Analyses of infectious disease data from household outbreaks by Markov chain Monte Carlo methods

The analysis of infectious disease data presents challenges arising from th e dependence in the data and the fact that only part of the transmission pr ocess is observable. These difficulties are usually overcome by making simp lifying assumptions. The paper explores the use of Markov chain Monte Carlo (MCMC) methods for the analysis of infectious disease data, with the hope that they will permit analyses to be made under more realistic assumptions. Two important kinds of data sets are considered, containing temporal and n on-temporal information, from outbreaks of measles and influenza. Stochasti c epidemic models are used to describe the processes that generate the data . MCMC methods are then employed to perform inference in a Bayesian context for the model parameters. The MCMC methods used include standard algorithm s, such as the Metropolis-Hastings algorithm and the Gibbs sampler, as well as a new method that involves likelihood approximation. It is found that s tandard algorithms perform well in some situations but can exhibit serious convergence difficulties in others. The inferences that we obtain are in br oad agreement with estimates obtained by other methods where they are avail able. However, we can also provide inferences for parameters which have not been reported in previous analyses.