TECHNICAL NOTE CONFIDENCE INTERVALS FOR INDIGENOUS CHILD MORTALITY RATES
INTRODUCTION
1 In 2008 there were 1,200 infant deaths (deaths of children less than one year of age) and 230 deaths of children aged 14 years, comprising 0.9% and 0.2% of all deaths in Australia respectively. Disaggregation of these data to more detailed levels  in particular, by Indigenous status and state/territory of usual residence  will necessarily lead to smaller numbers.
2 As a result of such numbers, derived mortality rates may have high levels of uncertainty associated with them. This Technical Note illustrates levels of uncertainty for infant and child (14 years) mortality rates for 20062008, by state/territory, sex and Indigenous status of the child, through the calculation of confidence intervals.
VARIABILITY IN DEATH RATES
3 Death rates in this publication are based on the mortality experience of an entire population, rather than from a sample. As there is no sampling error associated with this data, it might be considered that standard errors are not relevant to the question of variability in death rates.
4 However, observed death rates are commonly treated as estimates of an underlying death rate that gives the probability of death for individuals in a population. This presupposes a statistical model in which each person is subject to some risk of dying over a given period, and whether each person in fact dies is a random event. Considered in this sense, the underlying death rates are unknown, and the observed death rates measure them with some sampling error.
5 The standard errors used to derive confidence intervals presented in this Technical Note are calculated to measure the extent of such random variations in numbers of deaths, using the methods described in Chiang (1984).
INFANT MORTALITY RATES
6 Infant mortality rates (IMRs) by Indigenous status and state/territory of usual residence for 20062008 are presented in the following graph (for males and females combined).
Infant mortality rates  20062008
7 Confidence intervals associated with nonIndigenous IMRs are relatively small, apart from in the Northern Territory.
8 For Indigenous IMRs the range is larger, especially for the Northern Territory and South Australia, for which confidence intervals for males and females combined range from 10.316.9 infant deaths per 1,000 live births and 3.39.5 infant deaths per 1,000 live births respectively. Rates for males and females separately show wider ranges (see table below).
Infant mortality rates, 20062008 

    95% confidence intervals 
  Infant deaths  Infant mortality rate(a)  Lower limit  Upper limit 
INDIGENOUS 

Males     
 NSW  48  8.3  6.0  10.6 
 Qld  53  8.4  6.2  10.7 
 SA  9  6.8  2.4  11.2 
 WA  37  11.5  7.8  15.2 
 NT  37  15.1  10.3  19.9 
Females     
 NSW  39  7.1  4.9  9.4 
 Qld  45  7.4  5.3  9.6 
 SA  7  5.9  1.5  10.2 
 WA  29  8.8  5.6  12.0 
 NT  27  11.9  7.4  16.4 
Persons     
 NSW  87  7.7  6.1  9.4 
 Qld  98  7.9  6.4  9.5 
 SA  16  6.4  3.3  9.5 
 WA  66  10.1  7.7  12.6 
 NT  64  13.6  10.3  16.9 
NONINDIGENOUS 

Males     
 NSW  653  4.9  4.5  5.3 
 Qld  448  5.3  4.8  5.8 
 SA  97  3.5  2.8  4.2 
 WA  116  2.9  2.3  3.4 
 NT  15  4.4  2.2  6.6 
Females     
 NSW  465  3.7  3.3  4.0 
 Qld  322  4.1  3.6  4.5 
 SA  87  3.2  2.6  3.9 
 WA  121  3.2  2.6  3.7 
 NT  11  3.3  1.3  5.2 
Persons     
 NSW  1 118  4.3  4.0  4.6 
 Qld  770  4.7  4.4  5.0 
 SA  184  3.4  2.9  3.9 
 WA  237  3.0  2.6  3.4 
 NT  26  3.8  2.4  5.3 

(a) Infant deaths per 1,000 live births. 
AGESPECIFIC DEATH RATES, CHILDREN AGED 14 YEARS
9 Agespecific death rates for children aged 14 years by Indigenous status for NSW/Qld combined and SA/WA/NT combined for 20062008 are presented in the following graph (for males and females combined).
Agespecific death rates, 14 years
 20062008
10 Similar to nonIndigenous IMRs, confidence intervals associated with death rates for nonIndigenous children aged 14 years are relatively small.
11 However, confidence intervals for Indigenous children aged 14 years (males and females combined) show very large ranges for both NSW/Qld combined and SA/WA/NT combined, such that the lower limits are lower than the agespecific death rates for nonIndigenous children. Such wide ranges severely question the usefulness of these rates. Confidence intervals for males and females separately are wider still (table below).
Agespecific death rates, 14 years, 20062008 

    95% confidence intervals 
  Deaths, children aged 14 years  Agespecific death rate(a)  Lower limit  Upper limit 
Indigenous 

NSW/Qld     
 Males  24  51.3  15.8  86.8 
 Females  15  33.6  4.2  62.9 
 Persons  39  42.6  19.5  65.8 
SA/WA/NT     
 Males  13  55.2  3.3  106.9 
 Females  13  56.9  3.4  110.4 
 Persons  26  56.0  18.8  93.2 
NonIndigenous 

NSW/Qld     
 Males  199  23.9  18.2  29.7 
 Females  145  18.4  13.2  23.6 
 Persons  344  21.2  17.4  25.1 
SA/WA/NT     
 Males  67  24.4  14.3  34.5 
 Females  36  13.9  6.0  21.7 
 Persons  103  19.3  12.8  25.7 

(a) Deaths per 100,000 population. 
CONCLUSION
12 The death rates presented above for Indigenous Australians have large associated confidence intervals and should be interpreted with a high degree of caution. Making comparisons over time (for example, year to year comparisons), between jurisdictions or between Indigenous and nonIndigenous Australians is therefore problematic due to the high level of uncertainty. In particular, confidence intervals for death rates of Indigenous children aged 14 years are very large as a result of the very small numbers of deaths in these ages.
13 While methods such as aggregating data over jurisdictions and/or longer time periods may help to reduce the width of the confidence intervals, this may limit the usefulness of the data for comparisons over time. In the case of Indigenous children aged 14 years, aggregation has not improved the confidence intervals to a level at which the rates could be interpreted with confidence.
14 The confidence intervals presented in this Technical Note relate to random variations in
numbers of deaths only. No other sources of errors or deficiencies in either deaths or population data have been considered in these calculations. For example, variations in Indigenous death rates may arise from uncertainty in the recording of Indigenous status on the death registration form (in particular, underidentification of Indigenous deaths) and in the Census, from which population estimates are derived (for more information see Chapter 3: Deaths of Aboriginal and Torres Strait Islander Australians). Confidence intervals would differ to those presented here if all these sources of variations were considered.
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