A smoothed ANOVA model for multivariate ecological regression

Smoothed analysis of variance (SANOVA) has recently been proposed for carrying out disease mapping. The main advantage of this approach is its conceptual simplicity and ease of interpretation. Moreover, it allows us to fix the combination of diseases of particular interest in advance and to make specific inferences about them. In this paper we propose a reformulation of SANOVA in the context of ecological regression studies. This proposal considers the introduction in a non-parametric way of one (or several) covariate(s) into the model, explaining some pre-specified combinations of the outcome variables. In addition, random effects are also incorporated in order to model geographical variation in the combinations of outcome variables not explained by the covariate. Lastly, the model permits the decomposition of the variance in the set of outcome variables into different orthogonal components, quantifying the contribution of every one of them. The proposed model is applied to the geographical analysis of mortality due to malignant stomach neoplasm among women resident in the city of Barcelona (Spain). The available outcome variables are deaths grouped into two time periods, and a socioeconomic deprivation index is included as a covariate. The model has been implemented through INLA, a novel inference tool for Bayesian statistics.