Use of clustering to improve estimation of epidemic model parameters under a Bayesian hierarchical framework

We study infectious disease outbreaks that have evolved in isolation without the influence of one another. If stochastic effects are identified within each outbreak, it is necessary to model the dynamics with stochastic epidemic models. However, the accuracy of the estimated model parameters depends on several factors including the statistical inference methodologies that are used. One approach to making inferences from multiple outbreak data is the use of a Bayesian hierarchical model. This statistical framework allows simultaneous inference for multiple outbreaks and the estimation of model parameters at a group level. A hierarchical model will generally provide improved estimates; however, we show that this is not always true when the variability among model parameter values of the outbreaks is high. We further show that subsets of outbreaks with similar parameter values can be identified prior to a hierarchical analysis using common clustering algorithms such as k-means. When hierarchical analyses are carried out for these pre-identified subsets of outbreaks, parameter estimates are improved compared to those estimated under a hierarchical analysis for the complete set of outbreaks. We have applied our estimation framework within a simulation-based experiment using synthetic data generated from stochastic SIRS models. The framework is generalizable to other biological data.