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Life expectancy estimation in small administrative areas with non-uniform population sizes: application to Australian New South Wales local government areas

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      Abstract

      ObjectiveTo determine a practical approach for deriving life expectancy estimates in Australian New South Wales local government areas which display a large diversity in population sizes.DesignPopulation-based study utilising mortality and estimated residential population data.Setting153 local government areas in New South Wales, Australia.Outcome measuresKey performance measures of Chiang II, Silcocks, adjusted Chiang II and Bayesian random effects model methodologies of life expectancy estimation including agreement analysis of life expectancy estimates and comparison of estimate SEs.ResultsChiang II and Silcocks methods produced almost identical life expectancy estimates across a large range of population sizes but calculation failures and excessively large SEs limited their use in small populations. A population of 25 000 or greater was required to estimate life expectancy with SE of 1 year or less using adjusted Chiang II (a composite of Chiang II and Silcocks methods). Data aggregation offered some remedy for extending the use of adjusted Chiang II in small populations but reduced estimate currency. A recently developed Bayesian random effects model utilising the correlation in mortality rates between genders, age groups and geographical areas markedly improved the precision of life expectancy estimates in small populations.ConclusionsWe propose a hybrid approach for the calculation of life expectancy using the Bayesian random effects model in populations of 25 000 or lower permitting the precise derivation of life expectancy in small populations. In populations above 25 000, we propose the use of adjusted Chiang II to guard against violations of spatial correlation, to benefit from a widely accepted method that is simpler to communicate to local health authorities and where its slight inferior performance compared with the Bayesian approach is of minor practical significance.

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      Statistical methods for assessing agreement between two methods of clinical measurement.

      In clinical measurement comparison of a new measurement technique with an established one is often needed to see whether they agree sufficiently for the new to replace the old. Such investigations are often analysed inappropriately, notably by using correlation coefficients. The use of correlation is misleading. An alternative approach, based on graphical techniques and simple calculations, is described, together with the relation between this analysis and the assessment of repeatability.
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        Life expectancy as a summary of mortality in a population: statistical considerations and suitability for use by health authorities.

         R Reza,  P Silcocks,  D Jenner (2000)
        To investigate the sampling distribution and usefulness of expectation of life in comparisons of mortality at health district level or below. Derivation of a formula for the variance of the expectation of life, confirmation of the result and generation of the sampling distribution by Monte Carlo simulation; comparison of expectation of life with standardised mortality ratio (SMR) and other summary indices of mortality. A health district in Trent Region, England. Routinely available mortality statistics at electoral ward level and above. Given reasonable and simple assumptions the sampling distribution of the expectation of life is approximately normal. Expectation of life shows a high negative correlation with SMR even if the oldest age band for the SMR is open ended. Where sampling error is an issue, inference concerning differences in mortality rates between populations can be based on expectation of life, which is better for illustrative purposes than SMR. The formula for the variance of the expectation of life is more complex however. If the final age band is open ended, its lower bound should be as high as possible to avoid misleading results caused by hidden differences in age structure.
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          Evaluation of methodologies for small area life expectancy estimation.

           S. Williams,  D Eayres (2004)
          To evaluate methods for calculating life expectancy in small areas, for example, English electoral wards. The Monte Carlo method was used to simulate the distribution of life expectancy (and its standard error) estimates for 10 alternative life table models. The models were combinations of Chiang or Silcocks methodology, 5 or 10 year age intervals, and a final age interval of 85+, 90+, or 95+. A hypothetical small area experiencing the population age structure and age specific mortality rates of English men 1998-2000. Routine mortality and population statistics for England. Silcocks and Chiang based models gave similar estimates of life expectancy and its standard error. For all models, life expectancy was increasingly overestimated as the simulated population size decreased. The degree of overestimation depended largely on the final age interval chosen. Life expectancy estimates of small populations are normally distributed. The standard error estimates are normally distributed for large populations but become increasingly skewed as the population size decreases. Substitution methods to compensate for the effect of zero death counts on the standard error estimate did not improve the estimate. It is recommended that a population years at risk of 5000 is a reasonable point above which life expectancy calculations can be performed with reasonable confidence. Implications are discussed. Within the UK, the Chiang methodology and a five year life table to 85+ is recommended, with no adjustments to age specific death counts of zero.
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            Author and article information

            Affiliations
            [1 ]NSW Biostatistical Officer Training Program, NSW Ministry of Health , Sydney, Australia
            [2 ]Centre for Epidemiology and Evidence, NSW Ministry of Health , Sydney, Australia
            Author notes
            [Correspondence to ] Dr Alexandre S Stephens; astep@ 123456doh.health.nsw.gov.au
            Journal
            BMJ Open
            BMJ Open
            bmjopen
            bmjopen
            BMJ Open
            BMJ Publishing Group (BMA House, Tavistock Square, London, WC1H 9JR )
            2044-6055
            2013
            2 December 2013
            : 3
            : 12
            24302503
            3856616
            bmjopen-2013-003710
            10.1136/bmjopen-2013-003710
            Published by the BMJ Publishing Group Limited. For permission to use (where not already granted under a licence) please go to http://group.bmj.com/group/rights-licensing/permissions

            This is an Open Access article distributed in accordance with the Creative Commons Attribution Non Commercial (CC BY-NC 3.0) license, which permits others to distribute, remix, adapt, build upon this work non-commercially, and license their derivative works on different terms, provided the original work is properly cited and the use is non-commercial. See: http://creativecommons.org/licenses/by-nc/3.0/

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            Public Health
            Research
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            Medicine

            public health, epidemiology, mortality

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