 2010 Royal Statistical Society 0035–9254/11/60261 Appl. Statist. (2011) 60, Part 2, pp. 261–279 Using integrated nested Laplace approximations for the evaluation of veterinary surveillance data from Switzerland: a case-study Birgit Schrödle, Leonhard Held and Andrea Riebler University of Zurich, Switzerland and Jürg Danuser Federal Veterinary Office, Berne, Switzerland [Received June 2009. Final revision August 2010] Summary. Spatiotemporal disease mapping models have been used extensively to describe the pattern of surveillance data. They are usually formulated in a hierarchical Bayesian frame- work and posterior marginals are not available in closed form. Hence, the standard method for parameter estimation is Markov chain Monte Carlo algorithms. A new method for approximate Bayesian inference in latent Gaussian models using integrated nested Laplace approximations has recently been proposed as an alternative. This approach promises very precise results in short computational time. The aim of the paper is to show how integrated nested Laplace approximations can be used as an inferential tool for a variety of spatiotemporal models for the analysis of reported cases of bovine viral diarrhoea in cattle from Switzerland. Conclusions concerning the problem of under-reporting in the data are drawn via a multilevel modelling strategy. Furthermore, a comparison with Markov chain Monte Carlo methods with regard to the accuracy of the parameter estimates and the usability of both approaches in practice is conducted. Approaches to model choice using integrated nested Laplace approximations are also presented. Keywords: Disease mapping; Integrated nested Laplace approximations; Leave-one-out cross-validation; Spatiotemporal models 1. Introduction Spatiotemporal disease mapping models have been used extensively to describe the spatial and temporal pattern of registry data. Various specifications of the spatial and temporal trends and the space–time interaction term have been proposed in the literature (Bernardinelli et al., 1995b; Knorr-Held, 2000; Lagazio et al., 2003). From an inferential point of view, this class of models is formulated within a hierarchical Bayesian framework (Besag et al., 1991; Banerjee et al., 2004). As, in general, posterior marginals are not available in closed form, Markov chain Monte Carlo (MCMC) algorithms have been used for parameter estimation so far. But the often complex dependence structure in spatiotemporal models requires specific algorithms to obtain reliable estimates (Knorr-Held and Rue, 2002; Schmid and Held, 2004). Furthermore, MCMC methods may lead to a large Monte Carlo error and the computation time can be long. Address for correspondence: Birgit Schrödle, Biostatistics Unit, Institute of Social and Preventive Medicine, University of Zurich, Hirschengraben 84, Zurich, Switzerland. E-mail: birgit.schroedle@ifspm.uzh.ch