Bayesian spatial modeling of disease risk in relation to multivariate environmental risk fields

Abstract

The relationship between exposure to environmental chemicals during pregnancy and early childhood development is an important issue which has a spatial risk component. In this context, we have examined mental retardation and developmental delay (MRDD) outcome measures for children in a Medicaid population in South Carolina and sampled measures of soil chemistry (e.g. As, Hg, etc.) on a network of sites which are misaligned to the outcome residential addresses during pregnancy. The true chemical concentration at the residential addresses is not observed directly and must be interpolated from soil samples. In this study, we have developed a Bayesian joint model which interpolates soil chemical fields and estimates the associated MRDD risk simultaneously. Having multiple spatial fields to interpolate, we have considered a low-rank Kriging method for the interpolation which requires less computation than Bayesian Kriging. We performed a sensitivity analysis for a bivariate smoothing, changing the number of knots and the smoothing parameter. These analyses show that a low-rank Kriging method can be used as an alternative to a full-rank Kriging, reducing computational burden. However, the number of knots for the low-rank Kriging model need to be selected with caution as a bivariate surface estimation can be sensitive to the choice of the number of knots.

Associations between soil lead concentrations and populations by race/ethnicity and income-to-poverty ratio in urban and rural areas

“…The objectives of the current study were to compare two rural and two urban areas identified in our previous research as containing a cluster of ID in children (Cai et al 2011; Kim et al 2009, 2010; Zhen et al 2008, 2009), and to determine, within these sampling areas, whether high populations of racial/ethnic minorities, and individuals with a low income-to-poverty ratio (ITPR), were positively associated with spatially interpolated Pb concentrations at the United States (US) Census 2000 block group level. These groups, both historically and currently, have been disproportionately exposed to environmental contaminants (Brown 1995).…”

Flexible geostatistical modeling and risk assessment analysis of lead concentration levels of residential soil in the Coeur D’Alene River Basin

“…The effect of knots specificacion in two-dimensional data has not been investigated in depth. Kim et al (2010) performed a sensitivity analysis for the selection of the number and location of the knots and compared the results with the full-rank kriging. They suggest that the results can be very sensitive to the choice of the spatial parameters (if it is choosen to be fixed as suggested in French and Wand (2004)).…”

“…They suggest that the results can be very sensitive to the choice of the spatial parameters (if it is choosen to be fixed as suggested in French and Wand (2004)). However, the use of lowrank kriging models are very sensitive to the selection of the number and position of the knots, with few knots the separation between them increases and the estimation of the spatial dependence and parameters become difficult (Ruppert et al, 2003;Kim et al, 2010). For the lead concentration levels, we found that the existence of high variability within a few kilometers or even within the same residential property caused difficulties for variogram analysis and the choice of an appropriate covariance structure for the selection of a spatial correlation.…”

Bayesian importance parameter modeling of misaligned predictors: soil metal measures related to residential history and intellectual disability in children

“…This research is motivated by a study of ID cases in children who were born to mothers who were pregnant, and insured by Medicaid, in South Carolina between 1996 and 2002 (Aelion et al 2009a, b; Kim et al 2009, 2010; Liu et al 2010; McDermott et al 2012, 2011; Zhen et al 2008). In our analysis, we included only the first child for each mother.…”

“…Various approaches have been used in the literature to model residential history (Cook et al 2009; Hoffman et al 2010; Kim et al 2009, 2010; Manjourides and Pagano 2011; Van den Hooven et al 2012; Vieira et al 2002, 2005; Wheeler et al 2012). Recently, with the advancement of geographical information systems, it has become easier to obtain point location data, resulting in an increased need for the development of statistical methods appropriate for this type of data.…”