Geographically dependent individual-level models for infectious diseases transmission

Infectious disease models can be of great use for understanding the underlying mechanisms that influence the spread of diseases and predicting future disease progression. Modeling has been increasingly used to evaluate the potential impact of different control measures and to guide public health policy decisions. In recent years, there has been rapid progress in developing spatio-temporal modeling of infectious diseases and an example of such recent developments is the discrete-time individual-level models (ILMs). These models are well developed and provide a common framework for modeling many disease systems; however, they assume the probability of disease transmission between two individuals depends only on their spatial separation and not on their spatial locations. In cases where spatial location itself is important for understanding the spread of emerging infectious diseases and identifying their causes, it would be beneficial to incorporate the effect of spatial location in the model. In this study, we thus generalize the ILMs to a new class of geographically dependent ILMs, to allow for the evaluation of the effect of spatially varying risk factors (e.g., education, social deprivation, environmental), as well as unobserved spatial structure, upon the transmission of infectious disease. Specifically, we consider a conditional autoregressive (CAR) model to capture the effects of unobserved spatially structured latent covariates or measurement error. This results in flexible infectious disease models that can be used for formulating etiological hypotheses and identifying geographical regions of unusually high risk to formulate preventive action. The reliability of these models is investigated on a combination of simulated epidemic data and Alberta seasonal influenza outbreak data ($2009$). This new class of models is fitted to data within a Bayesian statistical framework using Markov chain Monte Carlo methods.

Use of a voluntary testing program to study the spatial epidemiology of Johne's disease affecting dairy herds in Minnesota: a cross sectional study

Background

One of the key steps in the management of chronic diseases in animals including Johne’s disease (JD), caused by Mycobacterium avium subsp. paratuberculosis (MAP), is the ability to track disease incidence over space and time. JD surveillance in the U.S. dairy cattle is challenging due to lack of regulatory requirements, imperfect diagnostic tests, and associated expenses, including time and labor. An alternative approach is to use voluntary testing programs. Here, data from a voluntary JD testing program, conducted by the Minnesota Dairy Herd Improvement Association, were used to: a) explore whether such a program provides representative information on JD-prevalence in Minnesota dairy herds, b) estimate JD distribution, and, c) identify herd and environmental factors associated with finding JD-positive cows. Milk samples (n = 70,809) collected from 54,652 unique cows from 600 Minnesota dairy herds between November 2014 and April 2017 were tested using a MAP antibody ELISA. Participant representativeness was assessed by comparing the number of JD-tested herds with the number of herds required to estimate the true disease prevalence per county based on official statistics from the National Agricultural Statistical Services. Multivariable logistic regression models, with and without spatial dependence between observations, were then used to investigate the association between herd status to JD (positive/negative), as indicated by milk ELISA results, and available covariates at the herd level.

Results

Within the study population, at least one test-positive cow was found in 414 of 600 (69%) herds. Results indicated that large herds that test frequently and herds located in loamy or silt soils are more likely to have at least one MAP test-positive cow. After adjusting for herd size, testing frequency, and soil type, there was no spatial dependence in JD risk between neighboring dairies within 5 to 20 km. Furthermore, the importance of collecting data on herd management, feed, and biosecurity for insightful interpretations was recognized. The study suggested that, although limited, the voluntary testing database may support monitoring JD status.

Conclusions

Results presented here help elucidate the spatial characteristics of JD in Minnesota and the study may ultimately contribute to the design and implementation of surveillance programs for the disease.

A spatially explicit hierarchical model to characterize population viability

Many of the processes that govern the viability of animal populations vary spatially, yet population viability analyses (PVAs) that account explicitly for spatial variation are rare. We develop a PVA model that incorporates autocorrelation into the analysis of local demographic information to produce spatially explicit estimates of demography and viability at relatively fine spatial scales across a large spatial extent. We use a hierarchical, spatial, autoregressive model for capture-recapture data from multiple locations to obtain spatially explicit estimates of adult survival (ϕ_ad ), juvenile survival (ϕ_juv ), and juvenile-to-adult transition rates (ψ), and a spatial autoregressive model for recruitment data from multiple locations to obtain spatially explicit estimates of recruitment (R). We combine local estimates of demographic rates in stage-structured population models to estimate the rate of population change (λ), then use estimates of λ (and its uncertainty) to forecast changes in local abundance and produce spatially explicit estimates of viability (probability of extirpation, P_ex ). We apply the model to demographic data for the Sonoran desert tortoise (Gopherus morafkai) collected across its geographic range in Arizona. There was modest spatial variation in λ^ (0.94-1.03), which reflected spatial variation in ϕ^ad (0.85-0.95), ϕ^juv (0.70-0.89), and ψ^ (0.07-0.13). Recruitment data were too sparse for spatially explicit estimates; therefore, we used a range-wide estimate ( R^  = 0.32 1-yr-old females per female per year). Spatial patterns in demographic rates were complex, but ϕ^ad , ϕ^juv , and λ^ tended to be lower and ψ^ higher in the northwestern portion of the range. Spatial patterns in P_ex varied with local abundance. For local abundances >500, P_ex was near zero (<0.05) across most of the range after 100 yr; as abundances decreased, however, P_ex approached one in the northwestern portion of the range and remained low elsewhere. When local abundances were <50, western and southern populations were vulnerable (P_ex  > 0.25). This approach to PVA offers the potential to reveal spatial patterns in demography and viability that can inform conservation and management at multiple spatial scales, provide insight into scale-related investigations in population ecology, and improve basic ecological knowledge of landscape-level phenomena.

Accommodating the ecological fallacy in disease mapping in the absence of individual exposures

In health exposure modeling, in particular, disease mapping, the ecological fallacy arises because the relationship between aggregated disease incidence on areal units and average exposure on those units differs from the relationship between the event of individual incidence and the associated individual exposure. This article presents a novel modeling approach to address the ecological fallacy in the least informative data setting. We assume the known population at risk with an observed incidence for a collection of areal units and, separately, environmental exposure recorded during the period of incidence at a collection of monitoring stations. We do not assume any partial individual level information or random allocation of individuals to observed exposures. We specify a conceptual incidence surface over the study region as a function of an exposure surface resulting in a stochastic integral of the block average disease incidence. The true block level incidence is an unavailable Monte Carlo integration for this stochastic integral. We propose an alternative manageable Monte Carlo integration for the integral. Modeling in this setting is immediately hierarchical, and we fit our model within a Bayesian framework. To alleviate the resulting computational burden, we offer 2 strategies for efficient model fitting: one is through modularization, the other is through sparse or dimension-reduced Gaussian processes. We illustrate the performance of our model with simulations based on a heat-related mortality dataset in Ohio and then analyze associated real data.

Support vector machine in crash prediction at the level of traffic analysis zones: Assessing the spatial proximity effects

In zone-level crash prediction, accounting for spatial dependence has become an extensively studied topic. This study proposes Support Vector Machine (SVM) model to address complex, large and multi-dimensional spatial data in crash prediction. Correlation-based Feature Selector (CFS) was applied to evaluate candidate factors possibly related to zonal crash frequency in handling high-dimension spatial data. To demonstrate the proposed approaches and to compare them with the Bayesian spatial model with conditional autoregressive prior (i.e., CAR), a dataset in Hillsborough county of Florida was employed. The results showed that SVM models accounting for spatial proximity outperform the non-spatial model in terms of model fitting and predictive performance, which indicates the reasonableness of considering cross-zonal spatial correlations. The best model predictive capability, relatively, is associated with the model considering proximity of the centroid distance by choosing the RBF kernel and setting the 10% of the whole dataset as the testing data, which further exhibits SVM models' capacity for addressing comparatively complex spatial data in regional crash prediction modeling. Moreover, SVM models exhibit the better goodness-of-fit compared with CAR models when utilizing the whole dataset as the samples. A sensitivity analysis of the centroid-distance-based spatial SVM models was conducted to capture the impacts of explanatory variables on the mean predicted probabilities for crash occurrence. While the results conform to the coefficient estimation in the CAR models, which supports the employment of the SVM model as an alternative in regional safety modeling.

Bayesian Inference for General Gaussian Graphical Models With Application to Multivariate Lattice Data

We introduce efficient Markov chain Monte Carlo methods for inference and model determination in multivariate and matrix-variate Gaussian graphical models. Our framework is based on the G-Wishart prior for the precision matrix associated with graphs that can be decomposable or non-decomposable. We extend our sampling algorithms to a novel class of conditionally autoregressive models for sparse estimation in multivariate lattice data, with a special emphasis on the analysis of spatial data. These models embed a great deal of flexibility in estimating both the correlation structure across outcomes and the spatial correlation structure, thereby allowing for adaptive smoothing and spatial autocorrelation parameters. Our methods are illustrated using a simulated example and a real-world application which concerns cancer mortality surveillance. Supplementary materials with computer code and the datasets needed to replicate our numerical results together with additional tables of results are available online.