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ABSTRACT
2.3 System created records
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 19911996 and 19962001 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 twoend census date population estimates and the registered deaths during the intercensal period to be consistent with one another. The observed agespecific 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 agespecific 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 19962001 period and different levels of unexplained growth, the consistency factors and adjusted life tables for 19962001 were calculated for Australia and the states and territories (Table 6). A final selection of the life tables for 19962001 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:
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:
Where:
P_{t+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. More specifically, in estimating the Indigenous population there are issues relating to:
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 'nonIndigenous' 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 nonIndigenous 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 19911996 intercensal period was accounted for by editing changes, while unexplained growth in the 19962001 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 nonsparsely 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 nonsparsely 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 noncontact dwellings. However, subsequent analysis of the 2001 census results showed that there had been a significant level of overimputation 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 nonresponse rates can be found in Fact Sheet: Effect of Census Processes on Nonresponse Rates and Person Counts. For information on how population estimates are adjusted for census overimputation of system created records in noncontact 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 QualityUndercount, 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 Nonresponse 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 nonresponse 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 nonresponse 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 onefifth (21%) of nonrespondents 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 overrepresented in the nonrespondent 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 nonrespondents 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 nonrespondents 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 nonresponse for Indigenous status where special Indigenous forms were administered by interviewers is lower than the overall nonresponse 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:
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 nonIndigenous. 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 19911996 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 Postcensal 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, 19912001
TABLE 2. REGISTERED DEATHS, Indigenous population, 19912001
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 postcensal 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 PrestonHill 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 PrestonHill method (1980) as the basis for determining the extent to which Indigenous deaths counted in the death registration system have been incomplete. The PrestonHill 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 19911996 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 PrestonHill correction factors has confirmed that it was inappropriate to use this method for Indigenous population estimates. PrestonHill 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 PrestonHill 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 underregistration 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 nonstable 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 PrestonHill 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 19911996 and 19962001 intercensal periods relative to the population at the beginning and end of each five year period. The observed agespecific death rates are multiplied by the reciprocal of the consistency factor (constant at each age group) to calculate adjusted agespecific death rates. The adjusted agespecific 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 19962001 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 19962001 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 19911996 and 19962001 for all states and territories. The results show that registered intercensal deaths and twoend census date population estimates are less consistent in 19911996 than in 19962001. 4.1 Data requirements The Bhat method is applied to calculate consistency factors for Indigenous death registrations for the 19911996 and 19962001 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 199697 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 19962001 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 199697 and 199798 were the same by age and sex as those recorded in 199899. These were then added to the deaths recorded in 19981999, 19992000 and 20002001 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 19911996 and 19962001. The consistency factors presented in the table are used to calculate adjustment factors applied to agespecific 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 19962001 (Table 3). Therefore, the male agespecific 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 twoend census date experimental Indigenous population estimates were less consistent in 19911996 than in 19962001. For the period 19911996, 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 19911996 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 19962001 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 19962001 intercensal period is likely to give more robust estimates of life expectancy for the Northern Territory. For the 19962001 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, 19911996 and 19962001
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 agespecific 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 19962001 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 0.40.5 years for males) and the Australian Capital Territory (0.70.8 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, 19962001
The proportionate age distribution of unexplained growth based on 19962001 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 childwomen ratio rather than the agespecific fertility rates (which are available based on undercoverage of registered births) to estimate the number of intercensal births and their survival to ages 04 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  19962001
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  19962001
The e(0) estimates in column 4 of Table 6 are calculated using the observed deaths. No adjustments are made to the agespecific death rates to make deaths data consistent with population data. These estimates are different from the observed e(0) estimates for the period 199601 shown in Table 3 for the following reasons:
The observed 19962001 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:
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, 56 years for Victoria and Queensland, and 45 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 19912009. These will be released on 27 September 2004 in Experimental Estimates and Projections, Aboriginal and Torres Strait Islander Australians, 19912009 (ABS cat. no. 3238.0). This publication will include retrospective estimates for 19912001 produced using the experimental Indigenous life tables for 19962001. In order to produce more reliable agespecific 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 19962001 intercensal period, and these have remained consistent on a yeartoyear basis (see Table 2). A ranking of the observed growth rate of the Indigenous population for 19962001 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 19962001, 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 19962001 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 19962001 estimates in this paper to be the most accurate currently available. At the national level, the life expectancy at birth of Indigenous males in 19962001 is estimated to be 59.4 years. The life expectancy at birth of Indigenous females in 19962001 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. Overprecise 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, 19912009
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 Nonresponse 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. 2334, 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 nonstable closed populations, Population Studies, Vol. 40, pp. 42536, London, England. Preston, S.H. and K.J. Hill (1980) Estimating the completeness of death registration, Population Studies, Vol. 34, pp. 349366, 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. 129155 APPENDIX. APPLICATION OF THE BHAT METHOD The basic demographic balancing equation applied in the Bhat method can be defined as:
Where:
P_{2} = 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:
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:
N_{a+} = the total number of persons aged a and over; D_{a+} = 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, N_{a} may be thought as being the number of persons in a year entering the group of those aged a and over, while the ratio N_{a}/N_{a+} can be interpreted as a 'birth rate' for the population aged a and over. D_{a+}/N_{a+} is the death rate corresponding to the same population; and if one denotes by r_{a+} the growth rate for the population aged a and over, the equation becomes
If we define the registered number of deaths as:
Where C_{a} is the correction factor for deaths of age a+, equation (5) becomes:
If C_{a} is the same for all values of a, it can be replaced by C. Also, in a stable population r_{a+}= r (ie growth rate is the same for all ages). Assuming 1/C = K the equation becomes
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.139140). 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:
Where
u_{a+}= the 'partial growth differential'; v_{a+} = 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.
Equation (A8.1) can be generalised to any population as follows
where m_{a+} 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:
where r is the growth rate of total population (and is equivalent to r_{0+}). Similarly, let the 'partial migration differential' of the population aged a and over be
where m is the migration rate of total population (and is equivalent to m_{0+}). Equation (A8.2) can now be rewritten as:
By assuming that the level of underreporting of deaths is constant by age, equation (A8.5) becomes
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 04 age group. The age group 7074 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 Rsquare, 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 undercoverage among population subgroups (such as between people living in different states and territories, or between men and women). Instead, its relevance lies in the adjustment of the agespecific death rates or various measures based on these (eg. expectation of life at birth) for the population for which it has been calculated. Document Selection These documents will be presented in a new window.
