Model choice using the deviance information criterion for latent conditional individual-level models of infectious disease spread

Abstract

Individual-level models (ILMs) are a class of complex, statistical models that are often fitted within a Bayesian framework, and which can be suitable for modeling infectious disease spread. The deviance information criterion (DIC) is a model comparison tool that is appropriate for complex, Bayesian models, and since its development a number of variants have been proposed, including those for its application to missing data models. Here, we assessed five variants of the DIC and their application to ILMs, in particular a class of infectious disease models known as latent conditional LC-ILMs, which depend on a potentially unknown latent grouping variable for each individual in the population. The effectiveness of the traditionally defined DIC was compared to alternative DIC definitions through a simulation study, to assess which is most applicable for this class of models. Epidemic data was generated under an LC-ILM, to which both a spatial ILM (SILM) and the LC-ILM were fitted. Each variant of the DIC was then calculated for every fitted model, and the DIC values obtained for the LC-ILM were compared to those from the SILM. The results of the simulation study indicate that the DIC can be effective for model comparison within complex Bayesian models; however, the degree to which it is effective is dependent upon the variant of the DIC used and the amount of available information on the latent grouping variable.