Bayesian monitoring of emerging infectious diseases

Abstract

We define data analyses to monitor a change in R, the average number of secondary cases caused by a typical infected individual. The input dataset consists of incident cases partitioned into outbreaks, each initiated from a single index case. We split the input dataset into two successive subsets, to evaluate two successive R values, according to the Bayesian paradigm. We used the Bayes factor between the model with two different R values and that with a single R value to justify that the change in R is statistically significant. We validated our approach using simulated data, generated using known R. In particular, we found that claiming two distinct R values may depend significantly on the number of outbreaks. We then reanalyzed data previously studied by Jansen et al. [Jansen et al. Science 301(5634), 804], concerning the effective reproduction number for measles in the UK, during 1995-2002. Our analyses showed that the 1995-2002 dataset should be divided into two separate subsets for the periods 1995-1998 and 1999-2002. In contrast, Jansen et al. take this splitting point as input of their analysis. Our estimated effective reproduction numbers R are in good agreement with those found by Jansen et al. In conclusion, our methodology for detecting temporal changes in R using outbreak-size data worked satisfactorily with both simulated and real-world data. The methodology may be used for updating R in real time, as surveillance outbreak data become available.