Latent likelihood ratio tests for assessing spatial kernels in epidemic models

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 are 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 - and compare its capacity to detect model misspecification with that of tests based on the use of infection-link residuals. We demonstrate that the new approach, which combines Bayesian and frequentist ideas by treating the statistical decision maker as a complex entity, can be used to formulate tests with greater power than infection-link residuals to detect kernel misspecification particularly when the degree of misspecification is modest. This new approach avoids the use of a fully Bayesian approach which may introduce undesirable complications related to computational complexity and prior sensitivity.