APPENDIX 1 CONFIDENCE INTERVALS
ESTIMATING SAMPLE ERROR
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 2011 by 5-year age groups; and
- Aboriginal and Torres Strait Islander deaths for 2010-2012 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, Jun 2011 (cat. no. 3238.0.55.001). The method of adjusting Aboriginal and Torres Strait Islander deaths for differential identification is given in
Chapter 3: 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 during 2010-2012, 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 August 2011 and September 2012 to the 2011 Census and from PES data. The inputs are:
- number of deaths in linked records reported as Aboriginal and Torres Strait Islander in death registrations, by state/territory and age groups;
- number of deaths in linked records by Census Indigenous status, by state/territory and age groups;
- 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
Chapter 3: Data linkage to derive Aboriginal and Torres Strait Islander deaths identification rates.
ESTIMATING SENSITIVITY ERROR
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 2010-2012 were assumed to be the same as those observed for August 2011 to September 2012;
- 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
- 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.
RESULTS
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 A1.1 and Table A1.2 below.
A1.1 CONFIDENCE INTERVALS FOR ABORIGINAL AND TORRES STRAIT ISLANDER LIFE EXPECTANCY AT BIRTH - 2010-2012 |
|
 | | | 95% CONFIDENCE INTERVALS |
| | Life expectancy at birth | Sensitivity error(a) | Sample error |
| State/territory | years | years | years |
|
| Males | | | |
| NSW | 70.5 | 69.0-72.0 | 69.8-71.2 |
| Qld | 68.7 | 67.3-70.1 | 68.0-69.4 |
| WA | 65.0 | 63.4-66.6 | 64.1-65.9 |
| NT | 63.4 | 61.3-65.5 | 62.4-64.4 |
| Aust.(b)(c) | 67.4 | 66.1-68.7 | 67.1-67.7 |
| Headline Aust.(c)(d) | 69.1 | 67.8-70.4 | 68.8-69.4 |
| Females | | | |
| NSW | 74.6 | 73.3-75.9 | 74.0-75.2 |
| Qld | 74.4 | 73.2-75.6 | 73.9-74.9 |
| WA | 70.2 | 68.8-71.6 | 69.4-71.0 |
| NT | 68.7 | 66.8-70.6 | 67.8-69.6 |
| Aust.(b)(c) | 72.3 | 71.2-73.4 | 72.0-72.6 |
| Headline Aust.(c)(d) | 73.7 | 72.5-74.9 | 73.4-74.0 |
|
| (a) Sensitivity to assumptions, includes sample error. |
| (b) These estimates are not the headline estimates for Australia, because they are calculated without an age-adjustment, but are provided to enable effective comparison with the state and territory, and remoteness area estimates. |
| (c) Includes all states and territories. |
| (d) Headline estimates for Australia are calculated using an improved methodology (taking into account age-specific identification rates) that could not be applied at the state and territory or remoteness area levels. Therefore this data should not be compared with data for any state or territory, or remoteness area. |
A1.2 CONFIDENCE INTERVALS FOR ABORIGINAL AND TORRES STRAIT ISLANDER LIFE EXPECTANCY AT BIRTH, Remoteness Areas - 2010-2012 |
|
| | | 95% CONFIDENCE INTERVALS |
| | Life expectancy at birth | Sensitivity error(a) | Sample error |
| Remoteness Area | years | years | years |
|
| Males | | | |
| Major Cities and Inner Regional | 68.0 | 67.1-68.9 | 67.7-68.3 |
| Outer Regional, Remote and Very Remote | 67.3 | 66.2-68.4 | 66.9-67.7 |
| Females | | | |
| Major Cities and Inner Regional | 73.1 | 72.2-74.0 | 72.8-73.4 |
| Outer Regional, Remote and Very Remote | 72.3 | 71.3-73.3 | 72.0-72.6 |
|
| (a) Sensitivity to assumptions, includes sample error. |
The 95% confidence intervals for Aboriginal and Torres Strait Islander deaths identification rates from the sensitivity analysis and sample error are given in Table A1.3 below. These are the final estimates of the confidence intervals and replace the preliminary estimates published on 15 November 2013.
These errors are produced during the process of calculating the errors for life expectancy, but because the sensitivity errors are applied at a finer level than the sample errors, the process for aggregating them to state level was slightly different.
A1.3 CONFIDENCE INTERVALS FOR ABORIGINAL AND TORRES STRAIT ISLANDER DEATHS IDENTIFICATION RATES - 2010-2012 |
|
| | 95% CONFIDENCE INTERVALS |
| Identification rate | Sensitivity error(a) | Sample error |
| State/territory | no. | no. | no. |
|
| NSW | 0.70 | 0.59-0.81 | 0.64-0.76 |
| Qld | 0.80 | 0.69-0.91 | 0.74-0.86 |
| WA | 0.88 | 0.75-1.01 | 0.82-0.94 |
| NT | 1.04 | 0.99-1.09 | 1.03-1.05 |
| Aust.(b)(c) | 0.72 | 0.63-0.81 | 0.67-0.77 |
| Headline Aust.(c)(d)(e) | 0.82 | 0.71-0.93 | 0.76-0.88 |
|
| (a) Sensitivity to assumptions. Includes sample error. |
| (b) These estimates are not the headline estimates for Australia, because they are calculated without an age-adjustment, but are provided to enable effective comparison with the state and territory, and remoteness area estimates. |
| (c) Includes all states and territories. |
| (d) Headline estimates for Australia are calculated using an improved methodology (taking into account age-specific identification rates) that could not be applied at the state and territory or remoteness area levels. Therefore this data should not be compared with data for any state or territory, or remoteness area. |
| (e) This identification rate is included for comparison purposes only. Refer to table 3.5 for age-specific identification rates. |
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