Modelling changes in small area disability free life expectancy: trends in London wards between 2001 and 2011

Existing analyses of trends in disability free life expectancy (DFLE) are mainly at aggregate level (national or broad regional). However, major differences in DFLE, and trends in these expectancies, exist between different neighbourhoods within regions, so supporting a small area perspective. However, this raises issues regarding the stability of conventional life table estimation methods at small area scales. This paper advocates a Bayesian borrowing strength technique to model trends in mortality and disability differences across 625 small areas in London, using illness data from the 2001 and 2011 population Censuses, and deaths data for two periods centred on the Census years. From this analysis, estimates of total life expectancy and DFLE are obtained. The spatio-temporal modelling perspective allows assessment of whether significant compression or expansion of morbidity has occurred in each small area. Appropriate models involve random effects that recognise correlation and interaction effects over relevant dimensions of the observed deaths and illness data (areas, ages), as well as major spatial trends (e.g. gradients in health and mortality according to area deprivation category). Whilst borrowing strength is a primary consideration (and demonstrated by raised precision for estimated life expectancies), so also is model parsimony. Therefore, pure borrowing strength models are compared with models allowing selection of random age-area interaction effects using a spike-slab prior, and in fact borrowing strength combined with random effects selection provides better fit.