APPENDIX A: CALCULATING ADJUSTED LINKAGE RATES

In order to produce indicative linkage rates that take account of death registrations for which there was no equivalent Census record, a Census undercount factor was applied to death registrations. This factor was based on the ratio between Census count and Estimated Resident Population (ERP) and applied by Indigenous status, age group, sex and state/territory (where Tasmania and the ACT were combined due to the small number of deaths). The result was an estimate of the (maximum) number of links that could be expected from the death registration data.

A number of adjustments are made to the Census count to produce ERP by Indigenous status. These are informed by the results of the Census Post Enumeration Survey conducted about six weeks after the Census and includes:

• an adjustment for net undercount, a component for mis-classification of Indigenous status
• an adjustment for Australian residents temporarily overseas at the time of the Census (RTOs)
• an adjustment for imputation of Indigenous status where it is not stated in the Census (both item and unit non-response). 'Item non response' refers to people for whom a Census form was returned but Indigenous status was not stated. 'Unit non-response' refers to Census records imputed for people in households that were identified as occupied at the time of collection but from whom no Census form was returned.

For more information, see Census of Population and Housing: Details of Undercount, August 2011 (cat no. 2940.0.) and Australian Demographic Statistics, September 2012 (cat. no. 3101.0).

For this project, two minor modifications were made to the ERP prior to calculating the linkage adjustment factor. Both of these slightly decrease the magnitude of the linkage adjustment factor from what it would otherwise have been based on the actual ERP.

First, for total deaths, the RTO adjustment was removed from the ERP. That is, it was assumed that, on balance, people temporarily overseas at the time of the Census were unlikely to be represented in the death registration data. While there may well have been a small number of instances in which this actually occurred, it was assumed that the full RTO component would overstate the level of adjustment required.

An additional modification was made to the ERP when the ratio was applied to deaths by Indigenous status. The number of imputed Census records for which Indigenous status was not stated (item non-response only) was removed from the ERP. A not stated category for Indigenous status is included in both death registration and Census data but not the ERP. Therefore, the ratio of Census to ERP by Indigenous status may overstate the amount of undercount in death registrations if the imputation for item non-response were not removed.

The expected number of links from the death registration data was calculated as follows:


The adjusted linkage rate is then calculated as the number of links as a proportion of expected links:


Note that this method assumes that the Census undercount rates (by Indigenous status, age group, sex and state of residence) for the general population are the same as for the population who died in the period 10 August 2011 to 27 September 2012.

As expected, the adjustments to death registration data were broadly aligned with estimates of Census undercount. Based on the results of the Post Enumeration Survey, the 2011 Census net undercount was estimated at 17.2% for the Aboriginal and Torres Strait Islander population and 6.2% for non-Indigenous persons. Comparable figures for the increase of actual death registrations over expected links were 10.5% for Aboriginal and Torres Strait Islander deaths and 3.3% for non-Indigenous deaths. Differences between the two sets of figures relate both to the minor modification to the ERP used for the adjustment factors, and the different population structure for death registrations compared with the total population.

	Aboriginal and Torres Strait Islander	Non-Indigenous	Total(a)
2011 PES population estimate(b)	662 335	21 216 926	21 879 261
2011 Census count	548 147	19 898 127	(c)21 504 721
Difference (no.)	114 188	1 318 799	374 540
Difference – Census undercount (%)	17.2	6.2	1.7
Death Registrations	2 345	150 238	153 455
Expected links	2 099	145 248	150 266
Difference (no.)	246	4 990	3 189
Difference (%)	10.5	3.3	2.1

(a) Includes death registrations that did not state an Indigenous status.
(b) Population as estimated by the Post Enumeration Survey (PES) as of Census night (9^th of August 2011).
(c) Includes imputed persons in non-responding dwellings.



While the calculation of adjusted linkage rates performed here is similar to the method used in 2006, other assumptions could be made about the likelihood of death registrations lacking a corresponding Census record. The ABS is undertaking further research to examine the effects of differential reporting of Indigenous status on raw and adjusted linkage rates.