Abstract
One of the most important issues in the critical assessment of spatio-temporal stochastic models for epidemics is the selection of the transmission kernel used to represent the relationship between infectious challenge and spatial separation of infected and susceptible hosts. As the design of control strategies is often based on an assessment of the distance over which transmission can realistically occur and estimation of this distance is very sensitive to the choice of kernel function, it is important that models used to inform control strategies can be scrutinised in the light of observation in order to elicit possible evidence against the selected kernel function. While a range of approaches to model criticism is in existence, the field remains one in which the need for further research is recognised. In this paper, building on earlier contributions by the authors, we introduce a new approach to assessing the validity of spatial kernels—the latent likelihood ratio tests—which use likelihood-based discrepancy variables that can be used to compare the fit of competing models, and compare the capacity of this approach to detect model mis-specification with that of tests based on the use of infection-link residuals. We demonstrate that the new approach can be used to formulate tests with greater power than infection-link residuals to detect kernel mis-specification particularly when the degree of mis-specification is modest. This new tests avoid the use of a fully Bayesian approach which may introduce undesirable complications related to computational complexity and prior sensitivity.
Highlights
Selection of spatial kernel functions in spatio-temporal epidemic models is a question of paramount practical importance
In this paper we have investigated methods for assessing and comparing spatiotemporal stochastic epidemic models— with regard to the specification
The methods that we consider can be implemented as relatively straightforward addenda to a Bayesian analysis where the model criticism is achieved by embedding classical testing methods within the Bayesian analysis—in the same spirit as posterior predictive checking
Summary
Selection of spatial kernel functions in spatio-temporal epidemic models is a question of paramount practical importance. We will assume that observations include times and locations of all transitions from E to I and from I to R, so that the subsets I (t) and R(t) are observed but individuals in S(t) cannot be distinguished from those in E(t) Such data which can be modelled by an SEIR model are encountered in many real-world situations, for example, concerning diseases with long latent periods or because of delay in reporting of cases, such as Foot-and-Mouth Disease (Keeling 2001; Jewell et al 2009; Chis Ster et al 2009; Ferguson 2001; Ferguson et al 2001; Jewell et al 2009; Morris et al 2001; Ster and Ferguson 2007; Streftaris and Gibson 2004a; Tildesley et al 2008) and Citrus Canker (Neri et al 2014; Gottwald et al 2002a, b).
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