Bayesian hierarchical models for disease mapping applied to contagious pathologies

Improving estimates of waning immunity rates in stochastic SIRS models with a hierarchical framework

As most disease causing pathogens require transmission from an infectious individual to a susceptible individual, continued persistence of the pathogen within the population requires the replenishment of susceptibles through births, immigration, or waning immunity. Consider the introduction of an unknown infectious disease into a fully susceptible population where it is not known how long immunity is conferred once an individual recovers from infection. If, initially, the prevalence of disease increases (that is, the infection takes off), the number of infectives will usually decrease to a low level after the first major outbreak. During this post-outbreak period, the disease dynamics may be influenced by stochastic effects and there is a non-zero probability that the epidemic will die out. Die out in this period following the first major outbreak is known as an epidemic fade-out. If the disease does not die out, the susceptible population may be replenished by the waning of immunity, and a second wave may start. In this study, we investigate if the rate of waning immunity (and other epidemiological parameters) can be reliably estimated from multiple outbreak data, in which some outbreaks display epidemic fade-out and others do not. We generated synthetic outbreak data from independent simulations of stochastic SIRS models in multiple communities. Some outbreaks faded-out and some did not. We conducted Bayesian parameter estimation under two alternative approaches: independently on each outbreak and under a hierarchical framework. When conducting independent estimation, the waning immunity rate was poorly estimated and biased towards zero when an epidemic fade-out was observed. However, under a hierarchical approach, we obtained more accurate and precise posterior estimates for the rate of waning immunity and other epidemiological parameters. The greatest improvement in estimates was obtained for those communities in which epidemic fade-out was observed. Our findings demonstrate the feasibility and value of adopting a Bayesian hierarchical approach for parameter inference for stochastic epidemic models.

Phylogeography as a Proxy for Population Connectivity for Spatial Modeling of Foot-and-Mouth Disease Outbreaks in Vietnam

Bayesian space-time regression models are helpful tools to describe and predict the distribution of infectious disease outbreaks and to delineate high-risk areas for disease control. In these models, structured and unstructured spatial and temporal effects account for various forms of non-independence amongst case counts across spatial units. Structured spatial effects capture correlations in case counts amongst neighboring provinces arising from shared risk factors or population connectivity. For highly mobile populations, spatial adjacency is an imperfect measure of connectivity due to long-distance movement, but we often lack data on host movements. Phylogeographic models inferring routes of viral dissemination across a region could serve as a proxy for patterns of population connectivity. The objective of this study was to investigate whether the effects of population connectivity in space-time regressions of case counts were better captured by spatial adjacency or by inferences from phylogeographic analyses. To compare these two approaches, we used foot-and-mouth disease virus (FMDV) outbreak data from across Vietnam as an example. We identified that accounting for virus movement through phylogeographic analysis serves as a better proxy for population connectivity than spatial adjacency in spatial-temporal risk models. This approach may contribute to design surveillance activities in countries lacking movement data.

Bayesian Hierarchical Spatial Modeling of COVID-19 Cases in Bangladesh

This research aimed to investigate the spatial autocorrelation and heterogeneity throughout Bangladesh's 64 districts. Moran I and Geary C are used to measure spatial autocorrelation. Different conventional models, such as Poisson-Gamma and Poisson-Lognormal, and spatial models, such as Conditional Autoregressive (CAR) Model, Convolution Model, and modified CAR Model, have been employed to detect the spatial heterogeneity. Bayesian hierarchical methods via Gibbs sampling are used to implement these models. The best model is selected using the Deviance Information Criterion. Results revealed Dhaka has the highest relative risk due to the city's high population density and growth rate. This study identifies which district has the highest relative risk and which districts adjacent to that district also have a high risk, which allows for the appropriate actions to be taken by the government agencies and communities to mitigate the risk effect.

A Model for Highly Fluctuating Spatio-Temporal Infection Data, with Applications to the COVID Epidemic

Spatio-temporal models need to address specific features of spatio-temporal infection data, such as periods of stable infection levels (endemicity), followed by epidemic phases, as well as infection spread from neighbouring areas. In this paper, we consider a mixture-link model for infection counts that allows alternation between epidemic phases (possibly multiple) and stable endemicity, with higher AR1 coefficients in epidemic phases. This is a form of regime-switching, allowing for non-stationarity in infection levels. We adopt a generalised Poisson model appropriate to the infection count data and avoid transformations (e.g., differencing) to alternative metrics, which have been adopted in many studies. We allow for neighbourhood spillover in infection, which is also governed by adaptive regime-switching. Compared to existing models, the observational (in-sample) model is expected to better reflect the balance between epidemic and endemic tendencies, and short-term extrapolations are likely to be improved. Two case study applications involve COVID area-time data, one for 32 London boroughs (and 96 weeks) since the start of the COVID epidemic, the other for a shorter time span focusing on the epidemic phase in 144 areas of Southeast England associated with the Alpha variant. In both applications, the proposed methods produce a better in-sample fit and out-of-sample short term predictions. The spatial dynamic implications are highlighted in the case studies.

A spatio-temporal autoregressive model for monitoring and predicting COVID infection rates

The COVID-19 epidemic has raised major issues with regard to modelling and forecasting outcomes such as cases, deaths and hospitalisations. In particular, the forecasting of area-specific counts of infectious disease poses problems when counts are changing rapidly and there are infection hotspots, as in epidemic situations. Such forecasts are of central importance for prioritizing interventions or making severity designations for different areas. In this paper, we consider different specifications of autoregressive dependence in incidence counts as these may considerably impact on adaptivity in epidemic situations. In particular, we introduce parameters to allow temporal adaptivity in autoregressive dependence. A case study considers COVID-19 data for 144 English local authorities during the UK epidemic second wave in late 2020 and early 2021, which demonstrate geographical clustering in new cases-linked to the then emergent alpha variant. The model allows for both spatial and time variation in autoregressive effects. We assess sensitivity in short-term predictions and fit to specification (spatial vs space-time autoregression, linear vs log-linear, and form of space decay), and show improved one-step ahead and in-sample prediction using space-time autoregression including temporal adaptivity.

Spatiotemporal high-resolution prediction and mapping: methodology and application to dengue disease

Dengue disease has become a major public health problem. Accurate and precise identification, prediction and mapping of high-risk areas are crucial elements of an effective and efficient early warning system in countering the spread of dengue disease. In this paper, we present the fusion area-cell spatiotemporal generalized geoadditive-Gaussian Markov random field (FGG-GMRF) framework for joint estimation of an area-cell model, involving temporally varying coefficients, spatially and temporally structured and unstructured random effects, and spatiotemporal interaction of the random effects. The spatiotemporal Gaussian field is applied to determine the unobserved relative risk at cell level. It is transformed to a Gaussian Markov random field using the finite element method and the linear stochastic partial differential equation approach to solve the "big n" problem. Sub-area relative risk estimates are obtained as block averages of the cell outcomes within each sub-area boundary. The FGG-GMRF model is estimated by applying Bayesian Integrated Nested Laplace Approximation. In the application to Bandung city, Indonesia, we combine low-resolution area level (district) spatiotemporal data on population at risk and incidence and high-resolution cell level data on weather variables to obtain predictions of relative risk at subdistrict level. The predicted dengue relative risk at subdistrict level suggests significant fine-scale heterogeneities which are not apparent when examining the area level. The relative risk varies considerably across subdistricts and time, with the latter showing an increase in the period January-July and a decrease in the period August-December.

SUPPLEMENTARY INFORMATION

The online version contains supplementary material available at 10.1007/s10109-021-00368-0.