Efficient Data Augmentation for Fitting Stochastic Epidemic Models to Prevalence Data

ABSTRACT

Stochastic epidemic models describe the dynamics of an epidemic as a disease spreads through a population. Typically, only a fraction of cases are observed at a set of discrete times. The absence of complete information about the time evolution of an epidemic gives rise to a complicated latent variable problem in which the state space size of the epidemic grows large as the population size increases. This makes analytically integrating over the missing data infeasible for populations of even moderate size. We present a data augmentation Markov chain Monte Carlo (MCMC) framework for Bayesian estimation of stochastic epidemic model parameters, in which measurements are augmented with subject-level disease histories. In our MCMC algorithm, we propose each new subject-level path, conditional on the data, using a time-inhomogenous continuous-time Markov process with rates determined by the infection histories of other individuals. The method is general, and may be applied to a broad class of epidemic models with only minimal modifications to the model dynamics and/or emission distribution. We present our algorithm in the context of multiple stochastic epidemic models in which the data are binomially sampled prevalence counts, and apply our method to data from an outbreak of influenza in a British boarding school. Supplementary material for this article is available online.

KEYWORDS:

• Bayesian data augmentation
• Continuous-time Markov chain
• Epidemic count data
• Hidden Markov model
• Stochastic epidemic model

Supplementary Materials

S1-S5: Additional mathematical and algorithmic details. S6-12: MCMC specification, supplementary results, and convergence diagnostics for simulations. S13: MCMC specification, additional results, and supplementary analysis of the British boarding school data.

Acknowledgments

J.F., J.W., and V.N.M. were supported by the NIH grant U54 GM111274. J.W. was supported by the NIH grant R01 CA095994. V.N.M. was supported by the NIH grant R01 AI107034. The authors thank Aaron King and the rest of the authors of the pomp package for their help with the PMMH algorithm that served as a benchmark for the methods presented in this article.