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3120.0 - Demography Working Paper 2000/2 - Draft Experimental Aboriginal and Torres Strait Islander Abridged Life Tables, Australia and States/Territories, 1995-97, 1995 to 1997  
Latest ISSUE Released at 11:30 AM (CANBERRA TIME) 16/05/2000   
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Shahidullah and Kim Dunstan

The authors welcome comment on the method and results contained in this draft paper. Comments should be sent to Shahidullah by July 2000, email shahidullah@abs.gov.au. Following feedback, ABS proposes publishing 1995-97 experimental life tables in Deaths, 1999 (ABS Cat. No. 3302.0).

OUTLINE

Summary
1. Introduction and aim
2. Estimating the completeness of death registration

    2.1 Preston-Hill method
    2.2 Application of Preston-Hill method to Indigenous data
      2.2.1 Survival ratios based on census counts and ERP
      2.2.2 Completeness of Indigenous death registration
3. Indigenous abridged life tables
    3.1 Comparison between 1991-96 and 1995-97 experimental life tables
4. Comparison between Indigenous and non-Indigenous population
    4.1 Life expectancy
    4.2 Standardised death rates
    4.3 Median age at death
5. Implications of assumptions
6. Conclusion
References

Appendix 1: Indigenous population and deaths, 1991-96
Appendix 2: The life table
    Introduction
    Life table functions
    Calculation of infant mortality
    Estimation of mortality at ages 1-74
    Estimation of mortality at ages 75+
    Estimation of lx, nLx, Tx and e0x
Appendix 3: Age-specific death rates, 1995-97
Appendix 4: Draft experimental abridged life tables, Australia and selected States/Territories, 1995-97


LIST OF TABLES

Table 1: Registered Indigenous Deaths, Occurring During 1995-97, by State/Territory
Table 2: Survival Ratio, Indigenous Males and Females, Australia and Selected States/Territories, 1991-96
Table 3: Estimates of Indigenous Deaths Coverage (%), Australia and States/Territories, 1991-96
Table 4: Observed and Expected Indigenous Life Expectancy at Birth, 1995-97
Table 5: Mortality Rates, Indigenous Males and Females, Australia, 1991-96 and 1995-97
Table 6: Crude and Standardised Death Rates, Indigenous and Non-Indigenous Males and Females, 1995-97
Table 7: Median Age at Death (Years), By Indigenous Status, Sex and Year of Registration, Australia, 1991-98
Table 8: Median Age at Death (Years), Indigenous Population, By Sex, Period of Registration and State/Territory, 1991-97
Table 9: Effect of Differential Coverage on Life Expectancy, Indigenous Males and Females, Australia, 1995-97

Table A1: Indigenous Population and Registered Deaths, Occurring During 1991-96, by Age at Census and Sex, Australia
Table A2: Calculation of Infant Mortality Rate, Indigenous Males and Females, Australia, 1995-97
Table A3: Age-Specific Deaths Rates (per 1,000 population), By Indigenous Status and Sex, 1995-97
Table A4: Draft Experimental Abridged Life Table, Indigenous Males and Females, Australia, 1995-97
Table A5: Draft Experimental Abridged Life Table, Indigenous Males and Females, South Australia, 1995-97
Table A6: Draft Experimental Abridged Life Table, Indigenous Males and Females, Western Australia, 1995-97
Table A7: Draft Experimental Abridged Life Table, Indigenous Males and Females, Northern Territory, 1995-97
Table A8: Draft Experimental Abridged Life Table, Indigenous Males and Females, South Australia, Western Australia and Northern Territory Combined, 1995-97


LIST OF FIGURES

Figure 1: Preston-Hill Curve, Indigenous Males and Females, Age at 1991 Census, Australia, 1991-96
Figure 2: Mortality Rates, Indigenous Males and Females, Australia, 1995-97
Figure 3: Mortality Rates, Indigenous and Total Population, Males and Females, Australia, 1995-97
Figure 4: Mortality Rates, Indigenous Males and Females, Australia, 1991-96 and 1995-97


SUMMARY

The life expectancy estimates presented in this paper are described as experimental because of the nature of the base population, which is affected by the intercensal volatility in the counts of the Indigenous population, and deficiencies in deaths and births registration data. Consequently, there is uncertainty about the accuracy of death rates which use census counts or census-based population estimates as their denominator. The life expectancy estimates are therefore sensitive to the inputs used and over-precise analysis is cautioned. They should be used only as an indicative summary measure of the level of mortality of the Indigenous population.

The standard approach to calculating death rates is based on applying the number of deaths in a given period to the 'exposed to risk' population during that period. Without accurate data on Aboriginal and Torres Strait Islander (Indigenous) births and deaths, and accurate data on the size and structure of the Indigenous population, the standard method for calculating Indigenous death rates cannot be used.

A demographic technique outlined by Preston and Hill was used to estimate the completeness of Indigenous death registration. Based on the analysis presented here, 39.1% of Indigenous male deaths and 39.5% of Indigenous female deaths in the 1991-96 intercensal period were estimated to be registered as such. These estimates were then applied across all age groups to obtain an adjusted number of Indigenous deaths which occurred during 1995-97. These estimated death numbers were then used in the construction of experimental abridged life tables.

Indigenous deaths are under-registered in all States/Territories, but with a high degree of variability. South Australia (SA), Western Australia (WA) and the Northern Territory (NT) had sufficient registration coverage in 1991-97 to provide enough Indigenous deaths to attempt estimates of life expectancy. Preston-Hill analysis indicates that SA, WA and the NT all had significantly higher coverage of Indigenous deaths than Australia overall.

At the national level, the life expectancy at birth in the period 1995-97 was estimated to be about 54 years for Indigenous males and 61 years for Indigenous females. However, life expectancy estimates derived from combining data from SA, WA and NT, the States/Territory with the best deaths coverage, are likely to be more reliable than the national estimate of Indigenous life expectancy. The combined data suggests life expectancy at birth of about 57 years for males and 63 years for females.

The estimates suggest life expectancy for each of SA, WA and NT are higher than the national estimates for both sexes. WA had the highest life expectancy at birth at around 58 years for males and 64 years for females. SA and NT had similar life expectancies for both sexes at around 55 years for males and 63 years for females.

No life tables were produced for other States/Territories. During 1991-97, there were too few Indigenous deaths registered in Victoria, Tasmania and the Australian Capital Territory. Over the same period, the completeness of death registration was too low in New South Wales and Queensland.

The Preston-Hill method assumes that the completeness of enumeration and of death registration do not vary with age. These are unlikely to be true for the Indigenous population. The implications of these assumptions are that life expectancy is probably within 1-2 years of the estimates given. Furthermore, the analysis presented in this paper also assumes that 1995-97 deaths coverage is the same as 1991-96 deaths coverage. For that reason, the estimates of life expectancy for 1995-97 presented here are probably under-estimates.


1. INTRODUCTION AND AIM

Australia has a very good system of population measurement by international standards. There are accurate censuses of population and housing every five years, birth and death registration has high coverage, and all movements into and out of Australia are monitored. Therefore it is possible to maintain high quality estimates of the total Australian population. However, there are a range of data quality issues associated with estimating the Aboriginal and Torres Strait Islander (Indigenous) population.

The standard approach to calculating death rates relies on applying the number of deaths in a given period to the 'exposed to risk' population during that period. Without accurate data on Indigenous births and deaths, and accurate data on the size and structure of the Indigenous population, the standard method for calculating Indigenous death rates cannot be used.

This paper describes how a demographic technique outlined by Preston and Hill (1980) is used to estimate the completeness of Indigenous death registration and calculate death rates for the Indigenous population. It then shows how these rates are used to produce Indigenous life tables for Australia and selected States/Territories for 1995-97. Comparison with the 1991-96 experimental Indigenous life table and non-Indigenous mortality are made. Finally, the implications of the assumptions made in this analysis are discussed.

Before attempting to estimate the completeness of Indigenous death registration, it is important to recognise the major data quality issues relating to the Indigenous population.
  • Coverage of Indigenous births and deaths

    While virtually all births and deaths are registered, not all Indigenous births and deaths are recorded as being Indigenous. The coverage of birth registrations is better than the coverage of death registrations. The total number of Indigenous births registered in Australia in 1998 was around 90% of the number of births projected in the 'low' series of the 1996-base experimental Indigenous population projections (ABS 1999b). By comparison, only about 61% of Indigenous deaths were registered in Australia in 1998 compared with the same population projection (ABS 1999c).

    During 1995-97, 4,237 Indigenous deaths were identified as occurring in Australia (Table 1). The number of Indigenous deaths ranged from an average of almost 400 per year in Northern Territory (NT) and Western Australia (WA) to less than 10 per year in Tasmania and Australian Capital Territory. As well as the differences in number, there is a high degree of variability in the deaths
    coverage among States/Territories. Prior to 1998, only South Australia (SA), WA and NT had relatively high coverage. These States/Territory provide sufficient Indigenous deaths to attempt to produce estimates of life expectancy.
Table 1: REGISTERED INDIGENOUS DEATHS (a), Occurring During 1995-97, by State/Territory

State/Territory
Male
Female
Total

NSW
286
209
495
Vic
116
82
198
Qld (b)
522
371
893
SA
236
140
376
WA
642
448
1,090
Tas
7
2
9
NT
650
508
1,158
ACT
10
8
18
Australia (c)
2,469
1,770
4,239

(a) Registered up to 1998
(b) Only 20 deaths were registered as occurring in 1995.
(c) Includes Other Territories

  • Coverage of Indigenous persons in the Census of Population and Housing

    Indigenous people are more likely to be missed than the rest of the population by the census. The 1996 Post-Enumeration Survey (PES) estimated a net undercount of 7.1% for Indigenous persons and 1.5% for non-Indigenous persons (ABS 1998a). Taking this into account and other adjustments (ABS 1998a, p.23), the estimated resident Indigenous population at 6 August 1996 (census date) was 9.6% higher than the enumerated Indigenous population census count (i.e. 386,913 compared with 352,949, ).

  • Changing propensity to identify as Indigenous

    Changes in the propensity of an individual to identify as being of Indigenous origin in the census is an important issue in considering the Indigenous population. The difference between the 1991 and 1996 census counts of Indigenous persons, as recorded on census forms, was significantly larger than expected, despite similar collection procedures for the two censuses. The number of people counted as Indigenous (including Other Territories) increased from 265,371 in the 1991 Census to 352,970 in the 1996 Census, an increase of 33%. Just under half of this increase was explainable from demographic factors such as births, deaths and migration (Ross 1999). Much of the remaining increase can be attributed to changes in the propensity of Indigenous people to identify as Indigenous on census forms (Ross 1999, ABS 1999a).

These issues impact on the size and age-sex structure of the Indigenous population and thus on the production of Indigenous life tables.


2. ESTIMATING THE COMPLETENESS OF DEATH REGISTRATION

2.1. PRESTON-HILL METHOD

In a population where net overseas migration is zero, the following relationship exists for age cohorts measured at two different points in time:


Pc2 = Pc1 - Dc
(1)

where:
Pc1 =
the true size of the population cohort c at time 1
Pc2 =
the true size of the population cohort c at time 2
Dc =
the number of deaths occurring for population cohort c, between time 1 and time 2.

Equation (1) describes an 'ideal' situation in which the population being studied is perfectly enumerated at time 1 and at time 2, and the number of deaths occurring between these times is also perfectly enumerated. In reality, this rarely occurs. Correction factors therefore need to be incorporated to compensate for under-enumeration when population counts are taken (i.e. under-enumeration in census counts) and under-registration of intercensal deaths. The equation then becomes:

YPc2 = XPc1 - ZDc
(2)

where:
X, Y, Z =
correction factors to adjust for under-enumeration in Pc1, Pc2 and Dc

Preston and Hill (1980) outlined a method which can be used to estimate the completeness of death registration. This method can cope with changes in the completeness of enumeration and omission of deaths from the death registration system at the same time. The method uses the linear relationship shown in equation (2). If deaths were the only cause of change in the size of a cohort (i.e. no migration and no change in census coverage/identification) then a cohort which experienced a certain death rate would decrease in size by the same amount. For example, a population experiencing a 2% death rate would fall by 2% in a year. The Preston-Hill method is based on this premise. A detailed discussion of the method can be found elsewhere (Cunningham and Paradies, 2000).

The basic data input for the Preston-Hill method is:
  • enumerated population at first census
  • enumerated population at second census
  • registered deaths during intercensal period to cohort of first census.

In a closed population, where the population is accurately measured and all deaths are registered and correctly attributed to the appropriate population age group, values of the inverse survival ratio between the censuses and apparent death rate for successive cohorts will lie on a straight line. The line can be expressed as:

SR-1 = 1d + 1
(3)

where:
SR-1 =
=
inverse survival ratio between the censuses
enumerated population at the first census enumerated population at the second census
d =
=
apparent death rate at the end of the period
registered intercensal deaths enumerated population at the second census.

In line (3), the intercept is equal to the completeness of enumeration of the first census relative to that of the second (in this case 1, meaning 100% complete) and slope is equal to the completeness of enumeration of the first census relative to that of intercensal death registration (in this case 1, meaning 100% complete). The intercept slope gives the completeness of intercensal death registration relative to the completeness of enumeration of the second census.

The method does not assume that perfect recording actually exists. On the contrary, it assumes that deaths are subject to under-coverage and it attempts to estimate the magnitude using observed data. This method, however, may not work well if the actual coverage is too low.


2.2 APPLICATION OF PRESTON-HILL METHOD TO INDIGENOUS DATA


To apply the Preston-Hill method to the 1991-96 period, the number of intercensal deaths occurring for each age cohort at the 1991 Census was estimated from data on age at death. This was derived from annual deaths registered with State Registrars. For example, to estimate the number of intercensal deaths to persons aged 0 years at the 1991 Census, the following data was used as a close approximation:

Year of deathDate of occurrenceAge (years)
1991From 7 August to 31 December
    0
1992January to December
    1
1993January to December
    2
1994January to December
    3
1995January to December
    4
1996From 1 January to 6 August
    5

Similarly, the intercensal deaths to persons aged 1 year, 2 years, 3 years up to 115+ years at the 1991 Census were obtained and then grouped into conventional five-year age groups (see Table A1 in Appendix 1). The Preston-Hill method is applied to intercensal deaths using five-year age cohorts, with a line of best fit determining the relationship between the inverse survival ratio between the censuses and the apparent death rate at the end of the period.


2.2.1 Survival ratios based on census counts and ERP

Census counts based survival ratios were calculated by dividing the 1991 Census counts by the 1996 Census counts of each age-sex cohort. Similarly, ERP based survival ratios were calculated by dividing the 1991 ERP (1996 Census based) by the 1996 ERP. As discussed further in 2.2.2, survival ratios were able to be calculated for Australia, SA, WA, NT, as well as SA, WA and NT combined (Table 2). Only survival ratios for cohorts up to age 70+ years in 1991 are able to be presented, as the Indigenous estimated resident population (ERP) was only generated up to age 75+ years in 1996.

Table 2: SURVIVAL RATIO, Indigenous Males and Females, Australia and Selected States/Territories, 1991-96

Indigenous Male
Age in 1991
(years)
SA
WA
NT
SA, WA and NT combined
Australia

Census counts based
ERP based
Census counts based
ERP based
Census counts based
ERP based
Census counts based
ERP based
Census counts based
ERP based

0-4
1.22
1.00
1.09
1.00
1.11
1.00
1.12
1.00
1.21
0.99
5-9
1.08
1.00
1.08
1.00
1.03
1.00
1.06
1.00
1.21
1.00
10-14
1.05
1.00
1.00
0.99
1.02
0.99
1.01
0.99
1.09
0.99
15-19
1.08
0.98
1.01
0.98
1.09
0.98
1.05
0.98
1.09
0.98
20-24
1.14
0.97
1.05
0.97
1.04
0.97
1.06
0.97
1.09
0.97
25-29
1.12
0.97
1.03
0.96
0.97
0.97
1.02
0.97
1.12
0.96
30-34
1.04
0.96
1.07
0.95
0.98
0.95
1.03
0.95
1.12
0.95
35-39
1.10
0.94
1.04
0.94
0.94
0.94
1.01
0.94
1.14
0.94
40-44
1.03
0.93
1.03
0.92
0.99
0.92
1.01
0.92
1.12
0.92
45-49
1.00
0.89
1.02
0.89
0.99
0.89
1.00
0.89
1.09
0.89
50-54
0.85
0.85
0.91
0.85
0.81
0.85
0.86
0.85
1.00
0.85
55-59
0.80
0.81
0.80
0.80
0.87
0.80
0.83
0.80
0.98
0.80
60-64
0.78
0.75
0.83
0.75
0.78
0.76
0.80
0.75
0.90
0.75
65-69
0.64
0.70
0.68
0.68
0.64
0.69
0.66
0.68
0.75
0.68
70+
0.69
0.39
0.57
0.46
0.82
0.55
0.67
0.47
0.69
0.48


Table 2 (continued): SURVIVAL RATIO, Indigenous Males and Females, Australia and Selected States/Territories, 1991-96

Indigenous Female
Age in 1991
(years)
SA
WA
NT
SA, WA and NT combined
Australia

Census counts based
ERP based
Census counts based
ERP based
Census counts based
ERP based
Census counts based
ERP based
Census counts based
ERP based

0-4
1.17
1.00
1.13
1.00
1.09
1.00
1.12
1.00
1.21
1.00
5-9
1.11
1.00
1.14
1.00
1.00
1.00
1.08
1.00
1.22
1.00
10-14
1.10
1.00
1.00
1.00
1.07
1.00
1.04
1.00
1.13
1.00
15-19
1.14
0.99
1.11
0.99
1.18
0.99
1.14
0.99
1.16
0.99
20-24
1.09
0.98
1.08
0.98
0.97
0.98
1.03
0.98
1.13
0.98
25-29
1.14
0.97
1.08
0.98
0.98
0.98
1.05
0.98
1.15
0.98
30-34
0.98
0.97
1.11
0.97
0.98
0.97
1.03
0.97
1.15
0.97
35-39
1.06
0.96
1.04
0.96
0.99
0.96
1.02
0.96
1.13
0.96
40-44
0.97
0.95
1.01
0.94
0.99
0.94
1.00
0.94
1.12
0.94
45-49
0.71
0.92
1.09
0.92
1.00
0.92
0.97
0.92
1.11
0.92
50-54
0.89
0.90
0.94
0.88
0.97
0.89
0.94
0.89
1.04
0.89
55-59
1.01
0.85
1.02
0.84
1.06
0.84
1.04
0.84
1.07
0.84
60-64
0.90
0.78
0.91
0.78
0.75
0.79
0.84
0.78
0.95
0.79
65-69
0.90
0.73
0.81
0.74
0.83
0.72
0.83
0.73
0.88
0.73
70+
0.67
0.72
0.60
0.48
0.84
0.60
0.69
0.56
0.76
0.54


A survival ratio cannot have a value greater than 1 if the Indigenous population is perfectly enumerated in both censuses. Quite a few of the male and female census-based survival ratios are greater than 1, meaning that there were more survivors in those age cohorts in 1996 than in 1991. None of the ERP-based survival ratios are greater than 1. For this reason, ERP rather than census counts were preferred in our Preston-Hill analysis to estimate the completeness of Indigenous death registration.

ERP-based survival ratios for the 70+ age group were also considerably lower than those for other age groups. This suggests a possible bias in age reporting or higher rates of mis-identification in the older age groups, either deliberate or accidental. Because of this particular unreliability in older age groups, Preston-Hill analysis was conducted without this upper age group which otherwise lowered confidence in the regression curve.


2.2.2. Completeness of Indigenous death registration

To estimate the completeness of Indigenous death registration in Australia, the 1991 and 1996 experimental estimates of Indigenous population and all Indigenous deaths occurring (and registered) in Australia between the 1991 and 1996 Censuses were used in Preston-Hill analysis. Figure 1 shows the relationship between the inverse survival ratio (i.e. 1 survival ratio) and apparent death rate for Indigenous males and females. The method suggests that only 39.1% (= intercept slope = 0.9985 2.5519), or 2 in every 5 Indigenous male deaths occurring in Australia between the 1991 and 1996 Censuses were registered as such. The corresponding figure for Indigenous females was 39.5%. In constructing Indigenous life tables for Australia, this is the factor by which observed death rates were inflated to equal true death rates. The use of cumulated data, starting with successive initial cohorts aged 0+, 5+, 10+, and so on, produces similar coverage estimates to those presented here.

Figure 1: PRESTON-HILL CURVE, Indigenous Males and Females, Age at 1991 Census, Australia, 1991-96
Figure 1 (continued): PRESTON-HILL CURVE, Indigenous Males and Females, Age at 1991 Census, Australia, 1991-96

The same coverage factor (39.1% for males and 39.5% for females) is used across all age groups to calculate adjusted death rates. In doing so, the Preston-Hill method assumes that the completeness of census enumeration and death registration does not vary with age. This is unlikely to be the case for Indigenous population. The implications of these assumptions are discussed in this paper in 'Implications of assumptions'.

Table 3 shows the estimates of proportions of Indigenous deaths registered in Australia and its States/Territories. Because of the small number of Indigenous deaths registered as occurring during 1991-96 in Victoria, Queensland, Tasmania and Australian Capital Territory, completeness of death registration could not be calculated for these jurisdictions.

Table 3: ESTIMATES OF INDIGENOUS DEATH COVERAGE (%), Australia and States/Territories, 1991-96

State/Territory
Preston-Hill analysis (a)
Projected deaths (b)
Male
Female
Total
Total

NSW
30.0
25.8
27.4
21.1
Vic
n.a.
n.a.
n.a.
24.6
Qld
n.a.
n.a.
n.a.
5.9
SA
72.7
61.8
66.3
63.5
WA
86.3
90.2
87.8
77.1
Tas
n.a.
n.a.
n.a.
2.9
NT
90.3
94.7
92.3
84.9
ACT
n.a.
n.a.
n.a.
40.2
SA, WA and NT combined
83.8
85.1
84.8
78.0
Australia
39.1
39.5
39.1
36.1

(a) Based on deaths registered up to 1998 that occurred in the 1991-96 intercensal period.
(b) Based on deaths registered in the 1992-96 calendar years compared with deaths projected from the 1992-96 experimental Indigenous population estimates (1996 Census based).

There exists a high degree of variability in the completeness of Indigenous deaths among the States/Territories. Coverage estimates are very low for New South Wales (NSW): 30% for males and 26% for females. Because of this low coverage and the small number of deaths registered as occurred in NSW during 1995-97, no life table has been produced for NSW. SA, WA and NT had significantly higher coverage of Indigenous deaths than Australia as a whole. NT had the highest coverage (male deaths 90%, female deaths 95%), followed by WA (male deaths 86%, female deaths 90%). These estimates are obtained from Preston-Hill analysis and are used to obtain adjusted death rates.

The coverage estimates presented above are different to those presented elsewhere. In ABS (1999c), coverage estimates are calculated by dividing the number of deaths registered by the number of deaths projected from the 1996 Census-based experimental projections ('low' series). To facilitate comparison, these estimates are also shown in Table 3. The estimates derived from Preston-Hill analysis are based on registered deaths that occurred in the 1991-96 intercensal period, whereas the estimates obtained using registered and projected deaths are based on 1992-96 death registrations. The coverage estimates based on the projected deaths are somewhat lower than those obtained from the Preston-Hill analysis (Table 3). This is because projected deaths were derived using mortality levels based on 1991-96 Indigenous life tables, which produced lower mortality than the experimental 1995-97 life tables.


3. INDIGENOUS ABRIDGED LIFE TABLES

Abridged life tables are generally constructed in preference to complete life tables when reliable age-specific death rates are not available by single years of age. Reliable single year age-specific deaths rates are not available for the Indigenous population. However, abridged life tables are generally sufficient for most purposes of demographic analysis.

In constructing 1995-97 experimental Indigenous abridged life tables, mortality rates based on 1995-97 data were used. Mortality rates were calculated by dividing the average annual number of deaths occurring during 1995-97 by the experimental Indigenous ERP at June 1996. Deaths were averaged over this three-year period to smooth out the irregularities from year to year in the number of deaths, bearing in mind the relatively small number of Indigenous deaths in many areas and age groups. Deaths were centred on the 1996 mid-year population estimate, which was based on 1996 Census counts. A general discussion of life tables, various functions and details of mortality calculations are given in the Appendix 2.

Five separate life tables have been produced: one for Australia; one each for SA, WA and NT; and another for SA, WA and NT combined. The all-Australia life table was produced by using all Indigenous deaths that had been registered up to 1998 that occurred in Australia during 1995-97. Each State/Territory life table was based on deaths that occurred to residents of that particular jurisdiction. The SA, WA and NT combined life table used deaths that occurred to residents of these three jurisdictions combined. All these life tables are presented in Appendix 4.

Table 4 presents the observed and adjusted life expectancies for Australia, SA, WA, NT and SA, WA and NT combined. The observed life expectancies are based on the actual number of deaths which are not adjusted for undercoverage. There is undercoverage of Indigenous deaths to some degree in all States/Territories. As a result, the observed life expectancies are over-estimates of the true life expectancies. The adjusted life expectancies, on the other hand, are based on the number of deaths which are obtained after inflating the observed number of deaths by the Preston-Hill under-coverage factor and hence are expected to be closer to reality than the observed life expectancies.

Table 4: OBSERVED AND EXPECTED INDIGENOUS LIFE EXPECTANCY AT BIRTH, 1995-97

Male
Female
State/Territory
Observed
Adjusted
Observed
Adjusted

SA
59.8
55.3
68.1
62.8
WA
59.7
57.7
65.5
64.4
NT
57.8
56.4
63.2
62.5
SA, WA and NT combined
59.0
56.5
64.8
63.0
Australia
66.4
54.1
70.8
61.3


At the national level, the adjusted life expectancy at birth in the period 1995-97 was estimated to be about 54 years for Indigenous males and 61 years for Indigenous females. SA and NT have similar adjusted life expectancies for both sexes. The life expectancies for WA are only slightly higher than those for SA and NT. Australian life expectancy estimates are lower than these State-specific estimates. Male life expectancy based on SA, WA and NT combined data is 3 years higher than that of the national estimate. The female life expectancy of these three States/Territory combined, on the other hand, is only 1 year higher than that of the national estimate. These combined estimates, as based on data of the States/Territory with the best coverage, are thought to be more reliable than the national estimates.

Indigenous males experience higher mortality than Indigenous females at all ages of life (Figure 2). Both male and female mortality rates commence with relatively high infant mortality. The rate falls rapidly to its lowest between ages 5-9: the chance of dying at these ages is lower than at any other age. The gap between male and female mortality is greatest in the young adult ages (15-24 years), with males more prone to accidental deaths and suicide.

Figure 2: MORTALITY RATES, Indigenous Males and Females, Australia, 1995-97



There are marked mortality differences between Indigenous Australians and total Australians (Figure 3). Total Australian males and females experience significantly lower mortality than their Indigenous counterparts at all ages of life. Both total and Indigenous male mortality show a steep rise during the teenage years, primarily associated with motor vehicle accidents and suicide.

Figure 3: MORTALITY RATES, Indigenous and Total Population, Males and Females, Australia, 1995-97



Figure 3 (continued): MORTALITY RATES, Indigenous and Total Population, Males and Females,
Australia, 1995-97





3.1 COMPARISON BETWEEN 1991-96 AND 1995-97 EXPERIMENTAL LIFE TABLES

At the national level, the life expectancy at birth of Indigenous males in 1995-97 was estimated to be 54.1 years (Table 4). This compares to the life expectancy of Indigenous males of 56.9 years previously estimated for 1991-96 (ABS 1999c), a decrease of 2.8 years (Table 5). The life expectancy at birth of Indigenous females in the 1995-97 period was estimated to be 61.3 years, 0.3 years less than that in 1991-96. What is the reason for the apparent decrease in Indigenous life expectancy? It could be due to improved recording of Indigenous deaths, particularly male deaths, including the introduction of a question on Indigenous status on Queensland death registration forms in 1996. It could also be due to the differences in methodology used. In estimating the completeness of Indigenous death registration, Indigenous ERP has been used for 1995-97 whereas the 1991-96 life table used Indigenous census counts. For these reasons, comparison of life expectancy estimates presented in this paper with estimates from other sources should only be undertaken with extreme caution. The lower life expectancy at birth in 1995-97 than in 1991-96 does not necessarily mean that the Indigenous mortality has declined during this period.

Table 5: MORTALITY RATES, Indigenous Males and Females, Australia, 1991-96 and 1995-97

Male qx
Female qx
Age
(years)
1991-96
1995-97
% change
1991-96
1995-97
% change

0
0.0257
0.0347
-0.90
0.0228
0.0318
-0.9000
1
0.0057
0.0055
0.02
0.0041
0.0044
-0.0300
5
0.0021
0.0032
-0.10
0.0016
0.0017
0.0000
10
0.0029
0.0042
-0.12
0.0021
0.0031
-0.1000
15
0.0128
0.0152
-0.25
0.0083
0.0045
0.3900
20
0.0239
0.0270
-0.31
0.0154
0.0072
0.8200
25
0.0323
0.0348
-0.25
0.0207
0.0124
0.8300
30
0.0411
0.0457
-0.46
0.0267
0.0198
0.6900
35
0.0528
0.0600
-0.72
0.0357
0.0284
0.7300
40
0.0699
0.0850
-1.51
0.0497
0.0437
0.6000
45
0.0945
0.1005
-0.60
0.0703
0.0591
1.1200
50
0.1283
0.1366
-0.82
0.0991
0.0938
0.5300
55
0.1726
0.1955
-2.29
0.1369
0.1354
0.1600
60
0.2277
0.2692
-4.14
0.1840
0.2052
-2.1100
65
0.2931
0.3510
-5.79
0.2399
0.2535
-1.3700
70
0.3671
0.4133
-4.62
0.3032
0.3322
-2.9000
75+
1.0000
1.0000
0.00
1.0000
1.0000
0.0000
Life expectancy at birth (years)
56.9
54.1
-2.8
61.7
61.3
0.4


In general, Indigenous male mortality is higher in the experimental 1995-97 life tables than in 1991-96 for all age groups (Table 5 and Figure 4). Conversely, Indigenous female mortality is lower for most age groups in the 1995-97 life table. The degree of change, however, varies with age. The greatest percentage change is observed in ages 20-54 years.

Figure 4: MORTALITY RATES, Indigenous Males and Females, Australia, 1991-96 and 1995-97



Figure 4 (continued): MORTALITY RATES, Indigenous Males and Females, Australia, 1991-96 and 1995-97



Both male and female life expectancy estimates in the period 1995-97 based on SA, WA and NT combined data are higher than the national estimates (Table 4). This result is inconsistent with that of a previous investigation where separate Indigenous experimental life tables for western (SA, WA and NT combined) and eastern (rest of the five States/Territories combined) parts of Australia have been produced. Although the life tables themselves have not been published, the resulting estimates of life expectancy at birth have been published (ABS, 1999a; Cunningham and Paradies, 2000) and reported that in 1991-96, the combined estimates of the three western States/Territories are lower than the Australian estimates. This inconsistency could also be due to the reasons mentioned above.


4. COMPARISON BETWEEN INDIGENOUS AND NON-INDIGENOUS POPULATION

4.1 LIFE EXPECTANCY

The life expectancy at birth for the Indigenous population differs greatly from that of the total Australian population. Indigenous males in 1995-97 are expected to live 54 years, around 21.5 years less than life expectancy for total males (75.7 years), while Indigenous females are expected to live 61 years, around 20 years less than the life expectancy for total females (81.4 years). The difference in life expectancy between Indigenous and total Australian populations, stems from the difference in age-specific death rates between the Indigenous and non-Indigenous populations.

4.2 STANDARDISED DEATH RATES

Death is strongly related to age. The age structure of the Indigenous population is very different to that of the non-Indigenous population. At June 1996, Australia's Indigenous population had a median age of 20 years, about 14 years younger than that of the total population (ABS 1998a). To compare the death rates of these vastly different populations, it is important to take this age difference into account. One way of adjusting for differences in age distributions is to calculate standardised death rates.

Standardised death rates for Indigenous and non-Indigenous males and females (Table 6) are calculated by deriving age-specific death rates and applying these to a standard population. The June 1991 total Australian ERP is used here as the standard population.

Table 6: CRUDE AND STANDARDISED DEATH RATES, Indigenous and
Non-Indigenous Males and Females, 1995-97

Death rate
Indigenous
Non-Indigenous
Male
Female
Male
Female

Crude (a)
4.32
3.02
7.47
6.63
Standardised (b)
10.33
7.16
7.94
5.25

(a) Number of deaths per 1,000 population.
(b) The crude death rate that would have prevailed if the total Australian estimated resident population at June 1991 had experienced at each age-sex the death rates of the respective Indigenous/non-Indigenous population.

Crude death rates for Indigenous males and females are much lower than for non-Indigenous males and females. This reflects the younger age structure of the Indigenous population. Standardised death rates, on the other hand, are higher for Indigenous males and females. The reason for higher standardised death rates for Indigenous people is that their age-specific death rates are higher than for their non-Indigenous counterparts at all ages (see Table A3 in Appendix 3). This is further support for the Indigenous population having lower life expectancy (at all ages) than the non-Indigenous population.

4.3 MEDIAN AGE AT DEATH

Half of the population dying are younger than the median age at death (and half are older). Median age at death represents another measure of relative mortality. A population with high life expectancy would be expected to have higher median age at death than another population with lower life expectancy, other factors being equal.

The non-Indigenous population has a markedly higher median age at death than the Indigenous population (Table 7). In 1998, a difference of over 26 years was observed between the median age at death of the Indigenous and non-Indigenous population. Females die older than males, on average. Over the period 1991-98, there was some fluctuation in median age at death. Median age at death for Indigenous males was 0.5 year higher in 1995-97 than in 1991-96. It might be affected by the improved recording of Indigenous male deaths. The median age at death for Indigenous females, however, declined 0.4 year between these two overlapping periods. For the non-Indigenous population, it increased from 76.6 years in 1991-96 to 77.1 years in 1995-97.


Table 7: MEDIAN AGE AT DEATH (YEARS), By Indigenous Status, Sex and Year of Registration,
Australia, 1991-98

Year
Period
Indigenous Status by Sex
1991
1992
1993
1994
1995
1996
1997
1998
1991-96
1995-97

Indigenous males
46.2
49.7
47.7
48.3
48.6
47.9
49.8
47.7
48.4
48.9
Indigenous females
55.5
56.8
57.4
59.7
57.6
57.7
56.8
57.0
57.6
57.2
Indigenous persons
49.7
52.8
51.9
52.5
52.3
52.0
52.4
51.3
52.4
52.3
Non-Indigenous males
72.3
72.7
73.0
73.6
73.6
74.2
74.4
74.7
73.5
74.1
Non-Indigenous females
78.9
79.4
79.6
80.2
80.4
80.8
81.1
81.2
80.1
80.8
Non-Indigenous persons
75.5
76.0
76.2
76.7
76.8
77.2
77.4
77.6
76.6
77.1
Total males
72.2
72.6
72.9
73.5
73.5
74.0
74.2
74.5
73.5
74.1
Total females
78.8
79.3
79.5
80.2
80.3
80.7
81.0
81.0
80.1
80.8
Total persons
75.4
75.9
76.1
76.6
76.6
77.0
77.2
77.4
76.6
77.1


There is a high degree of variability in the Indigenous median age at death among the States/Territories (Table 8). SA, WA and NT have the best coverage and consistently highest registrations of Indigenous deaths, so their median ages are likely to be more reliable than for other States/Territories. The relative median age at death in each State/Territory is consistent with the relative estimated life expectancy (Table 4) in each State/Territory. That means that if the median age at death of a State/Territory is high (low), its life expectancy is also high (low). For instance, among SA, WA and NT, WA has the highest median age at death (Table 8) and also the highest life expectancy at birth (Table 4). This is true for both males and females.

Table 8: MEDIAN AGE AT DEATH (YEARS), Indigenous Population, By Sex, Period of Registration and State/Territory, 1991-97

Male
Female
Total
State/Territory
1991-96
1995-97
1991-96
1995-97
1991-96
1995-97

NSW
48.4
48.8
59.1
59.4
52.8
53.9
Vic
47.3
48.7
60.0
64.7
52.3
56.3
Qld
49.3
50.3
59.0
58.2
53.2
53.4
SA
45.8
47.0
52.7
52.8
49.0
49.6
WA
50.3
48.8
60.1
58.3
54.9
53.0
Tas
49.5
38.8
37.5
65.0
49.0
49.5
NT
48.0
48.5
55.1
53.8
50.6
50.5
ACT
47.5
50.0
73.0
54.0
50.5
50.0
SA, WA and NT combined
48.5
48.4
57.2
55.4
52.2
51.2
Australia
48.4
48.9
57.6
57.2
52.4
52.3



5. IMPLICATIONS OF ASSUMPTIONS

This paper carried out an investigation into the production of Indigenous life tables for 1995-97 using a demographic technique outlined by Preston and Hill (1980). The Preston-Hill method is based on a number of assumptions including a closed population; that the completeness of enumeration and death registration are both constant across age; correct reporting of age in censuses and death registrations; and stable mortality during the intercensal period. The implications of these assumptions are discussed below.
  • Migration

Census data indicate that the in-migration rate of the Indigenous people is very low (ABS 1998b). The out-migration rate can be assumed to be similarly very low. The experimental Indigenous population projections assumed nil overseas migration (ABS 1998b). Although the levels of net interstate movement are more significant, interstate migration during 1991-97 should not significantly influence the results of this Preston-Hill analysis.
  • Changing propensity to identify as Indigenous

The issue of changes in the propensity of an individual to identify as being of Indigenous origin in the census deserves attention. The calculation of the completeness of coverage of Indigenous deaths by the Preston-Hill method assumes that the observed count at the 1996 Census is complete, which means that changes between 1991 and 1996 in the propensity of people to identify as Indigenous on census forms are taken into account.
  • Completeness of enumeration

The Preston-Hill method assumes that the completeness of enumeration does not vary with age. This is unlikely to be the case for the Indigenous population, given the experience of census under-enumeration. In the 1996 Census, young adult males among the Australian population had the highest undercount rate, with 4.3% for males aged 20-24 and 3.7% for males aged 25-29 compared with 1.6% average across the total Australian population (ABS 1997a). Such age-specific undercount rates were not available for the Indigenous population, but when estimating the experimental Indigenous population it was assumed that the enumeration of Indigenous population also varied considerably with age.

For simplicity in the Preston-Hill method, it is assumed that both the 1991 and 1996 Censuses had the same pattern of under-enumeration. In other words, the age pattern of undercount is assumed to be the same in 1991 and 1996. In that case, both the numerator and denominator of the inverse survival ratio, which is used in this analysis to estimate the coverage of death registration, will be subject to equal proportionate errors. The estimates of the proportion of deaths registered obtained using Preston-Hill analysis and hence the life expectancy estimates will therefore remain unchanged.
  • Coverage of death registration

The method also assumes that the coverage of death registration is the same across all ages. Following this assumption, the same coverage factor (0.391 for males and 0.395 for females) is used across all age groups to obtain adjusted death rates. This is unlikely to apply to the Indigenous population. Will the resultant life expectancy estimates be changed substantially if differential coverage factors are used? To examine this, some differential coverage factors are presented in Table 9.

Scenario 1 represents the undercoverage factors used in the 1995-97 draft experimental life table for Australia (Table A4 in Appendix 4).

In Scenario 2, for example, the male coverage factor for age groups 0-19 and 60+ years has been increased from 0.39 to 0.59. But coverage for age group 20-59 years has been decreased from 0.39 to 0.31 to offset the increase in the other age groups. This keeps the total number of deaths roughly the same and the overall coverage rate at about 0.39. Scenarios 3 and 4 represent alternative differential age inflation factors. The three broad age groups have been arbitrarily chosen, although they do approximate young dependents (0-19 years), the main working ages (20-59 years) and older dependents (60+ years). It could be argued that dependent age groups may or may not be more likely to be identified as Indigenous when they die.

Table 9: EFFECT OF DIFFERENTIAL COVERAGE ON LIFE EXPECTANCY, Indigenous Males and Females, Australia, 1995-97

Male Coverage
Age groups/Life expectancy
Scenario 1
Scenario 2
Scenario 3
Scenario 4
Scenario 5
Scenario 6

Total
0.39
0.39
0.39
0.39
0.45
0.50
0-19
0.39
0.59
0.79
0.28
0.45
0.50
20-59
0.39
0.31
0.27
0.59
0.45
0.50
60+
0.39
0.59
0.79
0.28
0.45
0.50
Life expectancy at birth (years)
54.1
53.4
52.9
55.2
56.2
57.7


Table 9 (continued): EFFECT OF DIFFERENTIAL COVERAGE ON LIFE EXPECTANCY, Indigenous Males and Females, Australia, 1995-97

Female Coverage
Age groups/Life expectancy
Scenario 1
Scenario 2
Scenario 3
Scenario 4
Scenario 5
Scenario 6

Total
0.39
0.39
0.39
0.39
0.45
0.50
0-19
0.39
0.59
0.79
0.32
0.45
0.50
20-59
0.39
0.27
0.23
0.59
0.45
0.50
60+
0.39
0.59
0.79
0.32
0.45
0.50
Life expectancy at birth (years)
61.3
60.8
60.3
62.7
63.4
64.6


This sensitivity analysis show that life expectancy would be lower by 1.2 year for males and 1.0 years for females if the coverage among the youngest and oldest age groups was increased by 40% (i.e. from Scenario 1 to Scenario 3), with an offsetting decrease in coverage in the middle age group. This suggests that even if the actual coverage of Indigenous deaths is substantially different from those used here, it is unlikely to have a major impact on life expectancy.
  • 1991-96 coverage compared with 1995-97 coverage

The analysis presented in this paper also assumes that the 1995-97 Indigenous deaths coverage is the same as the 1991-96 coverage. This is probably not true for the Indigenous population. For example, coverage estimates in ABS (1999c) suggest that 1997 death coverage is higher than 1996 coverage. Scenarios 5 and 6 (Table 9) illustrate the effect of increasing overall death coverage from 0.39 to 0.45 and 0.50, respectively. If death coverage is higher, then the adjustment needed to registered deaths is smaller. If the Indigenous death coverage was as high as 0.50 in 1995-97, male life expectancy at birth would be higher by 3.6 years (from 54.1 years in Scenario 1 to 57.7 years in Scenario 6) and female life expectancy by 3.3 years (from 61.3 years in Scenario 1 to 64.6 years in Scenario 6).
  • Correct reporting of age

Correct reporting of age is important to ensure that both population and deaths are correctly included in the appropriate age cohort. A systematic overstatement of age in censuses or in death registrations will result in an overestimate of the completeness of death registrations (Preston and Hill 1980). To minimise the effect of age overstatement, the fitting of Preston-Hill curves was conducted by excluding ages 70+.
  • Stable mortality during the intercensal period

The assumption that there are insignificant changes in mortality during the intercensal period is reasonable, but it is impossible to differentiate and quantify changes in mortality over time from improvement in the level of Indigenous identification (in both death registration and census enumeration).


6. CONCLUSION

The life expectancy estimates presented in this paper are described as experimental because of the nature of the base population, which is affected by the intercensal volatility in the counts of the Indigenous population, and deficiencies in deaths and births registration data. Consequently, there is uncertainty about the accuracy of death rates which use census counts or census-based population estimates as their denominator. The life expectancy estimates are therefore sensitive to the inputs used and over-precise analysis is cautioned. They should be used only as an indicative summary measure of the level of mortality of the Indigenous population.


REFERENCES

ABS, 1997a, Information Paper, Census of Population and Housing: Data Quality - Undercount, 1996, ABS Cat. No. 2940.0, Canberra.

ABS, 1997b, Population Distribution, Indigenous Australians, ABS Cat. No. 4705.0, Canberra.

ABS, 1998a, Experimental Estimates of the Aboriginal and Torres Straight Islander Population, Australia 1998, ABS Cat. No. 3230.0, Canberra.

ABS, 1998b, Experimental Projections, Aboriginal and Torres Strait Islander Population, ABS Cat. No. 3231.0, Canberra.

ABS, 1999a, The Health and Welfare of Australia's Aboriginal and Torres Straight Islander Peoples, ABS Cat. No. 4704.0, AIHW Cat. No. IHW 3, Canberra.

ABS, 1999b, Births, Australia 1998, ABS Cat. No. 3301.0, Canberra.

ABS, 1999c, Deaths, Australia 1998, ABS Cat. No. 3302.0, Canberra.

Australian Government Actuary, 1999, Australian Life Tables 1995-97, Canberra.

Cunningham J and Paradies Y, 2000, Occasional Paper, Mortality of Aboriginal and Torres Straight Islander Australians, 1997, ABS Cat. No. 3315.0, Canberra.

Preston S H and Hill K J, 1980, "Estimating the completeness of death registration", Population Studies, Vol. 34, pp. 349-66.

Ross K, 1999, Occasional Paper, Population Issues, Indigenous Australians, 1996, ABS Cat. No. 4708.0, Canberra.

Shyrock H S and Siegel J S, 1971, The Methods and Materials of Demography, US Bureau of the Census, Washington DC.


APPENDIX 1: INDIGENOUS CENSUS COUNTS AND DEATHS, 1991-96

Table A1: INDIGENOUS CENSUS COUNTS AND REGISTERED DEATHS, 1991-96 (a),
by Age at Census and Sex, Australia

Cohort size at 1991 Census
Cohort size at 1996 Census
Intercensal deaths to cohort
Age at 1991 Census
(years)
Age at 1996 Census
(years)
Male
Female
Male
Female
Male
Female

0-4
5-9
20,219
19,199
24,490
23,136
65
48
5-9
10-14
17,881
17,205
21,590
20,921
26
15
10-14
15-19
15,918
15,140
17,339
17,110
61
24
15-19
20-24
14,661
14,235
15,908
16,583
135
44
20-24
25-29
13,191
14,167
14,314
15,949
187
68
25-29
30-34
11,062
11,987
12,350
13,820
223
85
30-34
35-39
9,424
10,210
10,587
11,775
206
126
35-39
40-44
7,504
8,249
8,537
9,344
243
152
40-44
45-49
6,006
6,500
6,736
7,276
234
133
45-49
50-54
4,433
4,521
4,832
5,000
278
162
50-54
55-59
3,363
3,612
3,350
3,774
257
188
55-59
60-64
2,594
2,763
2,536
2,951
269
271
60-64
65-69
1,889
2,289
1,700
2,180
269
235
65-69
70-74
1,351
1,505
1,009
1,323
196
207
70-74
75-79
833
996
601
795
175
205
75-79
80-84
460
608
294
498
123
148
80-84
85-89
212
361
157
242
87
115
85-89
90-94
117
168
66
88
42
54
90+
95+
79
114
59
79
33
49
Total, 0+
Total, 5+
131,197
133,829
146,455
152,844
3,109
2,329


(a) Registered up to 1998 that occurred in the 1991-96 intercensal period.


APPENDIX 2: THE LIFE TABLE

INTRODUCTION

A life table is a useful demographic tool for combining and summarising mortality rates of a population at different ages into a single statistical model. In its simplest form, a life table is generated from age-specific mortality rates and the resulting values are used to measure mortality, survivorship and life expectancy.

The life table describes the mortality experience of a hypothetical group of new born babies throughout their entire lifetime. It is based on the assumption that this group is subject to the age-specific mortality rates of the reference period. Typically this hypothetical group is 100,000 in size. A life table population is therefore the population which would exist if the age-specific death rates prevailing at some particular time were to continue throughout the life span of all the individuals, with no change in the number of births each year and no migration.

Life tables may be complete or abridged, depending on the age interval used in their compilation. Complete life tables contain data for single years of age, while abridged life tables usually contain data for five-year age groups.

Life expectancy refers to the average number of additional years a person of a given age and sex might expect to live if the age-specific death rates of the given period continued through their lifetime. The life expectancy at birth is used as an index of the level of mortality prevailing in a community in a given period. It represents the average number of years a new born baby could expect to live if the mortality rates of today were to continue through that baby's life.

LIFE TABLE FUNCTIONS

Abridged life tables for the Indigenous population contain the following life table functions:
    nmx = Adjusted age-specific mortality rate for persons aged x to x + n;
    nqx = Proportion of persons dying between exact age x and exact age x + n;
    lx = Number of persons surviving at exact age x;
    ndx = Number of deaths between exact age x and exact age x + n;
    nLx = Number of persons-years lived during the interval age x to age x + n;
    Tx = Total number of person-years that would be lived after exact age x; and
    ex = Complete expectation of life at exact age x.

The principal step in life table construction is one of calculating age-specific mortality rates or probability of dying. Below is a discussion of how mortality rates at different ages are calculated.

CALCULATION OF INFANT MORTALITY (1q0)

The infant mortality rate is usually defined as the number of infant deaths per 1,000 live births in a particular year. However, this rate is not a true probability as the denominator (births during the year) does not represent the initial population 'exposed to risk' (Shyrock and Siegel). Some infant deaths occurring during any given year will be to infants born in the previous year. Therefore, in calculating infant mortality rate, appropriate separation factors are used to relate deaths occurred in a given year to infants born in the same year. Table A2 illustrates the calculation of infant mortality rates for Indigenous males and females for the period 1995-97

Table A2: CALCULATION OF INFANT MORTALITY RATE, Indigenous Males and Females, Australia, 1995-97

Indigenous male
1994
1995
1996
1997
Average
1995-97

Births (By)
3261
3458
4874
4885
Infant deaths (Dy )
D"
D'
D"
D'
D"
D'
D"
D'
4
34
6
39
12
54
12
53
Separation factors
f"
f'
f"
f'
f"
f'
0.133
0.867
0.182
0.818
0.185
0.815
Unadjusted infant mortality rate
13.11
14.30
13.31
13.57
Adjusted infant mortality rate (1)
13.57/0.391
=34.71


Table A2 (continued): CALCULATION OF INFANT MORTALITY RATE,
Indigenous Males and Females, Australia, 1995-97

Indigenous female
1994
1995
1996
1997
Average
1995-97

Births (By)
3057
3304
4575
4712
Infant deaths (Dy)
D"
D'
D"
D'
D"
D'
D"
D'
7
39
8
36
7
47
6
50
Separation factors
f"
f'
f"
f'
f"
f'
0.182
0.818
0.130
0.870
0.107
0.893
Unadjusted infant mortality rate
13.50
12.24
11.92
12.55
Adjusted infant mortality rate (1)
12.55/0.395
=31.80

(1) Based on the estimated proportion of Indigenous deaths registered obtained from Preston-Hill analysis (0.395 for males and 0.391 for females).

where:
    Dy = the registered number of deaths occurring in year y
    By = the registered number of births occurring in year y
    By-1 = the registered number of births occurring in year y-1
    D'y = the registered number of deaths occurring in year y to births in year y
    D"y= the registered number of deaths occurring in year y to births in year y-1
    f' = the proportion of deaths occurring in year y to births in year y
    f" = the proportion of deaths occurring in year y to births in year y-1

Value of nqx for infants (1q0) were calculated using the following equation:

1q0 = Dy / (f'By + f"By-1)
(5)

The 1q0 obtained in equation (5) was then divided by the estimate of proportions of deaths registered derived from Preston-Hill analysis.

The calculation of infant mortality rate can be better explained by the following example. For y = 1996 we have from Table A2:

By =
4,874
Dy =
D'y + D"y = 54 + 12 = 66
By-1 =
3,458
f' =
D'y / (D'y + D"y) = 54/(54 + 12) = 0.815
f" =
1 - f' = 0.185

Therefore the infant mortality rate for Indigenous males for the year 1996 was calculated as 1000* Dy / (f'By + f"By-1) = 14.30. The corresponding figures for 1995 and 1997 were 13.11 and 13.31 respectively giving an average infant mortality rate of 13.57 for the period 1995-97. The average infant mortality rate was then divided by the proportion of deaths registered according to Preston-Hill analysis to get an adjusted rate.

The estimates of adjusted infant mortality rates were found to be 35 per 1,000 live births for Indigenous males and 32 per 1,000 live births for Indigenous females.

ESTIMATION OF MORTALITY AT AGES 1-74

Mortality rates (nqx values) for persons aged 1-74 were derived from central death rates (nmx values). These nmx values were calculated for the period 1995-97 using the following equation:

nmx =( nDx95 + nDx96 + nDx97)/(3 * nPxC)
(6)
Where:nmx = the central death rate for persons aged x to x + n
nDx = registered deaths occurring during the year to persons aged x to x + n
nPx = the estimated Indigenous population at 30 June 1996

The nmx values were then divided by the estimated proportions of deaths registered obtained from Preston-Hill analysis to derive the adjusted nmx values.

nqx values were derived from adjusted nmx values as follows:

nqx = n * nmx/(1 + (n/2 * nmx))
(7)

ESTIMATION OF MORTALITY AT AGES 75+

Since all persons aged 75 and over will die while still within this age group, the probability of dying after age 75 is 1.

ESTIMATION OF lx, nLx, Tx AND e0x

The value for l0 (the radix) is set at 100,000. Remaining values of lx are calculated as:

lx+1 = lx (1 - nqx)
(8)

nLx, Tx and ex are calculated using the following equations:

nLx = n/2 (lx + lx+n)
(9)
(10)
e0x = Tx/lx
(11)

APPENDIX 3: AGE-SPECIFIC DEATH RATES, 1995-97

Table A3: AGE-SPECIFIC DEATH RATES (per 1,000 population), By Indigenous Status and Sex, 1995-97

Indigenous (a)
Non-Indigenous (b)
Age
(years)
Male
Female
Male
Female

0
10.76
9.25
5.91
4.78
1-4
0.54
0.43
0.38
0.27
5-9
0.25
0.13
0.16
0.13
10-14
0.33
0.25
0.20
0.15
15-19
1.20
0.35
0.80
0.33
20-24
2.14
0.57
1.22
0.38
25-29
2.77
0.98
1.22
0.41
30-34
3.66
1.58
1.35
0.54
35-39
4.84
2.28
1.49
0.70
40-44
6.95
3.52
1.86
1.04
45-49
8.28
4.80
2.59
1.61
50-54
11.47
7.77
9.38
2.74
55-59
16.96
11.46
7.20
4.31
60-64
24.34
18.04
13.04
6.95
65-69
33.32
22.92
21.62
11.43
70-74
40.77
31.44
35.91
19.27
75+
69.82
56.39
91.00
70.88

(a) Based on Indigenous deaths registered up to 1998 that occurred in 1995-97 and experimental Indigenous estimated resident population at 30 June 1996.
(b) Based on non-Indigenous deaths registered up to 1998 that occurred in 1995-97 and total Australian estimated resident population less experimental Indigenous estimated resident population at 30 June 1996.



APPENDIX 4: DRAFT EXPERIMENTAL ABRIDGED LIFE TABLES, 1995-97
Table A4: DRAFT EXPERIMENTAL ABRIDGED LIFE TABLE, Indigenous Males and Females, Australia, 1995-97

Age
(years)
Indigenous Male
nmx
nqx
lx
nLx
Tx
e0x

0-1
0.02749
0.03469
100,000
98,265
5,410,059
54.10
1-4
0.00137
0.00546
96,531
385,070
5,311,794
55.03
5-9
0.00063
0.00316
96,004
479,260
4,926,724
51.32
10-14
0.00083
0.00415
95,700
477,509
4,447,464
46.47
15-19
0.00307
0.01524
95,303
472,886
3,969,955
41.66
20-24
0.00548
0.02701
93,851
462,919
3,497,070
37.26
25-29
0.00709
0.03482
91,316
448,633
3,034,151
33.23
30-34
0.00936
0.04571
88,137
430,611
2,585,518
29.34
35-39
0.01237
0.05999
84,108
407,924
2,154,907
25.62
40-44
0.01776
0.08501
79,062
378,508
1,746,982
22.10
45-49
0.02117
0.10051
72,341
343,529
1,368,474
18.92
50-54
0.02932
0.13657
65,070
303,135
1,024,946
15.75
55-59
0.04334
0.19554
56,184
253,454
721,810
12.85
60-64
0.06220
0.26915
45,198
195,577
468,356
10.36
65-69
0.08515
0.35101
33,033
136,177
272,779
8.26
70-74
0.10419
0.41330
21,438
85,039
136,602
6.37
75 and over
0.17845
1.00000
12,578
51,563
51,563
4.10

    nmx = Adjusted age-specific death rate for persons aged x to x + n
    nqx = Proportion of persons dying between exact age x and exact age x + n
    lx = Number of persons surviving at exact age x
    nLx = Number of persons-years lived during the interval age x to age x + n
    Tx = Total number of person-years that would be lived after exact age x
    e0x = Complete expectation of life at exact age x

Table A4 (continued): DRAFT EXPERIMENTAL ABRIDGED LIFE TABLE,
Indigenous Males and Females, Australia, 1995-97

Age
(years)
Indigenous Female
nmx
nqx
lx
nLx
Tx
e0x

0-1
0.02135
0.03182
100,000
98,409
6,181,369
61.25
1-4
0.00101
0.00405
96,818
386,490
6,082,960
62.25
5-9
0.00030
0.00149
96,427
481,773
5,696,470
58.51
10-14
0.00059
0.00295
96,283
480,704
5,214,696
53.61
15-19
0.00085
0.00424
95,999
478,975
4,733,992
48.77
20-24
0.00141
0.00702
95,591
476,280
4,255,017
43.97
25-29
0.00239
0.01190
94,921
471,778
3,778,737
39.28
30-34
0.00367
0.01816
93,791
464,695
3,306,959
34.74
35-39
0.00551
0.02717
92,087
454,183
2,842,264
30.39
40-44
0.00835
0.04089
89,586
438,770
2,388,081
26.20
45-49
0.01153
0.05603
85,922
417,575
1,949,311
22.29
50-54
0.01921
0.09167
81,108
386,951
1,531,735
18.53
55-59
0.02801
0.13090
73,673
344,255
1,144,784
15.19
60-64
0.04259
0.19244
64,029
289,342
800,529
12.17
65-69
0.05526
0.24274
51,707
227,158
511,187
9.67
70-74
0.07448
0.31394
39,156
165,048
284,029
7.11
75 and over
0.14290
1.00000
26,863
118,982
118,982
4.40


Table A5: DRAFT EXPERIMENTAL ABRIDGED LIFE TABLE,
Indigenous Males and Females, South Australia, 1995-97

Age
(years)
Indigenous Male
nmx
nqx
lx
nLx
Tx
e0x

0-1
0.01855
0.02058
100,000
98,971
5,524,762
55.25
1-4
0.00150
0.00598
97,942
390,596
5,425,791
55.40
5-9
0.00059
0.00296
97,356
486,059
5,035,195
51.72
10-14
0.00035
0.00177
97,068
484,908
4,549,136
46.87
15-19
0.00671
0.03300
96,896
476,484
4,064,228
41.94
20-24
0.00499
0.02466
93,698
462,714
3,587,744
38.29
25-29
0.00854
0.04179
91,387
447,390
3,125,030
34.20
30-34
0.00943
0.04608
87,569
427,754
2,677,640
30.58
35-39
0.01139
0.05535
83,533
406,106
2,249,886
26.93
40-44
0.01240
0.06014
78,909
382,682
1,843,781
23.37
45-49
0.01620
0.07782
74,163
356,388
1,461,099
19.70
50-54
0.02545
0.11964
68,392
321,504
1,104,710
16.15
55-59
0.04288
0.19362
60,210
271,904
783,207
13.01
60-64
0.06994
0.29764
48,552
206,631
511,303
10.53
65-69
0.07278
0.30788
34,101
144,256
304,672
8.93
70-74
0.08688
0.35688
23,602
96,951
160,416
6.80
75 and over
0.12543
1.00000
15,179
63,466
63,466
4.18


Table A5 (continued): DRAFT EXPERIMENTAL ABRIDGED LIFE TABLE,
Indigenous Males and Females, South Australia, 1995-97

Age
(years)
Indigenous Female
nmx
nqx
lx
nLx
Tx
e0x

0-1
0.01551
0.01843
100,000
99,079
6,279,094
62.79
1-4
0.00179
0.00715
98,157
391,226
6,180,015
62.96
5-9
0.00000
0.00000
97,456
487,278
5,788,789
59.40
10-14
0.00000
0.00000
97,456
487,278
5,301,511
54.40
15-19
0.00051
0.00253
97,456
486,662
4,814,232
49.40
20-24
0.00000
0.00000
97,209
486,045
4,327,571
44.52
25-29
0.00410
0.02030
97,209
481,111
3,841,526
39.52
30-34
0.00229
0.01138
95,235
473,468
3,360,415
35.29
35-39
0.01085
0.05280
94,152
458,332
2,886,947
30.66
40-44
0.01138
0.05531
89,181
433,572
2,428,615
27.23
45-49
0.01512
0.07287
84,248
405,894
1,995,043
23.68
50-54
0.02501
0.11768
78,109
367,567
1,589,149
20.35
55-59
0.02305
0.10898
68,918
325,811
1,221,582
17.73
60-64
0.02758
0.12903
61,407
287,226
895,771
14.59
65-69
0.03909
0.17805
53,484
243,612
608,545
11.38
70-74
0.03909
0.17805
43,961
200,237
364,933
8.30
75 and over
0.11290
1.00000
36,134
164,695
164,695
4.56


Table A6: DRAFT EXPERIMENTAL ABRIDGED LIFE TABLE,
Indigenous Males and Females, Western Australia, 1995-97

Age
(years)
Indigenous Male
nmx
nqx
lx
nLx
Tx
e0x

0-1
0.02287
0.02510
100,000
98,745
5,770,763
57.71
1-4
0.00149
0.00595
97,490
388,799
5,672,018
58.18
5-9
0.00066
0.00331
96,910
483,746
5,283,219
54.52
10-14
0.00114
0.00571
96,589
481,566
4,799,473
49.69
15-19
0.00154
0.00766
96,037
478,348
4,317,908
44.96
20-24
0.00307
0.01521
95,302
472,886
3,839,559
40.29
25-29
0.00455
0.02250
93,852
463,983
3,366,674
35.87
30-34
0.00780
0.03825
91,741
449,932
2,902,691
31.64
35-39
0.01048
0.05108
88,232
429,894
2,452,759
27.80
40-44
0.01692
0.08114
83,725
401,642
2,022,866
24.16
45-49
0.01891
0.09030
76,931
367,290
1,621,224
21.07
50-54
0.02144
0.10173
69,985
332,125
1,253,933
17.92
55-59
0.03123
0.14484
62,865
291,563
921,808
14.66
60-64
0.05389
0.23746
53,760
236,885
630,246
11.72
65-69
0.05711
0.24986
40,994
179,363
393,361
9.60
70-74
0.08329
0.34468
30,751
127,258
213,997
6.96
75 and over
0.14050
1.00000
20,152
86,740
86,740
4.30


Table A6 (continued): DRAFT EXPERIMENTAL ABRIDGED LIFE TABLE,
Indigenous Males and Females, Western Australia, 1995-97

Age
(years)
Indigenous Female
nmx
nqx
lx
nLx
Tx
e0x

0-1
0.01862
0.02139
100,000
98,931
6,435,675
64.36
1-4
0.00063
0.00250
97,861
390,957
6,336,744
64.75
5-9
0.00019
0.00095
97,617
487,853
5,945,788
60.91
10-14
0.00032
0.00162
97,524
487,224
5,457,935
55.97
15-19
0.00054
0.00272
97,366
486,167
4,970,711
51.05
20-24
0.00181
0.00902
97,101
483,316
4,484,543
46.18
25-29
0.00125
0.00624
96,225
479,627
4,001,227
41.58
30-34
0.00243
0.01210
95,625
475,234
3,521,600
36.83
35-39
0.00432
0.02137
94,468
467,294
3,046,366
32.25
40-44
0.00839
0.04108
92,449
452,753
2,579,072
27.90
45-49
0.00806
0.03949
88,652
434,507
2,126,319
23.99
50-54
0.01594
0.07666
85,151
409,436
1,691,812
19.87
55-59
0.02626
0.12320
78,623
368,901
1,282,376
16.31
60-64
0.03886
0.17710
68,937
314,163
913,476
13.25
65-69
0.04829
0.21545
56,728
253,086
599,313
10.56
70-74
0.05673
0.24843
44,506
194,889
346,227
7.78
75 and over
0.09208
1.00000
33,449
151,338
151,338
4.52


Table A7: DRAFT EXPERIMENTAL ABRIDGED LIFE TABLE,
Indigenous Males and Females, Northern Territory, 1995-97

Age
(years)
Indigenous Male
nmx
nqx
lx
nLx
Tx
e0x

0-1
0.02151
0.02277
100,000
98,861
5,642,916
56.43
1-4
0.00116
0.00462
97,723
389,989
5,544,055
56.73
5-9
0.00063
0.00313
97,272
485,596
5,154,066
52.99
10-14
0.00048
0.00238
96,967
484,259
4,668,470
48.14
15-19
0.00174
0.00868
96,737
481,583
4,184,211
43.25
20-24
0.00485
0.02395
95,897
473,743
3,702,628
38.61
25-29
0.00538
0.02652
93,600
461,795
3,228,885
34.50
30-34
0.00835
0.04087
91,118
446,278
2,767,090
30.37
35-39
0.01248
0.06049
87,393
423,751
2,320,812
26.56
40-44
0.01390
0.06716
82,107
396,748
1,897,061
23.10
45-49
0.02432
0.11462
76,592
361,014
1,500,313
19.59
50-54
0.02670
0.12516
67,813
317,846
1,139,300
16.80
55-59
0.03624
0.16616
59,325
271,982
821,454
13.85
60-64
0.06426
0.27681
49,468
213,105
549,471
11.11
65-69
0.06551
0.28145
35,774
153,700
336,367
9.40
70-74
0.07535
0.31704
25,706
108,153
182,667
7.11
75 and over
0.10890
1.00000
17,556
74,514
74,514
4.24


Table A7 (continued): DRAFT EXPERIMENTAL ABRIDGED LIFE TABLE,
Indigenous Males and Females, Northern Territory, 1995-97

Age
(years)
Indigenous Female
nmx
nqx
lx
nLx
Tx
e0x

0-1
0.02220
0.02330
100,000
98,835
6,254,314
62.54
1-4
0.00159
0.00635
97,670
389,442
6,155,479
63.02
5-9
0.00022
0.00111
97,051
484,984
5,766,037
59.41
10-14
0.00082
0.00408
96,943
483,727
5,281,052
54.48
15-19
0.00053
0.00265
96,548
482,099
4,797,326
49.69
20-24
0.00063
0.00316
96,292
480,699
4,315,227
44.81
25-29
0.00258
0.01279
95,988
476,868
3,834,528
39.95
30-34
0.00408
0.02020
94,760
469,012
3,357,660
35.43
35-39
0.00631
0.03108
92,845
457,012
2,888,648
31.11
40-44
0.00850
0.04163
89,960
440,435
2,431,636
27.03
45-49
0.01433
0.06917
86,214
416,162
1,991,202
23.10
50-54
0.02024
0.09633
80,251
381,926
1,575,039
19.63
55-59
0.02147
0.10188
72,520
344,128
1,193,113
16.45
60-64
0.03597
0.16502
65,131
298,787
848,985
13.03
65-69
0.05317
0.23466
54,384
240,013
550,198
10.12
70-74
0.06771
0.28955
41,622
177,980
310,184
7.45
75 and over
0.09854
1.00000
29,570
132,204
132,204
4.47


Table A8: DRAFT EXPERIMENTAL ABRIDGED LIFE TABLE, Indigenous Males and Females, South Australia, Western Australia and Northern Territory Combined, 1995-97

Age
(years)
Indigenous Male
nmx
nqx
lx
nLx
Tx
e0x

0-1
0.02211
0.02398
100,000
98,801
5,650,673
56.51
1-4
0.00138
0.00550
97,602
389,331
5,551,872
56.88
5-9
0.00065
0.00325
97,064
484,532
5,162,541
53.19
10-14
0.00077
0.00383
96,748
482,816
4,678,009
48.35
15-19
0.00237
0.01178
96,378
479,051
4,195,193
43.53
20-24
0.00423
0.02091
95,242
471,234
3,716,142
39.02
25-29
0.00559
0.02756
93,251
459,830
3,244,908
34.80
30-34
0.00842
0.04123
90,681
444,057
2,785,078
30.71
35-39
0.01164
0.05657
86,942
422,414
2,341,021
26.93
40-44
0.01519
0.07316
82,023
395,115
1,918,608
23.39
45-49
0.02119
0.10061
76,023
360,992
1,523,493
20.04
50-54
0.02482
0.11685
68,374
321,897
1,162,501
17.00
55-59
0.03573
0.16400
60,385
277,167
840,603
13.92
60-64
0.06212
0.26885
50,482
218,481
563,436
11.16
65-69
0.06380
0.27512
36,910
159,164
344,956
9.35
70-74
0.08229
0.34125
26,756
110,952
185,791
6.94
75 and over
0.12813
1.00000
17,625
74,839
74,839
4.25


Table A8 (continued): DRAFT EXPERIMENTAL ABRIDGED LIFE TABLE, Indigenous Males and Females, South Australia, Western Australia and Northern Territory Combined, 1995-97

Age
(years)
Indigenous Female
nmx
nqx
lx
nLx
Tx
e0x

0-1
0.02014
0.02378
100,000
98,811
6,298,375
62.98
1-4
0.00121
0.00482
97,622
389,547
6,199,564
63.51
5-9
0.00018
0.00092
97,152
485,535
5,810,018
59.80
10-14
0.00051
0.00253
97,063
484,700
5,324,482
54.86
15-19
0.00055
0.00273
96,817
483,425
4,839,782
49.99
20-24
0.00108
0.00540
96,553
481,460
4,356,358
45.12
25-29
0.00222
0.01104
96,031
477,506
3,874,898
40.35
30-34
0.00316
0.01568
94,971
471,134
3,397,391
35.77
35-39
0.00610
0.03004
93,482
460,392
2,926,258
31.30
40-44
0.00900
0.04403
90,674
443,390
2,465,866
27.19
45-49
0.01199
0.05819
86,682
420,798
2,022,476
23.33
50-54
0.01941
0.09258
81,637
389,292
1,601,678
19.62
55-59
0.02427
0.11443
74,079
349,205
1,212,386
16.37
60-64
0.03742
0.17109
65,603
299,953
863,181
13.16
65-69
0.05021
0.22305
54,379
241,571
563,228
10.36
70-74
0.06203
0.26849
42,250
182,889
321,658
7.61
75 and over
0.09929
1.00000
30,906
138,769
138,769
4.49



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