“Achieving closure”: improving the estimation of life expectancy for small populations

Michael P. Grayer, University of London

Life expectancy is a useful indicator of mortality for policy-makers, though its calculation for small populations is problematic. In the UK, two technical reports, one from the Office of National Statistics (ONS), and the other from the South East Public Health Observatory (SEPHO), were commissioned to investigate life table methods applied to small populations. As a result, the ONS published “experimental” life expectancy indicators following their recommendations, and continue to do so. However, some of the life expectancy estimates produced by this methodology are implausibly high. This paper attempts to address a key reason why the current methodology is prone to error by examining a specific area of the life table: the method of closing the table. The applicability of the current method to small populations is critically assessed, with particular attention paid to how small numbers of deaths occurring in the final age band lead to implausibly long survival times being estimated. Two alternative methods of closing the life table are suggested. The first comes from the literature (Silcocks, 2004). The other is proposed here. This method uses a Brass relational model to extrapolate survivorship beyond the start of the final age interval, allowing for a smoother transition from the rest of the life table until its eventual culmination. The three methods are compared using empirical data: deaths and population estimates for 625 small areas (electoral wards) in London, for the years 2001-05. The Brass extrapolation method reduces the skew in life expectancy estimates seen when using the standard method, though the method appears to work better for males than for females. Reasons why this may be the case, and possible improvements, are suggested.