Search

An infectious disease typically spreads via contact between infected and susceptible individuals. Since the small-scale movements and contacts between people are generally not recorded, available data regarding infectious disease are often aggregations in space and time, yielding small-area counts of the number infected during successive, regular time intervals. In this paper, we develop a spatially descriptive, temporally dynamic hierarchical model to be fitted to such data. Disease counts are viewed as a realization from an underlying multivariate autoregressive process, where the relative risk of infection incorporates the space-time dynamic. We take a Bayesian approach, using Markov chain Monte Carlo to compute posterior estimates of all parameters of interest. We apply the methodology to an influenza epidemic in Scotland during the years 1989-1990., (Copyright 2002 John Wiley & Sons, Ltd.)

Disease incidence or disease mortality rates for small areas are often displayed on maps. Maps of raw rates, disease counts divided by the total population at risk, have been criticized as unreliable due to non-constant variance associated with heterogeneity in base population size. This has led to the use of model-based Bayes or empirical Bayes point estimates for map creation. Because the maps have important epidemiological and political consequences, for example, they are often used to identify small areas with unusually high or low unexplained risk, it is important that the assumptions of the underlying models be scrutinized. We review the use of posterior predictive model checks, which compare features of the observed data to the same features of replicate data generated under the model, for assessing model fitness. One crucial issue is whether extrema are potentially important epidemiological findings or merely evidence of poor model fit. We propose the use of the cross-validation posterior predictive distribution, obtained by reanalyzing the data without a suspect small area, as a method for assessing whether the observed count in the area is consistent with the model. Because it may not be feasible to actually reanalyze the data for each suspect small area in large data sets, two methods for approximating the cross-validation posterior predictive distribution are described., (Copyright 2000 John Wiley & Sons, Ltd.)