
    SAMales
    0.654
    0.983
    61.30
    61.58
    55.14
    61.35
    6.21
    Females
    0.758
    1.170
    65.45
    68.02
    62.15
    69.45
    7.30
    Persons
    0.722
    1.067
    63.36
    64.73
    59.05
    65.46
    6.41
    WAMales
    0.998
    1.074
    58.20
    60.91
    58.18
    61.84
    3.66
    Females
    1.111
    1.242
    64.22
    66.84
    65.37
    68.91
    3.54
    Persons
    1.060
    1.147
    61.10
    63.82
    61.83
    65.40
    3.57
    Tas. (c)Males
    0.060
    0.636
    78.37
    77.01
    62.87
    75.47
    12.60
    Females
    0.023
    0.476
    79.28
    77.91
    57.10
    75.83
    18.73
    Persons
    0.046
    0.721
    78.89
    77.52
    62.29
    76.62
    14.33
    NTMales
    1.540
    0.915
    56.59
    58.21
    62.50
    56.94
    -5.56
    Females
    1.867
    1.046
    61.55
    63.26
    68.33
    63.80
    -4.53
    Persons
    1.716
    0.975
    59.02
    60.70
    65.68
    60.36
    -5.32
    ACT (c)Males
    0.622
    0.376
    65.42
    70.97
    61.50
    64.12
    2.63
    Females
    1.753
    0.301
    72.02
    76.31
    75.00
    69.41
    -5.59
    Persons
    1.249
    0.452
    68.79
    74.34
    70.45
    69.15
    -1.30
    Aust. (b)Males
    0.632
    0.872
    67.21
    64.81
    61.94
    63.20
    1.25
    Females
    0.584
    0.873
    70.92
    69.56
    66.06
    68.35
    2.29
    Persons
    0.617
    0.872
    69.07
    67.18
    64.09
    65.75
    1.66

    (a) Life tables used 75+ as the highest age category.
    (b) NSW, Vic. and Qld deaths data are not adjusted for known deficiencies.
    (c) The consistency factors for ACT and Tas. are based on a very small number of intercensal deaths. See Table 2.

    These consistency factors were used to calculate adjusted life expectancy at birth estimates for both time periods and for all states and territories. However, only those estimates which are based on consistency factors of between 0.8 and 1.2 should be considered reasonable.
    For the period 1991-1996, the adjusted life expectancy at birth for Western Australia initially appears to be the only one where some reliance can be placed. This is because the consistency factor for this state was close to unity and required minimal adjustment to the registered intercensal deaths. For all other states and territories, the adjustment factor required to inflate or deflate the number of registered deaths had been large. However, the relatively large increase in life expectancy at birth over the two periods for Western Australia (3.57 years for persons) appears implausible and has not yet been able to be validated against other data. For the Northern Territory, the very large adjustment for 1991-1996 produces an implausibly large decline in adjusted life expectancy at birth over the two intercensal periods (5.32 years for persons). The 1991-1996 adjusted life expectancies will not be used in compiling experimental estimates and projections.


    5. SENSITIVITY ANALYSIS

    The analysis presented so far assumes that there is no unexplained growth in the Indigenous population (i.e. all growth is a result of births minus deaths). However, unexplained growth can be introduced into Bhat's procedure. Two inputs are required: the level of unexplained growth and the age structure of this growth.

    However, the level of unexplained growth during an intercensal period can only be approximated. The first census date population is survived to the second census date population using a representative life table and the age-specific fertility rates for the intercensal period. However, for the Indigenous population both of these inputs remain unreliable due to the quality of Indigenous identification in both death and birth registration data. Only a subjective judgement of the natural increase of the Indigenous population can be made.

    Table 4 below shows the impact of assuming different growth rates of the population on the consistency factor estimation and the life expectancy at birth calculations for 1996-2001 period. The observed growth rate of the population is shown in column 3 and the assumed growth rates in column 4. The difference in these two growth rates is the unexplained growth during the intercensal period.

    The impact on the consistency factors for registered deaths and the adjusted expectation of life at birth calculations assume that the age distribution of unexplained growth is the same as that of the estimated population at the second census date. The results obtained are not sensitive to the assumed level of unexplained growth. Estimated life expectancy at birth declines slightly when unexplained growth is assumed. This is because if the Indigenous population had not experienced any unexplained growth, the population at the second census date would be smaller with consequently higher death rates and lower life expectancy. Except for the adjusted life expectancies at birth for New South Wales (with a difference of 0.4-0.5 years for males) and the Australian Capital Territory (0.7-0.8 years) all other states and the Northern Territory show a difference of 0.1 years or less.

    TABLE 4. ADJUSTED LIFE EXPECTANCY AT BIRTH(a), Indigenous population, 1996-2001
    StateSex
    Annual growth rate 1996-2001
    Assumed growth rate 1996-2001
    Consistency factors
    Adjusted life expectancy at birth
    %
    %
    proportion
    years

    NSWMales
    0.044
    0.044
    0.709
    66.37
    Males
    0.044
    0.025
    0.684
    65.99
    Males
    0.044
    0.020
    0.678
    65.90
    Females
    0.038
    0.038
    0.651
    70.56
    Females
    0.038
    0.025
    0.636
    70.38
    Females
    0.038
    0.020
    0.631
    70.32
    Vic.Males
    0.043
    0.043
    0.734
    63.46
    Males
    0.043
    0.025
    0.728
    63.34
    Males
    0.043
    0.020
    0.726
    63.31
    Females
    0.041
    0.041
    0.594
    68.04
    Females
    0.041
    0.025
    0.597
    68.09
    Females
    0.041
    0.020
    0.598
    68.10
    QldMales
    0.035
    0.035
    0.822
    62.04
    Males
    0.035
    0.025
    0.821
    62.03
    Males
    0.035
    0.020
    0.820
    62.02
    Females
    0.038
    0.038
    0.841
    67.56
    Females
    0.038
    0.025
    0.834
    67.48
    Females
    0.038
    0.020
    0.831
    67.45
    SAMales
    0.031
    0.031
    0.983
    61.35
    Males
    0.031
    0.025
    0.977
    61.28
    Males
    0.031
    0.020
    0.973
    61.23
    Females
    0.028
    0.028
    1.170
    69.45
    Females
    0.028
    0.025
    1.164
    69.40
    Females
    0.028
    0.020
    1.155
    69.34
    WAMales
    0.034
    0.034
    1.074
    61.84
    Males
    0.034
    0.025
    1.072
    61.81
    Males
    0.034
    0.020
    1.070
    61.80
    Females
    0.030
    0.030
    1.242
    68.91
    Females
    0.030
    0.025
    1.236
    68.87
    Females
    0.030
    0.020
    1.231
    68.83
    Tas.Males
    0.027
    0.027
    0.636
    75.47
    Males
    0.027
    0.025
    0.643
    75.51
    Males
    0.027
    0.020
    0.659
    75.61
    Females
    0.024
    0.024
    0.476
    75.83
    Females
    0.024
    0.025
    0.478
    75.85
    Females
    0.024
    0.020
    0.469
    75.78
    NTMales
    0.020
    0.020
    0.915
    56.94
    Males
    0.020
    0.025
    0.915
    56.93
    Males
    0.020
    0.020
    0.915
    56.94
    Females
    0.017
    0.017
    1.046
    63.80
    Females
    0.017
    0.025
    1.049
    63.84
    Females
    0.017
    0.020
    1.047
    63.81
    ACTMales
    0.051
    0.051
    0.376
    64.12
    Males
    0.051
    0.025
    0.410
    64.80
    Males
    0.051
    0.020
    0.414
    64.88
    Females
    0.047
    0.047
    0.301
    69.41
    Females
    0.047
    0.025
    0.304
    69.50
    Females
    0.047
    0.020
    0.303
    69.49

    (a) Adjusted using the Bhat method.
    Varying the age structure of unexplained growth has a large impact on the consistency factor estimates and the resulting life expectancies at birth. However, there are no direct measures available which can give an age distribution of unexplained growth during an intercensal period. At best, the earlier census date population can be survived to the next census date and a difference between the next census date population estimate and the survived estimate at each age group and sex can be attributed to unexplained growth. Any misjudgment of the life tables used for the survival of the population and any inaccuracies in the estimated age distributions at the two end points will form part of unexplained growth.

    The proportionate age distribution of unexplained growth based on 1996-2001 data for Australia is given in Table 5 below. The distribution has used 'approximate' life tables which have been calculated for Australia after adjustment by Bhat's method and the use of the child-women ratio rather than the age-specific fertility rates (which are available based on undercoverage of registered births) to estimate the number of intercensal births and their survival to ages 0-4 years.

    There is some degree of circularity in the way the unexplained growth is calculated. The Bhat method is used to estimate the completeness of death registration data and then to produce an 'approximate' life table for Australia. This 'approximate' life table is then used to calculate unexplained growth of the Indigenous population. Therefore, the accuracy of the level and age distribution of unexplained growth obtained this way is very much dependent on the accuracy of the 'approximate' life table this method produced in the first place. However, without an independent source for data on unexplained growth, this is the only option available.
    TABLE 5 UNEXPLAINED GROWTH IN THE INDIGENOUS POPULATION, Percentage age distribution, Australia - 1996-2001
    Males
    Females
    Persons
    Age group (years)
    %
    %
    %

    0-4
    17.0
    20.6
    18.8
    5-9
    25.2
    20.0
    22.6
    10-14
    14.8
    13.5
    14.2
    15-19
    0.6
    1.9
    1.2
    20-24
    -1.9
    0.2
    -0.9
    25-29
    2.2
    6.4
    4.3
    30-34
    5.3
    6.1
    5.7
    35-39
    8.2
    7.8
    8.0
    40-44
    7.5
    3.7
    5.6
    45-49
    6.6
    3.8
    5.2
    50-54
    4.6
    3.3
    3.9
    55-59
    1.9
    1.8
    1.9
    60-64
    2.6
    3.3
    3.0
    65-69
    1.2
    0.3
    0.8
    70-74
    0.3
    0.0
    0.1
    75 and over
    4.1
    7.4
    5.8
    Total
    100.0
    100.0
    100.0

    While it is not possible to assess the accuracy of the age distribution of unexplained growth, it appears to be concentrated in age groups relating to children, i.e. persons aged 0-14 years. The age distribution of unexplained growth for the Indigenous population varies considerably across the states and territories. The national distribution shown in Table 5 above was therefore used for the sensitivity analysis presented in Table 6 below. This age distribution differs from that used to adjust for unexplained growth in Table 4.

    The male age distribution from Table 5 was used to calculate consistency factors for Indigenous male deaths in Table 6. Similarly, age distributions for females and persons (the latter defined as average of the male and female distribution) were used to calculate consistency factors for Indigenous females and all Indigenous persons, respectively.

    TABLE 6 CONSISTENCY FACTORS, OBSERVED AND ADJUSTED LIFE EXPECTANCIES AT BIRTH(a), Indigenous population, Australia - 1996-2001
    (1)(2)
    (3)
    (4)
    (5)
    (6)
    (7)
    (8)
    (9)
    State/ territorySex
    Consistency factor
    Observed e(0)
    Observed pop. growth rate
    (annual)
    Adjusted e(0)
    Obs. pop growth rate
    Assumed
    growth rate
    of 2.5%
    Assumed
    growth rate
    of 2.0%
    Range (upper, lower)
    proportion
    years
    %
    years
    years
    years
    years

    NSW (b)Males
    0.927
    68.6
    4.4
    67.6
    61.5
    60.2
    (67.6, 60.2)
    Females
    0.804
    75.3
    3.8
    72.8
    67.1
    65.4
    (72.8, 65.4)
    Persons
    0.864
    71.9
    4.1
    70.1
    63.9
    62.3
    (70.1, 62.3)
    Vic. (b)Males
    0.786
    67.7
    4.3
    64.4
    59.9
    58.8
    (64.4, 58.8)
    Females
    0.620
    74.8
    4.1
    69.2
    65.1
    64.1
    (69.2, 64.1)
    Persons
    0.691
    71.1
    4.2
    66.4
    61.9
    60.9
    (66.4, 60.9)
    Qld. (b)Males
    0.885
    65.3
    3.5
    63.6
    60.3
    58.9
    (63.6, 58.9)
    Females
    0.856
    71.2
    3.8
    69.2
    64.1
    62.6
    (69.2, 62.6)
    Persons
    0.880
    68.2
    3.7
    66.5
    62.1
    60.6
    (66.5, 60.6)
    SAMales
    0.983
    62.7
    3.1
    62.5
    60.1
    58.2
    (62.5, 58.2)
    Females
    1.170
    70.2
    2.8
    72.2
    70.3
    67.7
    (72.2, 67.7)
    Persons
    1.067
    66.4
    2.9
    67.3
    65.0
    62.7
    (67.3, 62.7)
    WAMales
    1.074
    62.0
    3.4
    63.1
    60.2
    58.6
    (63.1, 58.6)
    Females
    1.242
    69.1
    3.0
    71.9
    69.2
    66.9
    (71.9, 66.9)
    Persons
    1.147
    65.5
    3.2
    67.5
    64.4
    62.5
    (67.5, 62.5)
    TasMales
    0.636
    78.7
    2.7
    -
    -
    -
    -
    Females
    0.476
    79.7
    2.4
    -
    -
    -
    -
    Persons
    0.721
    79.3
    2.5
    -
    -
    -
    -
    NTMales
    0.915
    59.0
    2.0
    57.6
    59.4
    57.7
    (59.4, 57.6)
    Females
    1.046
    64.5
    1.7
    65.2
    69.0
    66.5
    (69.0, 65.2)
    Persons
    0.975
    61.7
    1.8
    61.3
    64.1
    62.0
    (64.1, 61.3)
    ACTMales
    0.376
    71.7
    5.1
    -
    -
    -
    -
    Females
    0.301
    77.9
    4.7
    -
    -
    -
    -
    Persons
    0.452
    75.7
    4.9
    -
    -
    -
    -
    Aust. (b)Males
    0.951
    65.3
    3.6
    64.6
    60.9
    59.4
    (64.6, 59.4)
    Females
    0.920
    72.8
    3.3
    70.5
    66.7
    64.8
    (70.5, 64.8)
    Persons
    0.934
    68.4
    3.4
    67.5
    63.6
    61.8
    (67.5, 61.8)

    (a) Life table calculations used 85+ as the highest age category.
    (b) Deaths data for NSW, Vic. and Qld have been adjusted for known deficiencies.


    The e(0) estimates in column 4 of Table 6 are calculated using the observed deaths. No adjustments are made to the age-specific death rates to make deaths data consistent with population data. These estimates are different from the observed e(0) estimates for the period 1996-01 shown in Table 3 for the following reasons:
    • e(0) estimates in column 4 of Table 6 are calculated after adjusting deaths data for New South Wales, Victoria and Queensland for known deficiencies; and
    • They are based on abridged life tables where the age-specific death rates and other functions are in five year age groups with an open ended category up to 85+ years. In comparison, analysis for Table 3 was based on age-specific death rates and other life table functions using data to 75+ years. While it is not possible from this analysis to quantify the impact of using 85+ data on e(0) estimates, in general, higher estimates of life expectancy at birth will be obtained when life tables are constructed with a higher open-ended category.

    The observed 1996-2001 growth rate of the Indigenous population is unreasonably high for all states and territories other than the Northern Territory (see column 5 of Table 6), although some of this growth may be unexplained growth. In the sensitivity analysis, three alternative levels of unexplained growth were assumed:
    • nil unexplained growth (i.e. the 'true' growth rate is assumed to be the same as the observed growth rate);
    • moderate unexplained growth (i.e. a 'true' growth rate of 2.5% is assumed, with unexplained growth being the difference between the observed growth rate and this assumed rate); and
    • high unexplained growth (i.e. a 'true' growth rate of 2.0% is assumed).

    The use of alternative levels and age structures for unexplained growth in the sensitivity analysis reduces life expectancy at birth estimates by approximately 6 years for Australia, 8 years for New South Wales, 5-6 years for Victoria and Queensland, and 4-5 years for South Australia and Western, with little change in life expectancy at birth estimates for the Northern Territory. However, these results are influenced by the subjectivity of their inherent assumptions, which themselves have associated uncertainties. The wide range of life expectancy estimates produced under various assumptions suggests that the estimates are not robust.


    6. OUTCOMES FOR USE IN POPULATION ESTIMATES AND PROJECTIONS

    While the estimates of life expectancy produced in this paper are not robust, there remains a need to compile estimates and projections of the Indigenous population. In deriving life expectancies at birth, population growth rates of 1.8% per annum for the Northern Territory (i.e. as observed) and 2% per annum for all other states, territories and Australia have been assumed. Estimates of life expectancy associated with these assumptions will form the basis for producing experimental estimates and projections of the Indigenous population for 1991-2009. These will be released on 27 September 2004 in Experimental Estimates and Projections, Aboriginal and Torres Strait Islander Australians, 1991-2009 (ABS cat. no. 3238.0). This publication will include retrospective estimates for 1991-2001 produced using the experimental Indigenous life tables for 1996-2001.

    In order to produce more reliable age-specific death rates, states with small numbers of Indigenous deaths (Victoria and South Australia) were grouped together with other states on the basis of geographic proximity. Victoria and New South Wales were combined and South Australia and Western Australia were combined and life tables compiled for these state aggregates.

    Of all the states and territories, Queensland recorded the largest number of Indigenous deaths during the 1996-2001 intercensal period, and these have remained consistent on a year-to-year basis (see Table 2). A ranking of the observed growth rate of the Indigenous population for 1996-2001 places Queensland between the two southern states (i.e. New South Wales and Victoria) and the western states (South Australia and Western Australia). However, this is inconsistent with the observed e(0) estimates for 1996-2001, which place Queensland closer to South Australia and Western Australia. This raises uncertainty about whether results for Queensland should be grouped with other states. As a result of these uncertainties, and the fact that the number of Indigenous deaths in Queensland is sufficiently large enough to produce a reliable life table, a separate life table has been produced for Queensland.

    In the case of the Northern Territory, counts of Indigenous deaths appear reasonable and have been fairly similar over the last ten years. The 1996-2001 population growth rate for the Territory was smaller than that of any of the states, and was almost completely accounted for by births and deaths (i.e. consistency factors close to 1.0). This implies that levels of unexplained growth in the Indigenous population are very small in the Northern Territory. Analysis of alternative levels and age structures for unexplained growth also produced little change to estimated Indigenous life expectancy at birth. As a result of this small level of unexplained growth, a separate life table was also produced for the Northern Territory.

    The numbers of Indigenous deaths registered in Tasmania and the Australian Capital Territory are very small. Together, these regions accounted for only 1.6% of all Indigenous deaths registered in 2001. It is therefore not possible to produce credible life tables for either of these regions in isolation. In the absence of these, the ABS will use e(0) estimates for New South Wales and Victoria (combined) to produce Indigenous population estimates and projections for Tasmania and the Australian Capital Territory.

    Table 7 presents experimental estimates of life expectancy at birth that will be used the compilation of experimental Indigenous population estimates and projections. The ABS assesses the 1996-2001 estimates in this paper to be the most accurate currently available. At the national level, the life expectancy at birth of Indigenous males in 1996-2001 is estimated to be 59.4 years. The life expectancy at birth of Indigenous females in 1996-2001 is estimated to be 64.8 years. The difference between these life expectancy estimates and those previously produced by the ABS, using a method no longer recommended for a population which is not closed, should not be construed as a change over time in actual life expectancy.

    While this analysis has produced estimates of Aboriginal and Torres Strait Islander mortality suitable for use in compiling short range population estimates and projections for Australia, states and territories, the differences between the respective life expectancy at birth values for the geographic areas presented may or may not be plausible. ABS therefore advises against using these life expectancy values for any other purpose. Over-precise analysis of these life expectancy estimates as measures of Indigenous health outcomes should be avoided. Geographic and sex differences will be sensitive to the various subjective judgements, assumptions and limitations in the quality of the data which may vary from state to state and between males and females.

    The ABS will be applying an assumption of no change in mortality to both its estimates of the Indigenous population from 1991 to 2001 and to its projections from 2002 to 2009.

    TABLE 7 LIFE EXPECTANCIES AT BIRTH TO BE USED FOR POPULATION ESTIMATES AND PROJECTIONS (a), Indigenous population, 1991-2009
    NSW and Vic.
    Qld
    SA and WA
    NT
    Australia
    PeriodSex
    years
    years
    years
    years
    years

    1991-2009 (b)Males
    60.0
    58.9
    58.5
    57.6
    59.4
    Females
    65.1
    62.6
    67.2
    65.2
    64.8

    (a) For Tasmania and the Australian Capital Territory, use data for NSW and Vic. (b) Based on 1996-2001 - see Table 6.


    7. CAUTIONARY REMARKS

    It should be noted that the correction to the registered Indigenous deaths, the level of the unexplained population growth and the age distribution of the unexplained growth are all based on subjective judgements, and any variations in these would influence the outcome as measured by the expectation of life at birth. Bhat's method is an indirect technique of mortality estimation. The results are driven by the subjectivity of the assumptions, which themselves have uncertainties associated with them. There is no single mortality level that can be estimated by the technique given the quality of Indigenous data and the assumptions made in applying the technique to these data.


    8. FUTURE DIRECTIONS

    The Australian Institute of Health and Welfare (AIHW) is undertaking in collaboration with ABS, an analysis of a range of health and mortality indicators to gain a broad assessment of whether it is possible, through indirect methods, to determine with some confidence whether Indigenous mortality (and hence life expectancy) has changed over recent decades. The results from this research, expected to be available in the second half of 2005, will be evaluated by ABS and AIHW to determine whether a recompilation of a new series of experimental Indigenous population estimates and projections is warranted.


    9. FURTHER INFORMATION

    For further information on estimated resident Indigenous population see:

    Experimental Estimates of the Aboriginal and Torres Strait Islander Population, 30 June 1991 - 30 June 1996 (ABS cat. no. 3230.0)
    Experimental Projections of the Aboriginal and Torres Strait Islander Population, 30 June 1996 to 30 June 2006 (ABS cat. no. 3231.0).
    Experimental Estimates and Projections, Aboriginal and Torres Strait Islander Australians, 1991 to 2009 (ABS cat. no. 3238.0) to be published on 27 September 2004.
    Experimental Projections of Aboriginal and Torres Strait Islander Australians, ATSIC regions - electronic release (ABS cat. no. 3238.0.55.001) to be published on 27 September 2004.

    For further information and statistics on Indigenous Australians see:

    Population Distribution, Aboriginal and Torres Strait Islander Australians, 2001 (ABS cat. no. 4705.0)
    Population Characteristics, Aboriginal and Torres Strait Islander Australians, 2001 (ABS cat. no. 4713.0)
    The Health and Welfare of Australia's Aboriginal and Torres Strait Islander Peoples, 2003 (ABS cat. no. 4704.0).

    More information on Indigenous statistics can be found on Indigenous theme page, which is available on the ABS website <http:\\www.abs.gov.au> and can be accessed by going to the home page and selecting Themes and then Indigenous (located under People).

    For more information please contact Shahidullah on (02) 6252 5129 or client.services@abs.gov.au.


    10. REFERENCES

    Australian Bureau of Statistics (2001) Demography Working Paper 2001/4 - Issues in Estimating the Indigenous Population, ABS, Canberra

    Australian Bureau of Statistics (2001) Fact Sheet: Effect of Census Processes on Non-response Rates and Person Counts, ABS, Canberra

    Australian Bureau of Statistics (2002) Demography Working Paper 2002/2 - Estimated Resident Population and Effects of Census Systems Created Records, ABS, Canberra

    Australian Bureau of Statistics (2002) Deaths, Australia, 2001, cat. no. 3302.0, ABS, Canberra.

    Bhat, P.N. Mari (2002) General growth balance method: a reformulation for populations open to migration, Population Studies, Vol. 56, pp. 23-34, London, England.

    Brass, William (1975) Methods of estimating fertility and mortality from limited and defective data, Laboratories for Population Studies, Carolina Population Centre, Chapel Hill, North Carolina.

    Commonwealth Bureau of Census and Statistics (CBCS) 1969, The Aboriginal Population of Australia: Summary of Characteristics, 30 June 1966, CBCS Ref. No. 2.23, CBCS, Canberra.

    Gray, A. (1986) Sectional growth balance analysis for non-stable closed populations, Population Studies, Vol. 40, pp. 425-36, London, England.

    Preston, S.H. and K.J. Hill (1980) Estimating the completeness of death registration, Population Studies, Vol. 34, pp. 349-366, London, England.

    Ross K. (1999) Occasional Paper, Population Issues, Indigenous Australians, 1996, cat. no. 4708.0, Canberra

    United Nations (1983) Indirect techniques for demographic estimation, Manual X, Chapter 5, pp. 129-155


    APPENDIX. APPLICATION OF THE BHAT METHOD

    The basic demographic balancing equation applied in the Bhat method can be defined as:

    Image - basic demographic balancing equation
    (A1)

    Where:
      P1 = the population at the time of the first census;
      P2 = the population at the time of the second census;
      B = the number of births occurring during the intercensal period;
      D = the number of deaths occurring during the intercensal period; and
      NM = net migration occurring during the intercensal period

    This equation can be rewritten as:

    Image - rewritten demographic balancing equation
    (A2)
    Where (P2 - P1) is the total population growth for the intercensal period.

    In the original formulation of the Brass Growth Balance Equation (upon which the Bhat method is ultimately based), net migration was not allowed and the above equation was converted to rates (instead of numbers) above age a. Using the stable population theory, Brass defined:


    Image - demographic equation using stable population theory
    (A3)
    Where:
      Na = the number of persons of exact age a;
      Na+ = the total number of persons aged a and over;
      Da+ = the total number of deaths occurring to persons aged a and over; and
      r = the growth rate of the population

    Brass proved that this equation is exact for a stable, closed population. According to Brass, Na may be thought as being the number of persons in a year entering the group of those aged a and over, while the ratio Na/Na+ can be interpreted as a 'birth rate' for the population aged a and over.
    Da+/Na+ is the death rate corresponding to the same population; and if one denotes by ra+ the growth rate for the population aged a and over, the equation becomes

    Image - demographic equation
    (A4)

    If we define the registered number of deaths as:

    Image - demographic equation
    (A5)

    Where Ca is the correction factor for deaths of age a+, equation (5) becomes:

    Image - demographic equation
    (A6)

    If Ca is the same for all values of a, it can be replaced by C. Also, in a stable population ra+= r (ie growth rate is the same for all ages). Assuming 1/C = K the equation becomes


    Image - demographic equation
    (A7)

    Equation (A7) represents a linear equation like Y = A+BX, where A (= r) is the intercept and B (=K) is the slope of the line.

    Fitting such a line with the observed data can determine r (the rate of growth of the population) and K (=1/C), the factor to adjust the registered deaths. (United Nations, 1983, pp.139-140).

    Having determined a plausible value of K, the number of registered deaths are adjusted and the mortality indicators are calculated. Different ways of fitting the straight line (least square, orthogonal regression, group mean method etc) give different values of r and K, but there is little difference between these. Bhat has advocated the use of the orthogonal regression method in his paper (Bhat, 2002) although an average based on these methods would be as good.

    In later developments of the Brass growth balance method, populations at two end points (5 or 10 years apart) have been used and the 'Y' component of the linear equation is modified to take into account some differentials in growth and migration rates above age a.

    In Bhat's formulation, equation (A7) becomes:

    Image - demographic equation Bhat's formulation
    (A8)

    Where
      ba+= the 'partial' birth rate;
      ua+= the 'partial growth differential';
      va+ = the 'partial migration differential';
      d*a+ = the 'partial' death rate in the population aged a and over;
      n = the natural increase rate;
      C = the coverage of the registered deaths.
    Equations (A8.1)-(A8.6) below explain the rationale behind this technique. The growth rate of a population aged a and over in a closed population can be expressed as

    Image - demographic equation
    (A8.1)

    Equation (A8.1) can be generalised to any population as follows

    Image - demographic equation
    (A8.2)

    where ma+ is the 'partial' net migration rate for a population aged a and over.

    Let the 'partial growth differential' of the population aged a and over be:

    Image - demographic equation; or
    Image - demographic equation
    (A8.3)

    where r is the growth rate of total population (and is equivalent to r0+).

    Similarly, let the 'partial migration differential' of the population aged a and over be

    Image - demographic equation; or
    Image - demographic equation
    (A8.4)

    where m is the migration rate of total population (and is equivalent to m0+).

    Equation (A8.2) can now be rewritten as:

    Image - demographic equation
    (A8.5)

    By assuming that the level of under-reporting of deaths is constant by age, equation (A8.5) becomes

    Image - demographic equation
    (A8.6)

    where d+a=d*a+/C (which is the partial death rate at ages a and over calculated from the reported deaths), and n is the rate of natural increase of the population.

    Equation (A8.6) is identical to fitting a line Y = A + BX, where A(=n) and B(=1/C) are as defined earlier. All of the input data for this equation are calculated from the population by age and sex at two points of time (5 or 10 years apart), age and sex data of registered deaths, and migration in the intervening period.

    The method has potential to calculate the 1/C factor for any specific age a and over. Deaths can therefore be adjusted at each age from ages a and over by this calculated factor. Death rates under age a can be calculated by other indirect techniques of mortality estimation ( eg. children ever born and children surviving for infant and childhood mortality estimation). The adjusted death rates (with those for early childhood and adult ages based on different data sets) can be combined to make a life table.

    In this paper, the 1/C factor based on registered deaths at all ages 5 to 64 is assumed to apply to deaths at all ages. The Bhat method restricts the inclusion of the 0-4 age group. The age group 70-74 is also recommended for exclusion and this has been accepted.

    Two methods of line fitting (the ordinary least square method and orthogonal regression) are used to estimate the factor 1/C. While similar results are obtained under each method, Bhat has recommended the use of the orthogonal regression method. This may be due to the fact that the causal relationship between Y and X inherent in the least square method is not applicable here. X could depend on Y or Y could depend on X. The orthogonal regression allows for this.

    The linear equation can be fitted to X,Y points using all ages, selected ages, or any other selection of the age range. The results would vary according to the age range selected. Other goodness of fit measures can be calculated, such as R-square, to gauge the accuracy of the fitted line. In this paper, X Y values derived from data relating to the 5 to 64 years age range have been used. The correction factor, 1/C, estimated from the fitted line is assumed to apply uniformly to deaths of all ages.

    Both the Brass Growth Balance Equation and its reformulation under Bhat are essentially measuring a 'correction factor' for deaths such that the age distributions of the two census date estimates and the recorded intercensal deaths are consistent with one another. In this light, the 'correction factor' is a consistency factor and its value, in its own right, cannot be used to measures differences in under-coverage among population sub-groups (such as between people living in different states and territories, or between men and women). Instead, its relevance lies in the adjustment of the age-specific death rates or various measures based on these (eg. expectation of life at birth) for the population for which it has been calculated.

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