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Life expectancy as a summary of mortality in a population: statistical considerations and suitability for use by health authorities
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  1. P B S Silcocksa,b,
  2. D A Jennerc,
  3. R Rezac
  1. aTrent Institute for Health Services Research, University of Nottingham, bTrent Cancer Registry, Weston Park Hospital, Sheffield, cSouthern Derbyshire Health Authority
  1. Dr Silcocks, Trent Institute for Health Services Research, University of Nottingham, Queen's Medical Centre, Nottingham NG7 2UH (p.b.silcocks{at}nottingham.ac.uk)

Abstract

OBJECTIVE To investigate the sampling distribution and usefulness of expectation of life in comparisons of mortality at health district level or below.

DESIGN 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.

SETTING A health district in Trent Region, England.

SUBJECTS Routinely available mortality statistics at electoral ward level and above.

MAIN RESULTS 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.

CONCLUSIONS 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.

  • life expectancy
  • sampling distribution
  • Monte Carlo method

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Footnotes

  • Funding: none.

  • Conflicts of interest: none.

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