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.

Laboratory data interpretation for the assessment of complex biological systems remains a great challenge, as occurs in mitochondrial function research studies. The classical biochemical data interpretation of patients versus reference values may be insufficient, and in fact the current classifications of mitochondrial patients are still done on basis of probability criteria. We have developed and applied a mathematic agglomerative algorithm to search for correlations among the different biochemical variables of the mitochondrial respiratory chain in order to identify populations displaying correlation coefficients >0.95. We demonstrated that coenzyme Q₁₀ may be a better biomarker of mitochondrial respiratory chain enzyme activities than the citrate synthase activity. Furthermore, the application of this algorithm may be useful to re-classify mitochondrial patients or to explore associations among other biochemical variables from different biological systems.