Disease mapping of zero-excessive mesothelioma data in Flanders

PURPOSE

To investigate the distribution of mesothelioma in Flanders using Bayesian disease mapping models that account for both an excess of zeros and overdispersion.

METHODS

The numbers of newly diagnosed mesothelioma cases within all Flemish municipalities between 1999 and 2008 were obtained from the Belgian Cancer Registry. To deal with overdispersion, zero inflation, and geographical association, the hurdle combined model was proposed, which has three components: a Bernoulli zero-inflation mixture component to account for excess zeros, a gamma random effect to adjust for overdispersion, and a normal conditional autoregressive random effect to attribute spatial association. This model was compared with other existing methods in literature.

RESULTS

The results indicate that hurdle models with a random effects term accounting for extra variance in the Bernoulli zero-inflation component fit the data better than hurdle models that do not take overdispersion in the occurrence of zeros into account. Furthermore, traditional models that do not take into account excessive zeros but contain at least one random effects term that models extra variance in the counts have better fits compared to their hurdle counterparts. In other words, the extra variability, due to an excess of zeros, can be accommodated by spatially structured and/or unstructured random effects in a Poisson model such that the hurdle mixture model is not necessary.

CONCLUSIONS

Models taking into account zero inflation do not always provide better fits to data with excessive zeros than less complex models. In this study, a simple conditional autoregressive model identified a cluster in mesothelioma cases near a former asbestos processing plant (Kapelle-op-den-Bos). This observation is likely linked with historical local asbestos exposures. Future research will clarify this.

Surveillance of individual level disease maps

Methods for the production of individual (address) level disease maps are often retrospective; they estimate a map of the average relative risk of disease over a study period. However, recently, epidemiologists have started to look at weekly or monthly reports of disease and assess them for any change in the distribution of relative risk. For example, in the United States of America, the Centre for Disease Control and Prevention now routinely collects information on over 50 notifiable diseases every week. In this paper we present a method for the detection of a sudden change in the geographical distribution of the disease in a prospective study. The method is based on an estimate of the directional derivative of the conditional probability of a case, given either a case or control has occurred. It is based on standard kernel approaches to nonparametric regression and it is readily applied in any standard statistical software package. Two simulated examples of sudden clustering around a fixed point are provided.

Hierarchical probability models and Bayesian analysis of mine locations

Based on remote sensing of a potential minefield, point locations are identified, some of which may not be mines. The mines and mine-like objects are to be distinguished based on their point patterns, although it must be emphasized that all one sees is the superposition of their locations. In this paper, we construct a hierarchical spatial point-process model that accounts for the different patterns of mines and mine-like objects and uses posterior analysis to distinguish between them. Our Bayesian approach is applied to minefield data obtained from a multispectral video remote-sensing system.

Bayesian spatially dependent variable selection for small area health modeling

Statistical methods for spatial health data to identify the significant covariates associated with the health outcomes are of critical importance. Most studies have developed variable selection approaches in which the covariates included appear within the spatial domain and their effects are fixed across space. However, the impact of covariates on health outcomes may change across space and ignoring this behavior in spatial epidemiology may cause the wrong interpretation of the relations. Thus, the development of a statistical framework for spatial variable selection is important to allow for the estimation of the space-varying patterns of covariate effects as well as the early detection of disease over space. In this paper, we develop flexible spatial variable selection approaches to find the spatially-varying subsets of covariates with significant effects. A Bayesian hierarchical latent model framework is applied to account for spatially-varying covariate effects. We present a simulation example to examine the performance of the proposed models with the competing models. We apply our models to a county-level low birth weight incidence dataset in Georgia.

Potential sources and racial disparities in the residential distribution of soil arsenic and lead among pregnant women

Exposure to arsenic (As) or lead (Pb) has been associated with adverse health outcomes, and high-risk populations can be disproportionately exposed to these metals in soils. The objectives of this study were: to examine if predicted soil As and Pb concentrations at maternal residences of South Carolina (SC) low-income mothers differed based on maternal race (non-Hispanic black versus white), to examine whether differences in predicted residential soil As and Pb concentrations among black and white mothers differed by socioeconomic status (SES), and to examine whether such disparities persisted after controlling for anthropogenic sources of these metals, including direction from, and distance to industrial facilities. Kriged soil As and Pb concentrations were estimated at maternal residences in 11 locations in SC, and models with maternal race and individual and US Census block group level SES measures were examined. US Environmental Protection Agency Toxics Release Inventory (TRI) facility As and Pb releases categorized by distance and direction to block groups in which mothers resided were also identified, as were proxy measures for historic use of leaded gasoline (road density) and Pb-based paint (categories of median year home built by US Census block group). Consistent racial disparities were observed for predicted residential soil As and Pb concentrations, and the disparity was stronger for Pb than As (betas from adjusted models for black mothers were 0.12 and 2.2 for As and Pb, respectively, all p<0.006). Higher road density and older homes in block groups were more closely associated with higher predicted soil As and Pb concentrations than on-site releases of As and Pb categorized by facility location. These findings suggest that non-Hispanic black mothers in this study population had elevated residential As and Pb soil concentrations, after adjusting for SES, and that soil As and Pb concentrations were not associated with recent industrial releases.

A Bayesian semiparametric approach with change points for spatial ordinal data

The change-point model has drawn much attention over the past few decades. It can accommodate the jump process, which allows for changes of the effects before and after the change point. Intellectual disability is a long-term disability that impacts performance in cognitive aspects of life and usually has its onset prior to birth. Among many potential causes, soil chemical exposures are associated with the risk of intellectual disability in children. Motivated by a study for soil metal effects on intellectual disability, we propose a Bayesian hierarchical spatial model with change points for spatial ordinal data to detect the unknown threshold effects. The spatial continuous latent variable underlying the spatial ordinal outcome is modeled by the multivariate Gaussian process, which captures spatial variation and is centered at the nonlinear mean. The mean function is modeled by using the penalized smoothing splines for some covariates with unknown change points and the linear regression for the others. Some identifiability constraints are used to define the latent variable. A simulation example is presented to evaluate the performance of the proposed approach with the competing models. A retrospective cohort study for intellectual disability in South Carolina is used as an illustration.

Bayesian multiple imputation for missing multivariate longitudinal data from a Parkinson's disease clinical trial

In Parkinson's disease (PD) clinical trials, Parkinson's disease is studied using multiple outcomes of various types (e.g. binary, ordinal, continuous) collected repeatedly over time. The overall treatment effects across all outcomes can be evaluated based on a global test statistic. However, missing data occur in outcomes for many reasons, e.g. dropout, death, etc., and need to be imputed in order to conduct an intent-to-treat analysis. We propose a Bayesian method based on item response theory to perform multiple imputation while accounting for multiple sources of correlation. Sensitivity analysis is performed under various scenarios. Our simulation results indicate that the proposed method outperforms standard methods such as last observation carried forward and separate random effects model for each outcome. Our method is motivated by and applied to a Parkinson's disease clinical trial. The proposed method can be broadly applied to longitudinal studies with multiple outcomes subject to missingness.

Spatial mixture multiscale modeling for aggregated health data

One of the main goals in spatial epidemiology is to study the geographical pattern of disease risks. For such purpose, the convolution model composed of correlated and uncorrelated components is often used. However, one of the two components could be predominant in some regions. To investigate the predominance of the correlated or uncorrelated component for multiple scale data, we propose four different spatial mixture multiscale models by mixing spatially varying probability weights of correlated (CH) and uncorrelated heterogeneities (UH). The first model assumes that there is no linkage between the different scales and, hence, we consider independent mixture convolution models at each scale. The second model introduces linkage between finer and coarser scales via a shared uncorrelated component of the mixture convolution model. The third model is similar to the second model but the linkage between the scales is introduced through the correlated component. Finally, the fourth model accommodates for a scale effect by sharing both CH and UH simultaneously. We applied these models to real and simulated data, and found that the fourth model is the best model followed by the second model.

Scale effects in food environment research: Implications from assessing socioeconomic dimensions of supermarket accessibility in an eight-county region of South Carolina

Choice of neighborhood scale affects associations between environmental attributes and health-related outcomes. This phenomenon, a part of the modifiable areal unit problem, has been described fully in geography but not as it relates to food environment research. Using two administrative-based geographic boundaries (census tracts and block groups), supermarket geographic measures (density, cumulative opportunity and distance to nearest) were created to examine differences by scale and associations between three common U.S. Census-based socioeconomic status (SES) characteristics (median household income, percentage of population living below poverty and percentage of population with at least a high school education) and a summary neighborhood SES z-score in an eight-county region of South Carolina. General linear mixed-models were used. Overall, both supermarket density and cumulative opportunity were higher when using census tract boundaries compared to block groups. In analytic models, higher median household income was significantly associated with lower neighborhood supermarket density and lower cumulative opportunity using either the census tract or block group boundaries, and neighborhood poverty was positively associated with supermarket density and cumulative opportunity. Both median household income and percent high school education were positively associated with distance to nearest supermarket using either boundary definition, whereas neighborhood poverty had an inverse association. Findings from this study support the premise that supermarket measures can differ by choice of geographic scale and can influence associations between measures. Researchers should consider the most appropriate geographic scale carefully when conducting food environment studies.

The bivariate combined model for spatial data analysis

To describe the spatial distribution of diseases, a number of methods have been proposed to model relative risks within areas. Most models use Bayesian hierarchical methods, in which one models both spatially structured and unstructured extra-Poisson variance present in the data. For modelling a single disease, the conditional autoregressive (CAR) convolution model has been very popular. More recently, a combined model was proposed that 'combines' ideas from the CAR convolution model and the well-known Poisson-gamma model. The combined model was shown to be a good alternative to the CAR convolution model when there was a large amount of uncorrelated extra-variance in the data. Less solutions exist for modelling two diseases simultaneously or modelling a disease in two sub-populations simultaneously. Furthermore, existing models are typically based on the CAR convolution model. In this paper, a bivariate version of the combined model is proposed in which the unstructured heterogeneity term is split up into terms that are shared and terms that are specific to the disease or subpopulation, while spatial dependency is introduced via a univariate or multivariate Markov random field. The proposed method is illustrated by analysis of disease data in Georgia (USA) and Limburg (Belgium) and in a simulation study. We conclude that the bivariate combined model constitutes an interesting model when two diseases are possibly correlated. As the choice of the preferred model differs between data sets, we suggest to use the new and existing modelling approaches together and to choose the best model via goodness-of-fit statistics. Copyright © 2016 John Wiley & Sons, Ltd.

Bayesian model selection methods in modeling small area colon cancer incidence

PURPOSE

Many types of cancer have an underlying spatial incidence distribution. Spatial model selection methods can be useful when determining the linear predictor that best describes incidence outcomes.

METHODS

In this article, we examine the applications and benefits of using two different types of spatial model selection techniques, Bayesian model selection and Bayesian model averaging, in relation to colon cancer incidence in the state of Georgia, United States.

RESULTS

Both methods produce useful results that lead to the determination that median household income and percent African American population are important predictors of colon cancer incidence in the Northern counties of the state, whereas percent persons below poverty level and percent African American population are important in the Southern counties.

CONCLUSIONS

Of the two presented methods, Bayesian model selection appears to provide more succinct results, but applying the two in combination offers even more useful information into the spatial preferences of the alternative linear predictors.

Impact of Income on Small Area Low Birth Weight Incidence Using Multiscale Models

Low birth weight (LBW) is an important public health issue in the US as well as worldwide. The two main causes of LBW are premature birth and fetal growth restriction. Socio-economic status, as measured by family income has been correlated with LBW incidence at both the individual and population levels. In this paper, we investigate the impact of household income on LBW incidence at different geographical levels. To show this, we choose to examine LBW incidences collected from the state of Georgia, in the US, at both the county and public health (PH) district. The data at the PH district are an aggregation of the data at the county level nested within the PH district. A spatial scaling effect is induced during data aggregation from the county to the PH level. To address the scaling effect issue, we applied a shared multiscale model that jointly models the data at two levels via a shared correlated random effect. To assess the benefit of using the shared multiscale model, we compare it with an independent multiscale model which ignores the scale effect. Applying the shared multiscale model for the Georgia LBW incidence, we have found that income has a negative impact at both the county and PH levels. On the other hand, the independent multiscale model shows that income has a negative impact only at the county level. Hence, if the scale effect is not properly accommodated in the model, a different interpretation of the findings could result.

Bayesian multi-scale modeling for aggregated disease mapping data

In disease mapping, a scale effect due to an aggregation of data from a finer resolution level to a coarser level is a common phenomenon. This article addresses this issue using a hierarchical Bayesian modeling framework. We propose four different multiscale models. The first two models use a shared random effect that the finer level inherits from the coarser level. The third model assumes two independent convolution models at the finer and coarser levels. The fourth model applies a convolution model at the finer level, but the relative risk at the coarser level is obtained by aggregating the estimates at the finer level. We compare the models using the deviance information criterion (DIC) and Watanabe-Akaike information criterion (WAIC) that are applied to real and simulated data. The results indicate that the models with shared random effects outperform the other models on a range of criteria.

Comparing INLA and OpenBUGS for hierarchical Poisson modeling in disease mapping

The recently developed R package INLA (Integrated Nested Laplace Approximation) is becoming a more widely used package for Bayesian inference. The INLA software has been promoted as a fast alternative to MCMC for disease mapping applications. Here, we compare the INLA package to the MCMC approach by way of the BRugs package in R, which calls OpenBUGS. We focus on the Poisson data model commonly used for disease mapping. Ultimately, INLA is a computationally efficient way of implementing Bayesian methods and returns nearly identical estimates for fixed parameters in comparison to OpenBUGS, but falls short in recovering the true estimates for the random effects, their precisions, and model goodness of fit measures under the default settings. We assumed default settings for ground truth parameters, and through altering these default settings in our simulation study, we were able to recover estimates comparable to those produced in OpenBUGS under the same assumptions.

Does the metal content in soil around a pregnant woman's home increase the risk of low birth weight for her infant?

Low birth weight (LBW) is associated with a number of maternal environmental exposures during pregnancy. This study explored the association between soil metal concentrations around the home where the mother lived during pregnancy and the outcome of LBW. We used a retrospective cohort of 9,920 mother-child pairs who were insured by Medicaid during pregnancy and lived in ten residential areas, where we conducted soil sampling. We used a grid that overlaid the residential areas and collected soil samples at the grid intersections. The soil was analyzed for the concentration of eight metals [arsenic (As), barium (Ba), chromium (Cr), copper (Cu), lead (Pb), manganese (Mn), nickel (Ni), and mercury (Hg)], and we then used Bayesian Kriging to estimate the concentration at the actual maternal addresses, since we had the GIS coordinates of the homes. We used generalized additive modeling, because the metal concentrations had nonlinear associations with LBW, to develop the best fitting multivariable model for estimating the risk of LBW. The final model showed significant associations for female infants, maternal smoking during pregnancy, non-white mothers, Cu, and As with LBW. The As variable was nonlinear in relation to LBW, and the association between higher concentrations of As with LBW was strong (p = 0.002). We identified a statistically significant association between soil concentrations of arsenic around the home of pregnant women and an increased risk of LBW for her infant.

Joint spatial Bayesian modeling for studies combining longitudinal and cross-sectional data

Design for intervention studies may combine longitudinal data collected from sampled locations over several survey rounds and cross-sectional data from other locations in the study area. In this case, modeling the impact of the intervention requires an approach that can accommodate both types of data, accounting for the dependence between individuals followed up over time. Inadequate modeling can mask intervention effects, with serious implications for policy making. In this paper we use data from a large-scale larviciding intervention for malaria control implemented in Dar es Salaam, United Republic of Tanzania, collected over a period of almost 5 years. We apply a longitudinal Bayesian spatial model to the Dar es Salaam data, combining follow-up and cross-sectional data, treating the correlation in longitudinal observations separately, and controlling for potential confounders. An innovative feature of this modeling is the use of Ornstein-Uhlenbeck process to model random time effects. We contrast the results with other Bayesian modeling formulations, including cross-sectional approaches that consider individual-level random effects to account for subjects followed up in two or more surveys. The longitudinal modeling approach indicates that the intervention significantly reduced the prevalence of malaria infection in Dar es Salaam by 20% whereas the joint model did not suggest significance within the results. Our results suggest that the longitudinal model is to be preferred when longitudinal information is available at the individual level.

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

In this paper, we propose a novel spatial importance parameter hierarchical logistic regression modeling approach that includes measurement error from misalignment. We apply this model to study the relationship between the estimated concentration of soil metals at the residence of mothers and the development of intellectual disability (ID) in their children. The data consist of monthly computerized claims data about the prenatal experience of pregnant women living in nine areas within South Carolina and insured by Medicaid during January 1, 1996 and December 31, 2001 and the outcome of ID in their children during early childhood. We excluded mother-child pairs if the mother moved to an unknown location during pregnancy. We identified an association of the ID outcome with arsenic (As) and mercury (Hg) concentration in soil during pregnancy, controlling for infant sex, maternal race, mother's age, and gestational weeks at delivery. There is some indication that Hg has a slightly higher importance in the third and fourth months of pregnancy, while As has a more uniform effect over all the months with a suggestion of a slight increase in risk in later months.

Associations between land cover categories, soil concentrations of arsenic, lead and barium, and population race/ethnicity and socioeconomic status

The potential of using land cover/use categories as a proxy for soil metal concentrations was examined by measuring associations between Anderson land cover category percentages and soil concentrations of As, Pb, and Ba in ten sampling areas. Land cover category and metal associations with ethnicity and socioeconomic status at the United States Census 2000 block and block group levels also were investigated. Arsenic and Pb were highest in urban locations; Ba was a function of geology. Consistent associations were observed between urban/built up land cover, and Pb and poverty. Land cover can be used as proxy for metal concentrations, although associations are metal-dependent.

Finding pathway-modulating genes from a novel Ontology Fingerprint-derived gene network

To enhance our knowledge regarding biological pathway regulation, we took an integrated approach, using the biomedical literature, ontologies, network analyses and experimental investigation to infer novel genes that could modulate biological pathways. We first constructed a novel gene network via a pairwise comparison of all yeast genes' Ontology Fingerprints--a set of Gene Ontology terms overrepresented in the PubMed abstracts linked to a gene along with those terms' corresponding enrichment P-values. The network was further refined using a Bayesian hierarchical model to identify novel genes that could potentially influence the pathway activities. We applied this method to the sphingolipid pathway in yeast and found that many top-ranked genes indeed displayed altered sphingolipid pathway functions, initially measured by their sensitivity to myriocin, an inhibitor of de novo sphingolipid biosynthesis. Further experiments confirmed the modulation of the sphingolipid pathway by one of these genes, PFA4, encoding a palmitoyl transferase. Comparative analysis showed that few of these novel genes could be discovered by other existing methods. Our novel gene network provides a unique and comprehensive resource to study pathway modulations and systems biology in general.

Prospective analysis of infectious disease surveillance data using syndromic information

In this paper, we describe a Bayesian hierarchical Poisson model for the prospective analysis of data for infectious diseases. The proposed model consists of two components. The first component describes the behavior of disease during nonepidemic periods and the second component represents the increase in disease counts due to the presence of an epidemic. A novelty of our model formulation is that the parameters describing the spread of epidemics are allowed to vary in both space and time. We also show how syndromic information can be incorporated into the model to provide a better description of the data and more accurate one-step-ahead forecasts. These real-time forecasts can be used to identify high-risk areas for outbreaks and, consequently, to develop efficient targeted surveillance. We apply the methodology to weekly emergency room discharges for acute bronchitis in South Carolina.

Spatial environmental modeling of autoantibody outcomes among an African American population

In this study of autoimmunity among a population of Gullah African Americans in South Carolina, the links between environmental exposures and autoimmunity (presence of antinuclear antibodies (ANA)) have been assessed. The study population included patients with systemic lupus erythematosus (n = 10), their first degree relatives (n = 61), and unrelated controls (n = 9) where 47.5% (n = 38) were ANA positive. This paper presents the methodology used to model ANA status as a function of individual environmental influences, both self-reported and measured, while controlling for known autoimmunity risk factors. We have examined variable dimension reduction and selection methods in our approach. Following the dimension reduction and selection methods, we fit logistic spatial Bayesian models to explore the relationship between our outcome of interest and environmental exposures adjusting for personal variables. Our analysis also includes a validation "strip" where we have interpolated information from a specific geographic area for a subset of the study population that lives in that vicinity. Our results demonstrate that residential proximity to exposure site is important in this form of analysis. The use of a validation strip network demonstrated that even with small sample numbers some significant exposure-outcome relationships can be detected.

Temporal and spatial variation in residential soil metal concentrations: implications for exposure assessments

Understanding temporal and spatial variation in soil chemicals is critical in exposure assessments. We measured eight metals in subsamples, duplicates (~0.3 m), and repeat soil samples taken 1-6 years after initial sampling (~5 m). We estimated variance components (VCs) of metal concentrations using nested analyses accounting for sampling area, land use and soil type, and calculated coefficients of variation (CVs) for repeat sample pairs. Total variance for all metals was similar, but VCs were proportioned differently by metal and sample type. Spatial variation explained the majority of variance in duplicate samples. CVs of metal concentrations were not significantly different over the long time interval, but repeat samples had larger VCs for unexplained error. Sampling area and land use were important for Ba and Mn, and Pb and Hg, respectively. Results suggest metals are stable over long times and suitable for exposure assessments, but that individual metal behavior should be considered.