Residual Spatial Correlation Between Geographically Referenced Observations

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Abstract
Analytic methods commonly used in epidemiology do not account for spatial correlation between observations. In regression analyses, this omission can bias parameter estimates and yield incorrect standard error estimates. We present a Bayesian hierarchical model (BHM) approach that accounts for spatial correlation, and illustrate its strengths and weaknesses by applying this modeling approach to data on Wuchereria bancrofti infection in Haiti. A program to eliminate lymphatic filariasis in Haiti assessed prevalence of W. bancrofti infection in 57 schools across Leogane Commune. We analyzed the spatial pattern in the prevalence data using semi-variograms and correlograms. We then modeled the data using (1) standard logistic regression (GLM); (2) non-Bayesian logistic generalized linear mixed models (GLMMs) with school-specific nonspatial random effects; (3) BHMs with school-specific nonspatial random effects; and (4) BHMs with spatial random effects. An exponential semi-variogram with an effective range of 2.15 km best fit the data. GLMM and nonspatial BHM point estimates were comparable and also were generally similar with the marginal GLM point estimates. In contrast, compared with the nonspatial mixed model results, spatial BHM point estimates were markedly attenuated. The clear spatial pattern evident in the Haitian W. bancrofti prevalence data and the observation that point estimates and standard errors differed depending on the modeling approach indicate that it is important to account for residual spatial correlation in analyses of W. bancrofti infection data. Bayesian hierarchical models provide a flexible, readily implementable approach to modeling spatially correlated data. However, our results also illustrate that spatial smoothing must be applied with care.

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