Bayesian approaches to epidemiological surveillance: a review and introduction for risk-assessors and decision-makers.

Quality decision making in public health and animal health surveillance relies on addressing the challenge of synthesizing health-related information from disparate sources into actionable information. In the case of early warning systems for impending outbreaks this challenge is compounded with the need for evidence generation in real-time, and timely decision-making. The analysts running and interpreting the output from the epidemiological surveillance algorithms must present those in a format that is appropriate to those who have responsibility for taking action. We argue that the Bayesian inference framework, which provides a posterior probability for a given disease state, can be easily combined with a decision theory framework to support decision-making for disease surveillance and control in a transparent way. We provide a simple introduction to Bayesian approaches to epidemiological surveillance, with a particular focus on syndromic surveillance (SyS), that covers:(i) full Bayes (hierarchical) models; (ii) empirical Bayes models; and (iii) semi-Bayes models that use Bayesian approaches to estimate model parameter distributions but that produce an output not intended for Bayesian inference.  We illustrate the flexibility and robustness of applying Bayesian probabilistic reasoning with three working examples based on animal SyS data from France and Norway.

In more complex SyS scenarios, the main drawback of applying full Bayesian methods resides in the challenge of setting prior probabilities and the demanding computations, which may necessitate the use of approximate solutions. As an alternative approach, a framework for communicating SyS results based on the Bayes factor, i.e. the ratio between the posterior and prior odds that an outbreak is ongoing against an alternative hypothesis, is presented. Such explicit separation of prior information about a hypothesis and evidence from the data makes the framework useful for presenting results even when the modelling approach is not in itself Bayesian.