New Zealand Subnational Abridged Period Life Tables 2012–14

Method used for the 2012–14 subnational abridged and national complete period life tables:

In calculating the 2012–14 subnational abridged and national complete period life tables, we used a new statistical model for deriving measures of mortality and life expectancy that is consistent across all population groups. The statistical model was developed to estimate the death rate at each age (0, 1, 2, ..., 100+) by sex for national total and ethnic group populations and for age intervals (0, 1–4, 5–9,...,90+) for subnational populations.

This release includes subnational life tables for the 2005–07 period based on this new method. These tables supersede the previously released 2005–07 life tables. The change in how the methods deal with estimation of death rates for small populations created differences in historic published subnational life tables and the latest life tables. The subnational life tables will be revised back to 1995–97 soon. These revised tables will make use of the latest geographic boundaries (2013). In comparison, we did not revise the national and ethnic historic life tables, because of smaller differences between methods.

This release includes a measure of uncertainty (credible intervals) for each of the life table functions, with the median as well as 95 percent limits. The true value of the death rate will be within the 2.5th and 97.5th percentiles, 95 percent of the time, given the input data and the assumed statistical model. For example we can say that 95 percent of the time life expectancy at birth for a male in Northland will be between 78.1 and 78.8 years, based on the 2012–14 period life tables.

Additional subnational life tables included for 2012–14

Subnational period life tables: 2012–14 extends on subnational life tables released in the past (eg New Zealand Life Tables: 2005–07 subnational trends in longevity and mortality). We can do this because the new statistical model enables us to show uncertainty measures, which display the greater uncertainty associated in estimating smaller populations, particularly in small geographic areas. New life tables included in the 2012–14 release include:

• life tables for all 67 territorial authorities, with Auckland further disaggregated into 21 local board areas.
• Māori and non-Māori life tables by regional council
• life tables based on the 2013 New Zealand deprivation index (NZDep2013).

Data sources

The data used to construct the 2012–14 subnational life tables comprises:

1. Deaths registered in New Zealand of people resident in New Zealand in the December years 2005–07 and 2012–14, respectively, by date of death, date of birth, sex, ethnicity, and geographic area of usual residence.

2. The estimated resident population of New Zealand at 30 June 2006 and 2013, by single year of age, sex, ethnic group, and geographic area of usual residence.

For statistical modelling purposes, we used data from two periods to estimate each period (ie 2005–07 and 2012–14 to model 2012–14). Regional council of usual residence was a variable input to the imputation model for missing ethnicity response (see Ethnicity non-response in deaths data).

Death registrations

We use death registrations as the numerator to derive the death rates. In 2012–14, 90,730 deaths of New Zealand residents were registered in New Zealand, made up of 45,641 male and 45,089 female deaths.

The level of non-response to the ethnicity question in death registrations has been declining over time. There was no response to the ethnicity question for 173 deaths in 2012–14 (0.2 percent of all deaths).

Death records with missing ethnicity response are imputed using a statistical approach based on records with observed ethnicity response. Read Ethnicity non-response in deaths data below for more information.

Population estimates

The 2012–14 subnational life table calculations use, as the population denominator, the estimated resident population at 30 June 2013 – the mid-point of the period.

We used demographic analysis using cumulated counts of deaths from the highest ages to compare counts of the population previously alive (‘extinct generation method’) with the estimated resident population for each population group at 30 June for both 2006 and 2013. As a result of this analysis, ages 90 years or over are represented by one open age group in the subnational life tables, and life table calculations use population data generated by the ‘extinct generation method’ for the oldest ages.

Methodology

Period life tables present a period’s mortality experience using a number of age-specific functions: death probabilities, probabilities of survival between two ages, years of life lived, and the number of survivors. These indicators are centred on the transformation of the directly observed age-specific death rates to a set of age-specific probabilities of dying for the period.

We generated the New Zealand period life tables using a standard demographic framework and a description of the mathematical derivation is available for each of the elements of the life table (Preston et al, 2001).

The following sections report on methodologies we implemented to derive the New Zealand 2012–14 period life tables (and revised subnational life tables).

Deaths

The life tables are compiled from deaths registered, rather than deaths occurring, in each respective three-year period. Most death statistics refer to registrations rather than occurrences for a given time period, because there is generally a time lag between when the death occurred and when it is registered. For this reason, the number of death registrations can be determined before the number of death occurrences for a given time period. For periods of a year or more, the difference between registrations and occurrences is generally small, so death statistics referring to registrations are suitable for most purposes.

Ethnicity non-response in deaths data

Individual death records with missing ethnicity responses are assigned combinations of ethnicity indicators based on a statistical multiple imputation approach. Death records with observed ethnicity response for the two time periods (2012–14 and 2005–07), and the population exposure at the period mid-point (at 30 June 2013 and 30 June 2006) are the inputs to the statistical model. The model uses 10-year age groups, sex, regional council, and the two time periods.

The statistical model fitted to the data generates estimates of rates for identifying with an ethnic group or combination of ethnicities. We generated values for the ethnic indicators in death records with a missing response using a probability distribution given the observed rates for identifying with an ethnic indicator estimated by the model.

Death rates and probabilities

The subnational life tables use age-sex-specific death rates for the geographic area, calculated using the average number of deaths over three years. Doing this reduces the effect of year-to-year statistical variations, particularly at younger ages where there is a small number of deaths or no registrations, and at very old ages where the population-at-risk is small. The observed age-sex-specific death rate for the period and geographic area is calculated as the ratio of the average number of deaths between ages x and x+1 (x = 0, 1–4, 5–9, …, 90+) and the estimated population at the period mid-point (at 30 June 2013).

The observed death rate is likely to show some random variation at ages with small death counts (or missing counts) or population-at-risk, and observed rates are likely to fluctuate considerably from one period to another for these ages. Implementing a hierarchical statistical model provides a coherent solution for deriving estimates of the age-sex-specific death rate. We fit data for the two periods, 2012–14 and 2005–07, to the model, and use model estimates of age-sex-period-specific death rates (including uncertainty measures) to derive death probabilities for the geographic area.

Converting the age-sex-period-specific death rates to probabilities of dying at each age x to x+1 includes the derivation of average number of person-years lived in the period by those dying in the same period (Preston et al, 2001). For single year cohorts aged 1, …, 100+ years, we assume that, on average, people dying in the period do so halfway through this period (0.5). Infant mortality observed in the youngest cohort (age 0 years) will be more concentrated at the earlier stages of infancy. Based on date of birth information for deaths in their first year of life, the average number of person-years lived for this cohort was estimated at 0.1 of a year.

Measures of uncertainty

The statistical approach for estimating period death rates offers an explicit way of including uncertainty in the data and the parameters of the chosen model. This includes integrating a measure of uncertainty derived at the imputation step for assigning ethnic indicators to records with missing ethnicity responses (described above). The 50th percentile (median), 2.5th percentile, and 97.5th percentile estimates of the death rate and other life table variables are available at the detailed demographic level. Under the model, 95 percent credible intervals include the true underlying value 95 percent of the time. For example, 95 percent of the time life expectancy at birth for males in Northland is between 78.1 and 78.8 years. There is only a 2.5 percent chance that the true value is lower than 78.1 years, and a 2.5 percent chance it is higher than 78.8 years.

Age contribution to longevity differences

We can determine the contribution that each age group has made to longevity differences, between periods or between populations (eg Māori and non-Māori). Ages do not contribute equally to life expectancy at birth, with the youngest ages contributing relatively more. The comparison involves calculating and comparing hypothetical or temporary life expectancies at each age. Hypothetical life expectancy is the average number of years that a group of people will live from age x to x + i years (where i is the age interval). For more information see Arriaga (1984).

Ethnic concept

The ethnic concept used in these period life tables is the ethnic group or groups that people identify with or feel they belong to. Ethnicity is self-perceived and people can belong to more than one ethnicity. Ethnicity is different from ancestry, birthplace, and nationality. For example, people can identify with Māori ethnicity even though they may not be descended from a Māori ancestor. Conversely, people may choose to not identify with the Māori ethnicity even though they are descended from a Māori ancestor.

For births and deaths registrations, ethnicity is identified by the person completing the registration form. For deaths, this person is most likely to be the funeral director (on the advice of a family member).

Availability of ethnic life tables

In this 2012–14 subnational release, we published Māori and non-Māori life tables by region. Life tables for other ethnic groups carry a larger uncertainty associated with the death rate due to smaller numbers of death registrations and smaller populations. Additional ethnic life tables are not currently available.

There may be inconsistencies in the reporting and hence identification of ethnicity in death registration data compared with the population-at-risk data (which is based on individuals’ census responses to the ethnicity question). The numerator-denominator ethnic differences observed for the purpose of the 2012–14 life tables for the Māori and non-Māori ethnic groups were small. The differences at the detailed demographic level were not significant enough to make any further adjustments.

Comparability of ethnic life tables

All ethnic mortality measures should be interpreted with caution because of changes in ethnic concepts and data sources. This includes changes over time as well as differences in measurements between data sources:

• We applied the statistical model used for the derivation of death rates at the detailed demographic level in 2012–14. All life table components are derived based on the estimated death rates including uncertainty measures. The release of the 2012–14 life tables includes the availability of the 2005–07 life tables based on a consistent statistical methodology.

• Due to changes to the census ethnicity question, population estimates for ethnic groups are not necessarily comparable.

• Death registrations and population data are broadly comparable for ethnic groups. However, the death registration form has been redesigned in the past (eg in 1995).

Read New Zealand Period Life Tables – Significant events impacting this study series for more detailed information on historic changes to the two data collections and other changes.

Deprivation index (NZDep2013)

The life tables by deprivation area use the New Zealand 2013 index of socio-economic deprivation. It combines census data relating to income, home ownership, employment, qualifications, family structure, housing, and access to transport and communication, to produce a score for each meshblock in New Zealand. These scores are grouped into 10 categories (deciles), where 1 represents the areas with the least deprived scores and 10 the areas with the most deprived scores. A value of 10 therefore indicates that a meshblock is in the most deprived 10 percent of areas in New Zealand.

To enable comparison over time, we also produced the 2005–07 life tables by deprivation index using the NZDep2013 classification of meshblocks (instead of the NZDep2006).

More information

We produce national abridged period life tables on an annual basis. These are not as detailed as complete life tables, as abridged life tables present functions for grouped ages rather than single years of age, and are not derived by ethnicity.

Abridged period life tables for 2013–15 will be available in February 2016 (provisional) and May 2016 (final).

See New Zealand Subnational Abridged Period Life Tables in DataInfo+ for more information about life tables, including information about methods.

Statistics in this release have been produced in accordance with the Official Statistics System principles and protocols for producers of Tier 1 statistics for quality. They conform to the Statistics NZ Methodological Standard for Reporting of Data Quality.

References

Ajwani S, Blakely, Robson, Tobias, and Bonne (2003). Decades of disparity: Ethnic mortality trends in New Zealand 1980–1999, Wellington: Ministry of Health and University of Otago. Available from www.health.govt.nz.

Arriaga, EE (1984). 'Measuring and Explaining the Change in Life Expectancies', Demography, 21(1), 83–96.

Blakely, Tobias, Atkinson, Yeh, and Huang (2007). Tracking disparity: Trends in ethnic and socioeconomic inequalities in mortality, 1981–2004, Wellington: Ministry of Health. Available from www.health.govt.nz.

Preston, S.H, Heuveline, P, Guillot, M (2001). Demography: Measuring and modelling population processes. Oxford, United Kingdom: Blackwell Publishers Ltd.

method prior to the 2012–14 life tables

The data used to construct the 1995–97 (revised), 2000–02 and 2005-07 subnational abridged period life tables and standardised death rates comprised:

• deaths registered in New Zealand of people resident in each area in the December years 1995–97, 2000–02, and 2005–07, respectively, by age groups (0, 1–4, 5–9, 10–15, ... , 80–84, 85 and over) and sex
• live births registered in New Zealand to mothers resident in each area in the December years 1995–97, 2000–02, and 2005–07, respectively, by sex
• the estimated resident population of each area at 30 June 1996, 30 June 2001, and 30 June 2006, respectively, by age groups (1–4, 5–9, 10–15, ... , 80–84, 85 and over) and sex.

Deaths numerator

The period life tables were compiled from deaths registered, rather than deaths occurring, in each respective three-year period. Most death statistics refer to registrations rather than occurrences for a given time period, because there is generally a time lag between when the death occurred and when it is registered. Hence, the number of death registrations can be confirmed before the number of death occurrences for a given time period. For periods of a year or more, the difference between registrations and occurrences is generally small, so death statistics referring to registrations are suitable for most purposes.

An adjustment for address non-response among deaths was made. There was no response to the address question for 0.0 percent of deaths in 1995–97, 0.2 percent of deaths in 2000–02, and 0.5 percent of deaths in 2005–07.

Population denominator (exposed-to-risk population)

The estimated resident population of each area at 30 June (the midpoint) for each period was used as the denominator to calculate death rates.

The estimated resident populations at 30 June 1996, 30 June 2001, and 30 June 2006 were based on the census usually resident population counts at 5 March 1996, 6 March 2001, and 7 March 2006 respectively, and adjusted for:

• net census undercount
• residents temporarily overseas on census night
• births, deaths and net migration between census night and 30 June of the census year
• reconciliation with demographic estimates at ages 0–9 years.

Derived rates

The period life tables were based on deaths averaged over three years. This is designed to reduce the impact of year-to-year statistical variations, particularly at younger ages where there may be a small number of deaths and at very old ages where the population at risk may be small. In some cases the subnational data does not enable death rates to be reliably estimated at all ages.

The construction of each abridged period life table involves three stages.

• First, central death rates (mx) were calculated for each age interval, except the first year of life.
• Second, the Brass logit system was used to smooth age-specific death rates for all areas.
• Third, the smoothed rates were used to calculate a set of age-specific probabilities of death (qx),which were then used to derive other life table functions.

The derivation of the mortality rate in the first year of life differed from all other ages and required special formulae. More detailed methodology is available on request.

• derivation of the mortality rate in the first year of life(Age 0); Age 1–4 years; Age 5–84 years; Age 85 years and over is available on request.

Brass logit system

The Brass logit technique enables the calculation of smooth abridged period life tables for areas that have unreliable and/or zero age-specific death rates, by adjusting the observed rates with reference to a standard life table. The technique does not alter the overall level of mortality, but the age-specific functions of the life table are smoothed. Essentially, the technique compares mortality between the area and a standard life table across ages, then a line of best fit is calculated to describe that relationship by age. The line of best fit is then used in conjunction with the standard life table to determine death rates for the small area life table.

The subnational abridged period life tables for 1995–97 to 2005–07 use the Brass logit system and the complete period life tables for New Zealand for 1995–97 to 2005-07, respectively, as the standard.