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

Abstract

Spatial and spatio-temporal disease mapping models are widely used for the analysis of registry data and usually formulated in a hierarchical Bayesian framework. Explanatory variables can be included by a so-called ecological regression. It is possible to assume both a linear and a nonparametric association between disease incidence and the explanatory variable. Integrated nested Laplace approximations (INLA) can be used as a tool for Bayesian inference. INLA is a promising alternative to Markov chain Monte Carlo (MCMC) methods which provides very accurate results within short computational time. It is shown in this paper, how parameter estimates for well-known spatial and spatio-temporal models can be obtained by running INLA directly in $${\texttt{R}}$$ using the package $${\texttt{INLA}}$$ . Selected $${\texttt{R}}$$ code is shown. An emphasis is given to the inclusion of an explanatory variable. Cases of Coxiellosis among Swiss cows from 2005 to 2008 are used for illustration. The number of stillborn calves is included as time-varying covariate. Additionally, various aspects of INLA such as model choice criteria, computer time, accuracy of the results and usability of the $${\texttt{R}}$$ package are discussed.