Using Integrated Nested Laplace Approximations for the Evaluation of Veterinary Surveillance Data from Switzerland: A Case-Study

Abstract

Spatiotemporal disease mapping models have been used extensively to describe the pattern of surveillance data. They are usually formulated in a hierarchical Bayesian framework 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.

A primer on disease mapping and ecological regression using $${\texttt{INLA}}$$

“…The cantonal veterinary authorities are responsible for the realization of federal veterinary legislation in each affiliated region. In Schrödle et al (2010) it was found that the number of reported cases within one region might depend on the canton it belongs to. Hence, cantons are considered as a second, coarser spatial grid.…”

“…As discussed in Schrödle et al (2010), the number of reported cases per region might depend on the canton a region belongs to. For investigation of this fact, (2) is extended to a second, coarser spatial level: An i.i.d.…”

“…Four parameters have to be specified within the "2diidwishartpart0"-component. In this application these parameters are chosen as prior.wishart=c(4,1,1,0); this choice was used in Schrödle et al (2010) for a similar setting and checked for sensitivity. For the differential trend δ j appropriate weights (vn: time) given by the timepoints have to be introduced additionally.…”

Spatial and spatio-temporal models with R-INLA

“…For this reason, INLA can be successfully used in a great variety of applications (e.g. Li et al, 2012;Riebler et al, 2012;Ruiz-Cárdenas et al, 2012;Martino et al, 2011;Roos and Held, 2011;Schrö-dle and Held, 2011a,b;Schrödle et al, 2011;Paul et al, 2010), also thanks to the availability of an R package named R-INLA (Martino and Rue, 2010). Furthermore, INLA can be combined with the Stochastic Partial Differential Equation (SPDE) approach proposed by Lindgren et al (2011) in order to implement spatial and spatio-temporal models for point-reference data.…”

Space–time airborne disease mapping applied to detect specific behaviour of varicella in Valencia, Spain

“…Different extensions of the parametric and non-parametric models have been proposed by Schrödle and Held (2011b) and applied to counts of salmonellosis in cattle reported to the Swiss Federal Veterinary Office from 1991 to 2008. Schrödle et al (2011) propose another application for these models to analyse reported cases of bovine viral diarrhoea in Swiss cattle from 2003 to 2007. Blangiardo et al (2013) study the pattern of low birth weight for the 159 counties of US state of Georgia from 2000 to 2010, using the parametric formulation in Bernardinelli et al (1995) and the non-parametric formulation in Knorr-Held (2000) with INLA.…”