Spatial modeling using mixed models: an ecologic study of visceral leishmaniasis in Teresina, Piauí State, Brazil

Most ecologic studies use geographical areas as units of observation. Because data from areas close to one another tend to be more alike than those from distant areas, estimation of effect size and confidence intervals should consider spatial autocorrelation of measurements. In this report we demonstrate a method for modeling spatial autocorrelation within a mixed model framework, using data on environmental and socioeconomic determinants of the incidence of visceral leishmaniasis (VL) in the city of Teresina, Piauí, Brazil. A model with a spherical covariance structure indicated significant spatial autocorrelation in the data and yielded a better fit than one assuming independent observations. While both models showed a positive association between VL incidence and residence in a favela (slum) or in areas with green vegetation, values for the fixed effects and standard errors differed substantially between the models. Exploration of the data's spatial correlation structure through the semivariogram should precede the use of these models. Our findings support the hypothesis of spatial dependence of VL rates and indicate that it might be useful to model spatial correlation in order to obtain more accurate point and standard error estimates.