Multivariate spatial models for event data

This paper describes how estimates made for event rates in small areas may be enhanced through spatial modelling of the data - taking the geographical location of each area into account - and through the addition of further information from each area. In particular we consider the use of spatial models to predict more than one outcome simultaneously. This is done by writing the spatial model as a multi-level model and subsequently enhancing this to encompass a multivariate data structure; estimates are obtained using iterative generalized least squares in the software package MLwiN. The example given considers mortality due to two causes--neoplasms and circulatory disease--in 143 postcode sectors in Greater Glasgow Health Board, Scotland. In addition, a measure of socio-economic deprivation is available for each area. Correlations between causes within areas, between areas within causes and between areas and causes are quantified, as are the relative contributions of the heterogeneous and spatial parts of the model. The results suggest a tendency for there to be pockets with high mortality rates due to neoplasms, whilst mortality due to circulatory disease follows a much smoother pattern. After taking deprivation into account, the spatial component accounts for just 19 per cent of the variation in the mortality due to neoplasms in Greater Glasgow but 66 per cent of the mortality due to circulatory disease.