Spatio-temporal disease mapping comprises a wide range of models used to describe the distribution of a disease in space and its evolution in time. These models have been commonly formulated within a hierarchical Bayesian framework with two main approaches: an empirical Bayes (EB) and a fully Bayes (FB) approach. The EB approach provides point estimates of the parameters relying on the well-known penalized quasi-likelihood (PQL) technique. The FB approach provides the posterior distribution of the target parameters. These marginal distributions are not usually available in closed form and common estimation procedures are based on Markov chain Monte Carlo (MCMC) methods. However, the spatio-temporal models used in disease mapping are often very complex and MCMC methods may lead to large Monte Carlo errors and a huge computation time if the dimension of the data at hand is large. To circumvent these potential inconveniences, a new technique called integrated nested Laplace approximations (INLA), based on nested Laplace approximations, has been proposed for Bayesian inference in latent Gaussian models. In this paper, we show how to fit different spatio-temporal models for disease mapping with INLA using the Leroux CAR prior for the spatial component, and we compare it with PQL via a simulation study. The spatio-temporal distribution of male brain cancer mortality in Spain during the period 1986–2010 is also analysed.

Summary: Crimes against women in India have been continuously increasing lately as reported by the National Crime Records Bureau. Gender-based violence has become a serious issue to such an extent that it has been catalogued as a high impact health problem by the World Health Organization. However, there is a lack of spatiotemporal analyses to reveal a complete picture of the geographical and temporal patterns of crimes against women. We focus on analysing how the geographical pattern of ‘dowry deaths’ changes over time in the districts of Uttar Pradesh during the period 2001–2014. The study of the geographical distribution of dowry death incidence and its evolution over time aims to identify specific regions that exhibit high risks and to hypothesize on potential risk factors. We also look into different spatial priors and their effects on final risk estimates. Various priors for the hyperparameters are also reviewed. The risk estimates seem to be robust in terms of the spatial prior and hyperprior choices and final results highlight several districts with extreme risks of dowry death incidence. Statistically significant associations are also found between dowry deaths, sex ratio and some forms of overall crime.