Evaluation of methodologies for small area life expectancy estimation

Abstract

Study objective : To evaluate methods for calculating life expectancy in small areas, for example, English electoral wards. Design: 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+. Setting: A hypothetical small area experiencing the population age structure and age specific mortality rates of English men 1998-2000. Participants: Routine mortality and population statistics for England. Main results: 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. Conclusions: 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.

Significance of life table estimates for small populations: Simulation-based study of estimation errors

“…Using the Monte Carlo simulation approach, Silcocks, Jenner, and Reza (2001), Toson, Baker, and the Office of National Statistics (2003), Eayres and Williams (2004), as well as Williams et al (2005) evaluated methodologies for the estimation of smallarea life expectancy in the United Kingdom (UK) context. They showed that life expectancy at birth is distributed normally and estimates of its standard error are distributed with a significant skew for the small population size.…”

Variance models of the last age interval and their impact on life expectancy at subnational scales

“…As first noted in 2004 (Eayres and Williams 2004), however, the Chiang variance formula incorrectly omits the variance contribution of the mortality rate of the last age interval 6 . While a subsequent assessment (Toson and Baker 2003) concluded that the magnitude of this contribution to the total LE variance was negligible for populations above 5,000 PY in size, a more recent study (Scherbov and Ediev 2012) suggested a more critical role of the last age interval in the statistical efficiency of LE and the need for further studies.…”

“…For this reason, the various derived expressions for variance are in fact first order approximations. However, validation studies that have compared the delta method standard error with Monte Carlo simulated standard errors have shown that the delta method is accurate (Eayres and Williams 2004). The delta method was used by Chiang in his original derivation of the LE variance (though the contribution the last age interval was neglected): it also sees widespread use for variance estimation in biostatistics in general (Cox 2005).…”

“…The corrected variance model for the Chiang LE is then = ( , | , ). Application of the delta method and using a Poisson distribution for yields the following corrected LE variance formula, which has been termed the 'adjusted' Chiang variance in previous studies (Eayres and Williams 2004;Toson and Baker 2003) (cf. Appendix 1 for further details):…”

“…He derived the only analytic equation for the variance of LE, which he expressed, using the delta method, as a weighted sum of the variances of the underlying age-specific survival probabilities. More recent investigations (Eayres and Williams 2004;Scherbov and Ediev 2012;Toson and Baker 2003) have further examined the statistical properties of the Chiang LE estimator down to extremely small population sizes, and established a total population size threshold of 5,000 person-years (PY) above which the LE estimate and its normality remain valid. Due to its accessibility and robustness, the Chiang LE estimator, as well as its associated variance formula, have become an established standard used in both monitoring and scientific studies (von Gaudecker and Scholz 2007;Geruso 2012;Kyte and Wells 2010;Page et al 2007).…”