Adaptive autoregressive priors for area and time structured mortality data

Mortality counts by age and area are relevant to obtaining small area life tables and summary statistics such as life expectancy. A Bayesian approach to small area life tables is proposed here based on the principle of smoothing (or “pooling strength”) over adjacent ages or areas. Several schemes have been suggested to reflect dependence between age categories x or areas i  , such as conditional autoregressive priors based on the principle of local smoothing, determined by adjacency of age groups or spatial proximity. It is argued here that a more flexible approach is to allow a mix of local and global smoothing over age groups and areas, as determined by the data and additional parameters κ∈0,1]$\kappa \in 0,1]$ and λ∈0,1]$\lambda \in 0,1]$ for age and area, respectively. An extension is also proposed to reflect the fact that the appropriate mix between local and global smoothing may not be constant across age bands or across the region being studied. For example, local spatial smoothing will not be appropriate if an area is disparate from its neighbours (e.g. in terms of social distance), and so area specific mixing parameters _λi${\lambda }_i$ are introduced. The _λi${\lambda }_i$ may be modelled by logit regression on observed sources of disparity between neighbouring areas. The application considers small area life tables for males over 625 small areas (electoral wards) in London over 2003–2005.