Life Tables for Aboriginal and Torres Strait Islander Australians methodology

This appendix describes the basis for estimating the sample error of estimates of Aboriginal and Torres Strait Islander life expectancy at birth and for assessing the sensitivity of this life expectancy to assumptions made when calculating it. Broadly, a process of replication was used where the inputs to the Aboriginal and Torres Strait Islander life expectancy calculations were replicated based on sample error information obtained from the Post Enumeration Survey (PES) and on plausible deviations from the assumptions. Variation between the replicate estimates of Aboriginal and Torres Strait Islander life expectancy corresponding to replicate estimates from PES gave estimates of the sample error of life expectancy and the additional variation from deviations from the assumptions measured the sensitivity of the method to the assumptions.

The immediate inputs to Aboriginal and Torres Strait Islander life expectancy are:

• Aboriginal and Torres Strait Islander estimated resident population (ERP) at 30 June 2016 (mid-point of the period from 2015 to 2017) by five-year age groups; and
• Average number of Aboriginal and Torres Strait Islander deaths over the period from 2015 to 2017, adjusted for differences in reporting Indigenous status.
   

The method of calculating Aboriginal and Torres Strait Islander ERP is described in Estimates of Aboriginal and Torres Strait Islander Australians, June 2016. The method of adjusting Aboriginal and Torres Strait Islander deaths for differential identification is given in Data linkage to derive Aboriginal and Torres Strait Islander deaths identification rates.

The inputs to the calculation of Aboriginal and Torres Strait Islander ERP are:

• Census counts at fine levels;
• estimates of total population (both Aboriginal and Torres Strait Islander and non-Indigenous) at intermediate levels; and
• estimates of Aboriginal and Torres Strait Islander population at broad levels.
   

The main input for adjusted Aboriginal and Torres Strait Islander deaths are Aboriginal and Torres Strait Islander deaths registered in 2015, 2016 2017, modified using the Aboriginal and Torres Strait Islander deaths identification rate. This adjusts the Indigenous status of death registrations to correspond to the Indigenous status in ERP, which is as reported in PES. The identification rate is calculated from a probabilistic linking of death registrations between 9 August 2016 and 28 September 2017 to the 2016 Census and from PES data.

Other inputs are:

• number of deaths in linked records reported as Aboriginal and Torres Strait Islander in death registrations, by age groups, state/territory and remoteness, and
• number of deaths in linked records by Census Indigenous status, by state/territory and age groups;
   

From these inputs, the following propensities were calculated:

• propensity of being Aboriginal and Torres Strait Islander in PES given Census Indigenous status is 'Aboriginal and Torres Strait Islander', by state/territory and age groups; and
• propensities of being Aboriginal and Torres Strait Islander in PES given Census Indigenous status is 'non-Indigenous' and 'not stated' by age groups.
   

Estimates of the total and Aboriginal and Torres Strait Islander populations incorporate components of PES undercount adjustment and the propensities are calculated from PES, and so the sample error in PES generates sample error in Aboriginal and Torres Strait Islander life expectancy. Standard errors (SEs) were calculated by replication of PES inputs, based on estimated PES sampling error.

Note that PES data are weighted to estimate the propensities but unweighted data were used to illustrate the methodology in Data linkage to derive Aboriginal and Torres Strait Islander deaths identification rates.

In calculating and applying the identification rate the following assumptions were made:

• identification rates for unlinked deaths were assumed to be the same as those for linked deaths;
• identification rates for the period from 2015 to 2017 were assumed to be the same as those observed for August 2016 to September 2017;
• identification rates were assumed to apply uniformly across sex and within each broad age group;
• propensities for Aboriginal and Torres Strait Islander identification in the Census and PES were assumed to be applicable to death registrations, in spite of the different age distributions and method of collection; and
• Census/PES non-Indigenous and not stated propensities for Australia were assumed to apply uniformly across states/territories.
   

There was no direct information on possible deviation from the first two assumptions, but deviations within plus or minus five percentage points of identification rate for each state were used for the first assumption, and within plus or minus two percentage points for each sex and state for the second assumption. Data from the linked file and PES were analysed to give ranges of deviations in identification rates for the last three assumptions.

The 95% confidence intervals for Aboriginal and Torres Strait Islander life expectancy at birth estimates from the sensitivity analysis and sample error are given in Table 1, Table 2 and Table 3 below.

The 95% confidence intervals for Aboriginal and Torres Strait Islander death identification rates from the sensitivity analysis and sample error are given in Table 4, Table 5 and Table 6 below.

In Life Tables for Aboriginal and Torres Strait Islander Australians, 2010-2012 the ABS presented four alternative approaches for adjusting deaths data as an input to compilation of life tables. While not the best method each of these approaches does provide useful insights into the official method and adds particular value. These four methods have been included for the period from 2015 to 2017.

The four alternative approaches for which illustrative estimates were produced were

1. using deaths identified as Aboriginal and Torres Strait Islander in death registrations without any adjustment;
2. using deaths identified as Aboriginal and Torres Strait Islander in either the Census or death registrations in the CDE linked data only;
3. using deaths identified as Aboriginal and Torres Strait Islander in either the Census or death registrations in the CDE linked and unlinked data; and
4. using Aboriginal and Torres Strait Islander identification based on the 2016 Census.

The first approach shows what life expectancy would have been if no adjustment was made for the underidentification of Indigenous status in deaths registration data.

The second and third approaches are provided here as approaches that were explored by the ABS for the periods from 2005 to 2007 and 2010 to 2012 estimates but were considered to be unsuitable for estimating Aboriginal and Torres Strait Islander mortality. The main reason for this is that the identification of Indigenous status in the numerator (deaths) and the denominator (population estimates) are not consistent with each other, thus introducing bias to life expectancy estimates.

The fourth approach was also explored by the ABS, but the resultant life expectancy at birth estimates were considerably higher than the other estimates and not considered to be plausible.

A brief discussion of each of the different approaches and the results obtained are presented below.

This method produces life expectancy estimates based on no adjustment made to the number of Aboriginal and Torres Strait Islander deaths to account for underidentification. This shows that no adjustment to the number of deaths leads to higher life expectancy for New South Wales and Western Australia, and slightly lower life expectancy for Queensland and the Northern Territory females.

For the 2005 to 2007 and 2010 to 2012 estimates, ABS explored an option to derive identification rates for Aboriginal and Torres Strait Islander deaths and life expectancy estimates using the CDE linked data only.

This approach uses a concept of Indigenous status which is different from that used for the denominator for death rates; that is, population estimates where Indigenous status is as reported in PES only but not augmented by other sources of information. In calculating life expectancy estimates, it is important to ensure that the classification of records as Aboriginal and Torres Strait Islander occurs in a consistent manner in the numerator (deaths) and the denominator (population estimates) as different population scopes feed directly into bias in death rates.

This approach, like the previous approach, is based on Aboriginal and Torres Strait Islander deaths identified in either the Census or death registrations, but uses the Aboriginal and Torres Strait Islander deaths identified in the CDE linked file plus those Aboriginal and Torres Strait Islander deaths which were unable to be linked to a Census record.

Like the previous approach, this approach also produces life expectancy estimates which are biased as the identification of Indigenous status in the numerator and the denominator are inconsistent.

The CDE linked dataset can be used to derive direct estimates of mortality of the Aboriginal and Torres Strait Islander population counted in the 2016 Census. The method of estimation involves a three stage process. Firstly, people who identified themselves as Aboriginal and Torres Strait Islander in the 2016 Census were selected from the Census. Secondly, only those death records for which Indigenous status was reported as Aboriginal and Torres Strait Islander in the Census were taken from the linked file. Thirdly, age-specific death rates were calculated by dividing the Aboriginal and Torres Strait Islander deaths by the Aboriginal and Torres Strait Islander Census counts. These rates were then used to derive Aboriginal and Torres Strait Islander life tables. No adjustments were made to the death rates to account for potential undercoverage of deaths, hence the method is referred to as 'direct'.

This approach was intended to make Aboriginal and Torres Strait Islander counts for deaths and for the population at risk (that is, Aboriginal and Torres Strait Islander usual residents of Australians) consistent. However, this is not the case. Due to undercount in Census a proportion of death records could not be linked, as there was no corresponding Census record to link with. Such people are removed from the counts of deaths and from the counts of the population at risk. However, people whose information from death registrations or Census is not accurate enough to make a link are not included in the death counts, but it is not possible to remove from the Census count the corresponding count of people with unlinkable information in Census or what would have been unlinkable information from death registrations, had they died.

The life tables in this release are based on the average number of Aboriginal and Torres Strait Islander deaths registered in 2015, 2016 and 2017 adjusted for under/over identification of Indigenous Status in registrations.

Death registrations are collected in the form of administrative data from the Registrars of Births, Deaths and Marriages in each state/territory. For all states and territories, death registration forms (DRFs) use a standard question to elicit information about a person's Aboriginal and Torres Strait Islander origin. The death of a person is recorded as Aboriginal, Torres Strait Islander or both on the Death Registration Form (DRF). From 2007, Indigenous status for deaths registered in South Australia, Western Australia, Tasmania, the Northern Territory and the Australian Capital Territory was also derived from the Medical Certificate of Cause of Death (MCCD). The Queensland Registry of Births, Deaths and Marriages introduced the MCCD in 2015.

The population used in this release is the final Aboriginal and Torres Strait Islander population estimates for 30 June 2016 based on the 2016 Census. For information on the method of calculating the Aboriginal and Torres Strait Islander estimated resident population, see: Technical Note 1 - Estimated Resident Aboriginal and Torres Strait Islander Population - Method of calculation in the publication: Estimates of Aboriginal and Torres Strait Islander Australians, June 2016.

The number of deaths (occurred or registered) during the calendar year, at a specified age, per 1,000 of the estimated resident population of the same age at the mid-point of the year (30 June). Pro rata adjustment is made in respect of deaths for which the age of the deceased is not given.

The complete enumeration of a population or groups at a point in time with respect to well-defined characteristics (e.g. Population, Manufacturing, etc.). In this release the word "Census" refers to the ABS Census of Population and Housing.

A confidence interval is a range of values that is used to describe the uncertainty around an estimate, usually from a sample survey. Confidence intervals describe how different the estimate could have been if a different sample was selected from the population. Confidence intervals are calculated with a stated probability (commonly 95%). This means that there is a 95% chance that the true population value will lie within the particular range.

The permanent disappearance of all evidence of life after birth has taken place. The definition excludes deaths prior to live birth. For the purposes of the ABS Death Registration collection, a death refers to any death which occurs in, or en route to Australia and is registered with a state or territory Registry of Births, Deaths and Marriages.

The official measure of the population of Australia is based on the concept of usual residence. It refers to all people, regardless of nationality, citizenship or legal status, who usually live in Australia, with the exception of foreign diplomatic personnel and their families. It includes usual residents who are overseas for less than 12 months over a 16 month period. It excludes overseas visitors who are in Australia for less than 12 months over a 16 month period.

Estimates of the Australian resident population are generated on a quarterly basis by adding natural increase (the excess of births over deaths) and net overseas migration (NOM) occurring during the period to the population at the beginning of each period.

The ratio of observed to expected deaths.

A statistical process for predicting values where no response was provided to a question and a response could not be derived.

The Index of Relative Socio-Economic Disadvantage (IRSD) used in this release was developed by the ABS and ranks areas in Australia according to most disadvantaged to least disadvantaged using variables from the 2016 Census of Population and Housing. A low score on this index indicates a high proportion of relatively disadvantaged people in an area. It cannot be concluded that an area with a very high score has a large proportion of relatively advantaged people, as there are no variables in the index to indicate this.

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 each period continued throughout his/her lifetime.

A tabular, numeric representation of mortality and survivorship of a cohort of births at each age of life. The conventional life table is based on the assumption that as the cohort passes through life it experiences mortality at each age in accordance with a predetermined pattern of mortality rates which do not change from year to year. The life table this is a hypothetical model of mortality, and even though it is usually based upon death rates from a real population during a particular period of time, it does not describe the real mortality which characterises a cohort as it ages.

Life tables may be complete or abridged, depending on the age interval used in their compilation. Complete life tables such as those for the Australian population contain data by single years of age, while abridged life tables, such as those for the Aboriginal and Torres Strait Islander population, contain data for five-year age groups. Due to differences in mortality patterns between males and females at different ages, life tables are generally constructed separately for each sex.

Excess of births over deaths.

The difference between the actual Census count (including imputations) and an estimate of the number of people who should have been counted in the Census. This estimate is based on the Post Enumeration Survey (PES) conducted after each Census. For a category of person (e.g. based on age, sex and state of usual residence), net undercount is the resultant of Census undercount, overcount, misclassification and imputation error.

Error which arises from inaccuracies in collecting, recording and processing the data. Every effort is made to minimise non-sampling error by the careful design of questionnaires, intensive training and supervision of interviewers, and efficient data processing procedures. Non-sampling error also arises because information cannot be obtained from all people selected in the collection.

Following the 1992 amendments to the Acts Interpretation Act to include the Indian Ocean Territories of Christmas Island and the Cocos (Keeling) Islands as part of geographic Australia, another category of the state and territory level has been created, known as Other Territories. Other Territories include Norfolk Island, Jervis Bay, Christmas Island, and the Cocos (Keeling) Islands.

A household survey conducted three to four weeks after the Census. The PES allows the ABS to estimate the number of people who should have been counted in the Census compared to the number who were. Results from the PES contribute to a more accurate calculation of the estimated resident population (ERP) for Australia and the states and territories which is then backdated to 30 June of the Census year.

Error which occurs because a sample, rather than the entire population, is surveyed. One measure of the likely difference resulting from not including all dwellings in the survey is given by the standard error.

Socio-Economic Indexes for Areas (SEIFA) is a product developed by the ABS that ranks areas in Australia according to relative socio-economic advantage and disadvantage. The indexes are based on information from the five-yearly Census.

SEIFA 2016 is the latest version of this product and consists of four indexes:

• The Index of Relative Socio-Economic Disadvantage (IRSD)
• The Index of Relative Socio-Economic Advantage and Disadvantage (IRSAD)
• The Index of Education and Occupation (IEO)
• The Index of Economic Resources (IER). 

Each index is a summary of a different subset of Census variables and focuses on a different aspect of socio-economic advantage and disadvantage.

A measure of the spread of the difference between the Census value and an estimate. There are about two chances in three that a sample estimate will differ by less than one standard error from the figure that would have been obtained from a Census, and about nineteen chances in twenty that the difference will be less than two standard errors.

The intercensal growth in the Indigenous population counts that cannot be fully explained by births, deaths and migration.

The year the death occurred.

The year the death was registered.

Australian Bureau of Statistics, Census of Population and Housing - Details of Undercount, 2016, ABS, Canberra.

Australian Bureau of Statistics, Census of Population and Housing: Understanding the Increase in Aboriginal and Torres Strait islander Counts, 2016, ABS, Canberra.

Australian Bureau of Statistics, Births, Australia, ABS, Canberra.

Australian Bureau of Statistics, Deaths, Australia, ABS, Canberra.

Australian Bureau of Statistics, Estimates and Projections, Aboriginal and Torres Strait Islander Australians, 2001 to 2026, ABS, Canberra.

Australian Bureau of Statistics, Estimates of Aboriginal and Torres Strait Islander Australians, Jun 2016, ABS, Canberra.

Australian Bureau of Statistics, Information Paper: Death registrations to Census linkage project - Key Findings for Aboriginal and Torres Strait Islander peoples, 2011-2012, ABS, Canberra

Australian Bureau of Statistics, Population Projections, Australia, 2017 to 2066, ABS, Canberra.

Australian Bureau of Statistics and the Australian Institute of Health and Welfare, The Health and Welfare of Australia's Aboriginal and Torres Strait Islander Peoples, ABS, Canberra.

Australian Institute of Health and Welfare 2017, Trends in Indigenous mortality and life expectancy, 2001-2015: evidence from the Enhanced Mortality Database, Cat. no. IHW 174, Canberra, AIHW.

Council of Australian Governments, Closing the gap in Indigenous disadvantage, http://www.coag.gov.au/closing_the_gap_in_indigenous_disadvantage

Shyrock H, Siegel J and Associates (1976), The Methods and Materials of Demography, Condensed Edition, Academic Press, New York

Statistics Canada 2015, Life expectancy, at birth and at age 65, by sex, five-year average, Canada and Inuit regions. http://www.statcan.gc.ca