A Bayesian Ensemble Approach for Epidemiological Projections

Mathematical models are powerful tools for epidemiology and can be used to compare control actions. However, different models and model parameterizations may provide different prediction of outcomes. In other fields of research, ensemble modeling has been used to combine multiple projections. We explore the possibility of applying such methods to epidemiology by adapting Bayesian techniques developed for climate forecasting. We exemplify the implementation with single model ensembles based on different parameterizations of the Warwick model run for the 2001 United Kingdom foot and mouth disease outbreak and compare the efficacy of different control actions. This allows us to investigate the effect that discrepancy among projections based on different modeling assumptions has on the ensemble prediction. A sensitivity analysis showed that the choice of prior can have a pronounced effect on the posterior estimates of quantities of interest, in particular for ensembles with large discrepancy among projections. However, by using a hierarchical extension of the method we show that prior sensitivity can be circumvented. We further extend the method to include a priori beliefs about different modeling assumptions and demonstrate that the effect of this can have different consequences depending on the discrepancy among projections. We propose that the method is a promising analytical tool for ensemble modeling of disease outbreaks.Author Summary: Policy decisions in response to emergent disease outbreaks use simulation models to inform the efficiency of different control actions. However, different projections may be made, depending on the choice of models and parameterizations. Ensemble modeling offers the ability to combine multiple projections and has been used successfully within other fields of research. A central issue in ensemble modeling is how to weight the projections when they are combined. For this purpose, we here adapt and extend a weighting method used in climate forecasting such that it can be used for epidemiological considerations. We investigate how the method performs by applying it to ensembles of projections for the UK foot and mouth disease outbreak in UK, 2001. We conclude that the method is a promising analytical tool for ensemble modeling of disease outbreaks.