Using Bayes' Rule to Define the Value of Evidence from Syndromic Surveillance

In this work we propose the adoption of a statistical framework used in the evaluation of forensic evidence as a tool for evaluating and presenting circumstantial “evidence” of a disease outbreak from syndromic surveillance. The basic idea is to exploit the predicted distributions of reported cases to calculate the ratio of the likelihood of observing n cases given an ongoing outbreak over the likelihood of observing n cases given no outbreak. The likelihood ratio defines the Value of Evidence (V). Using Bayes' rule, the prior odds for an ongoing outbreak are multiplied by V to obtain the posterior odds. This approach was applied to time series on the number of horses showing clinical respiratory symptoms or neurological symptoms. The separation between prior beliefs about the probability of an outbreak and the strength of evidence from syndromic surveillance offers a transparent reasoning process suitable for supporting decision makers. The value of evidence can be translated into a verbal statement, as often done in forensics or used for the production of risk maps. Furthermore, a Bayesian approach offers seamless integration of data from syndromic surveillance with results from predictive modeling and with information from other sources such as disease introduction risk assessments.

本研究提出将用于法医证据（forensic evidence）评估的统计框架，作为评估与呈现症状监测（syndromic surveillance）中疾病暴发间接‘证据’的工具。其核心思路为利用报告病例的预测分布，计算“疫情持续暴发前提下观测到n例病例”与“无暴发前提下观测到n例病例”的似然比（likelihood ratio）。该似然比即为证据价值（Value of Evidence，V）。依托贝叶斯法则（Bayes' rule），将疫情持续暴发的先验赔率（prior odds）与V相乘，即可得到后验赔率（posterior odds）。
本方法被应用于记录呈现临床呼吸道症状或神经系统症状的马匹数量的时间序列（time series）。将疫情暴发概率的先验认知与症状监测所得证据强度相分离，可形成透明化的推理流程，适用于辅助决策者开展工作。
证据价值可转化为文字表述，一如法医学领域的常规做法，或用于生成风险地图（risk maps）。此外，贝叶斯方法能够无缝整合症状监测数据、预测建模（predictive modeling）结果，以及疾病引入风险评估等其他来源的信息。