We extend an interesting class of space–time models for infectious disease data proposed by Held and co-workers, to analyse data on hand, foot and mouth disease, collected in the central north region of China over 2009–2011. We provide a careful derivation of the model and extend the model class in two directions. First, we model the disease transmission between age–gender strata, in addition to space and time. Second, we use our model for inference on effective local reproductive numbers. For the hand, foot and mouth data, for each of the six age–gender strata we consider that transmission is greatest between individuals within the same strata, with also relatively high transmission between individuals of the same age group but the opposite gender. The local reproductive numbers show strong seasonality, and between-area differences.
Many diseases arise due to exposure to one of multiple possible pathogens. We consider the situation in which disease counts are available over time from a study region, along with a measure of clinical disease severity, for example, mild or severe. In addition, we suppose a subset of the cases are lab tested in order to determine the pathogen responsible for disease. In such a context, we focus interest on modeling the probabilities of disease incidence given pathogen type. The time course of these probabilities is of great interest as is the association with time‐varying covariates such as meteorological variables. In this set up, a natural Bayesian approach would be based on imputation of the unsampled pathogen information using Markov Chain Monte Carlo but this is computationally challenging. We describe a practical approach to inference that is easy to implement. We use an empirical Bayes procedure in a first step to estimate summary statistics. We then treat these summary statistics as the observed data and develop a Bayesian generalized additive model. We analyze data on hand, foot, and mouth disease (HFMD) in China in which there are two pathogens of primary interest, enterovirus 71 (EV71) and Coxackie A16 (CA16). We find that both EV71 and CA16 are associated with temperature, relative humidity, and wind speed, with reasonably similar functional forms for both pathogens. The important issue of confounding by time is modeled using a penalized B‐spline model with a random effects representation. The level of smoothing is addressed by a careful choice of the prior on the tuning variance.
In recent years, the availability of infectious disease counts in time and space has increased, and consequently, there has been renewed interest in model formulation for such data. In this paper, we describe a model that was motivated by the need to analyze hand, foot, and mouth disease surveillance data in China. The data are aggregated by geographical areas and by week, with the aims of the analysis being to gain insight into the space–time dynamics and to make short‐term predictions, which will aid in the implementation of public health campaigns in those areas with a large predicted disease burden. The model we develop decomposes disease‐risk into marginal spatial and temporal components and a space–time interaction piece. The latter is the crucial element, and we use a tensor product spline model with a Markov random field prior on the coefficients of the basis functions. The model can be formulated as a Gaussian Markov random field and so fast computation can be carried out using the integrated nested Laplace approximation approach. A simulation study shows that the model can pick up complex space–time structure and our analysis of hand, foot, and mouth disease data in the central north region of China provides new insights into the dynamics of the disease.
Hierarchical modeling has been used extensively for small area estimation. However, design weights that are required to reflect complex surveys are rarely considered in these models. We develop computationally efficient, Bayesian spatial smoothing models that acknowledge the design weights. Computation is carried out using the integrated nested Laplace approximation, which is fast. A simulation study is presented that considers the effects of non-response and non-random selection of individuals. We examine the impact of ignoring the design weights and the benefits of spatial smoothing. The results show that, when compared with standard approaches, mean squared error can be greatly reduced with the proposed models. Bias reduction occurs through the inclusion of the design weights, with variance reduction being achieved through hierarchical smoothing. We analyze data from the Washington State 2006 Behavioral Risk Factor Surveillance System. The models are easily and quickly fitted within the R environment, using existing packages.