Poisson-Gamma Mixture Spatially Varying Coefficient Modeling of Small-Area Intestinal Parasites Infection

Abstract

Understanding the spatially varying effects of demographic factors on the spatio-temporal variation of intestinal parasites infections is important for public health intervention and monitoring. This paper presents a hierarchical Bayesian spatially varying coefficient model to evaluate the effects demographic factors on intestinal parasites morbidities in Ghana. The modeling relied on morbidity data collected by the District Health Information Management Systems. We developed Poisson and Poisson-gamma spatially varying coefficient models. We used the demographic factors, unsafe drinking water, unsafe toilet, and unsafe liquid waste disposal as model covariates. The models were fitted using the integrated nested Laplace approximations (INLA). The overall risk of intestinal parasites infection was estimated to be 10.9 per 100 people with a wide spatial variation in the district-specific posterior risk estimates. Substantial spatial variation of increasing multiplicative effects of unsafe drinking water, unsafe toilet, and unsafe liquid waste disposal occurs on the variation of intestinal parasites risk. The structured residual spatial variation widely dominates the unstructured component, suggesting that the unaccounted-for risk factors are spatially continuous in nature. The study concludes that both the spatial distribution of the posterior risk and the associated exceedance probability maps are essential for monitoring and control of intestinal parasites.

Identifying Spatiotemporal Clusters by Means of Agglomerative Hierarchical Clustering and Bayesian Regression Analysis with Spatiotemporally Varying Coefficients: Methodology and Application to Dengue Disease in Bandung, Indonesia

“…The approximated marginal posterior distribution can be used to compute summary statistics of interest such as the posterior mean, variance or quantile. For the impact of the k-th risk factor, we take from the estimated Poisson regression model (i) its posterior marginal mean and (ii) its cluster-specific effect as a fraction of its posterior marginal variance across the spatiotemporal clusters relative to the total of the posterior marginal variances of the cluster-specific effects and the structured and unstructured spatial and temporal pure effects, and their interaction (Osei, Stein, and Ofosu 2019). The global effect is commonly presented as the percentage change of the relative risk for a unit change of the risk factor, because it = ln it is the dependent variable, that is, it = e it with it as a linear function of the risk factors (Blangiardo and Cameletti 2015).…”

“…posterior distribution. The relative contribution of the k-th cluster-specific effect is thus given by Osei, Stein, and Ofosu 2019). Risk factors such as weather or socioeconomic variables tend to be highly correlated, which can lead to unstable parameter estimates and inflated standard errors, such that the impacts of the risk factors cannot adequately be identified (Meloun et al 2002;Dormann et al 2013).…”

“…There is also an identification problem between the overall effects of the covariates ( k ) and the random cluster-specific effects ( lk ). To control for it, a sum-to-zero constraint on the cluster-specific effect ∑ g l = 1 lk = 0 can be imposed (Ugarte, Adin, and Goicoa 2017;Osei, Stein, and Ofosu 2019). The above sum-to-zero constrains are imposed in INLA by using the constr = TRUE argument in the function f(•) defining the spatial, temporal, spatiotemporal interaction and cluster-specific vectors of the random effects.…”

Spatiotemporally Varying Coefficients (STVC) model: a Bayesian local regression to detect spatial and temporal nonstationarity in variables relationships

“…, then the conditional distribution of μ i is given (Osei, Stein, and Ofosu 2019;Bakka et al 2018), where w ij is a spatial proximity matrix, w ij ¼ 1 if i and j are neighbours i ~ j (e.g., sharing a common boundary in this case), and 0 otherwise. The mean of the joint prior distribution ρðμ i σ 2 μ � � � Þ is therefore set to zero with precision matrix σ À 2 μ Q μ , where Q μ is a structural matrix deduced from the binary proximity matrix w ij .…”

Bayesian Spatiotemporal Modeling and Mapping of Infectious Diseases

“…The approximated marginal posterior distribution can be used to compute summary statistics of interest such as the posterior mean, variance or quantile. For the impact of the eth risk factor, we take from the estimated Poisson regression model (i) its posterior marginal mean and (ii) its cluster-specific effect as a fraction of its posterior marginal variance across the spatiotemporal clusters relative to the total of the posterior marginal variances of the cluster-specific effects and the structured and unstructured spatial and temporal pure effects, and their interaction (Osei et al 2019). The global effect is commonly presented as the percentage change of the relative risk for a unit change of the risk factor, because È 56 = log(-56 )…”