A Network-based Analysis of the 1861 Hagelloch Measles Data
Article first published online: 24 FEB 2012
© 2012, The International Biometric Society
Volume 68, Issue 3, pages 755–765, September 2012
How to Cite
Groendyke, C., Welch, D. and Hunter, D. R. (2012), A Network-based Analysis of the 1861 Hagelloch Measles Data. Biometrics, 68: 755–765. doi: 10.1111/j.1541-0420.2012.01748.x
- Issue published online: 26 SEP 2012
- Article first published online: 24 FEB 2012
- Received October 2011. Revised December 2011. Accepted January 2012.
- Exponential family Random Graph Model;
Summary In this article, we demonstrate a statistical method for fitting the parameters of a sophisticated network and epidemic model to disease data. The pattern of contacts between hosts is described by a class of dyadic independence exponential-family random graph models (ERGMs), whereas the transmission process that runs over the network is modeled as a stochastic susceptible-exposed-infectious-removed (SEIR) epidemic. We fit these models to very detailed data from the 1861 measles outbreak in Hagelloch, Germany. The network models include parameters for all recorded host covariates including age, sex, household, and classroom membership and household location whereas the SEIR epidemic model has exponentially distributed transmission times with gamma-distributed latent and infective periods. This approach allows us to make meaningful statements about the structure of the population—separate from the transmission process—as well as to provide estimates of various biological quantities of interest, such as the effective reproductive number, R. Using reversible jump Markov chain Monte Carlo, we produce samples from the joint posterior distribution of all the parameters of this model—the network, transmission tree, network parameters, and SEIR parameters—and perform Bayesian model selection to find the best-fitting network model. We compare our results with those of previous analyses and show that the ERGM network model better fits the data than a Bernoulli network model previously used. We also provide a software package, written in R, that performs this type of analysis.