Geospatial estimation of the impact of Deepwater Horizon oil spill on plant oiling along the Louisiana shorelines.

Stranded oil covering soil and plant stems in fragile Louisiana marshes was one of the most visible impacts of the 2010 Deepwater Horizon (DWH) oil spill. As part of the assessment of marsh injury after the DWH spill, plant stem oiling was broken into five categories (0%, 0-10%, 10-50%, 50-90%, 90-100%) and used as the independent variable for estimating death of vegetation, accelerated erosion, and other metrics of injury. The length of shoreline falling into each of these stem oiling categories was therefore a key measure of the total extent of marsh injury, and its accurate estimation is the focus of this paper. First, we used geographically-weighted logistic regression (GWR) to explore and model spatially varying relationships between stem oiling field data and secondary information (oiling exposure category) collected during shoreline surveys. We then combined GWR probability estimates with field data using indicator cokriging to predict the probability of exceeding four stem oiling thresholds (0, 10, 50, and 90%) at 50 m intervals along the Louisiana shoreline. Cross-validation using Receiver Operating Characteristic (ROC) Curves demonstrate the greater prediction accuracy of the multivariate geostatistical approach relative to either aspatial regression or indicator kriging that ignores secondary information.

Evaluating susceptibility of karst dolines (sinkholes) for collapse in Sango, Tennessee, USA.

Dolines or sinkholes are earth depressions that develop in soluble rocks complexes such as limestone, dolomite, gypsum, anhydrite, and halite; dolines appear in a variety of shapes from nearly circular to complex structures with highly curved perimeters. The occurrence of dolines in the studied karst area is not random; they are the results of geomorphic, hydrologic, and chemical processes that have caused partial subsidence, even the total collapse of the land surface when voids and caves are present in the bedrock and the regolith arch overbridging these voids is unstable. In the study area, the majority of collapses occur in the regolith (bedrock cover) that bridges voids in the bedrock. Because these collapsing dolines may result in property damage and even cause the loss of lives, there is a need to develop methods for evaluating karst hazards. These methods can then be used by planners and practitioners for urban and economic development, especially in regions with a growing population. The purpose of this project is threefold: 1) to develop a karst feature database, 2) to investigate critical indicators associated with doline collapse, and 3) to develop a doline susceptibility model for potential doline collapse based on external morphometric data. The study has revealed the presence of short range spatial dependence in the distribution of the dolines' morphometric parameters such as circularity, the geographic orientation of the main doline axes, and the length-to-width doline ratios; therefore, geostatistics can be used to spatially evaluate the susceptibility of the karst area for doline collapse. The partial susceptibility estimates were combined into a final probability map enabling the identification of areas where, until now, undetected dolines may cause significant hazards.

Evaluation of geostatistical estimators and their applicability to characterise the spatial patterns of recreational fishing catch rates.

Western Australians are heavily engaged in recreational fishing activities with a participation rate of approximately 30%. An accurate estimation of the spatial distribution of recreational catch per unit effort (catch rates) is an integral component for monitoring fish population changes and to develop strategies for ecosystem-based marine management. Geostatistical techniques such as kriging can provide useful tools for characterising the spatial distributions of recreational catch rates. However, most recreational fishery data are highly skewed, zero-inflated and when expressed as ratios are impacted by the small number problem which can influence the estimates obtained from the traditional kriging. The applicability of ordinary, indicator and Poisson kriging to recreational catch rate data was evaluated for three aquatic species with different behaviours and distribution patterns. The prediction performance of each estimator was assessed based on cross-validation. For all three species, the accuracy plot of the indicator kriging (IK) showed a better agreement between expected and empirical proportions of catch rate data falling within probability intervals of increasing size, as measured by the goodness statistic. Also, indicator kriging was found to be better in predicting the latent catch rate for the three species compared to ordinary and Poisson kriging. For each species, the spatial maps from the three estimators displayed similar patterns but Poisson kriging produced smoother spatial distributions. We show that the IK estimator may be preferable for the spatial modelling of catch rate data exhibiting these characteristics, and has the best prediction performance regardless of the life history and distribution patterns of those three species.

GEOGRAPHICALLY-WEIGHTED REGRESSION ANALYSIS OF PERCENTAGE OF LATE-STAGE PROSTATE CANCER DIAGNOSIS IN FLORIDA.

This study assessed spatial context and the local impacts of putative factors on the proportion of prostate cancer diagnosed at late-stages in Florida during the period 2001-2007. A logistic regression was performed aspatially and by geographically-weighted regression (GWR) at the nodes of a 5 km spacing grid overlaid over Florida and using all the cancer cases within a radius of 125 km of each node. Variables associated significantly with high percentages of late-stage prostate cancer included having comorbidities, smoking, being Black and living in census tracts with farmhouses. Having private or public insurance, being married or diagnosed in a for-profit facility, as well as living in census tracts with high household income reduced significantly this likelihood. Geographically-weighted regression allowed the identification of areas where the local odds ratio is significantly different from the ratio estimated using aspatial regression (State-level). For example, the local odds ratios for the comorbidity covariates were significantly smaller than the State-level odds ratio in Tallahassee and Pensacola, while they were significantly larger in Palm Beach. This emphasizes the need for local strategies and cancer control interventions to reduce the percentage of prostate cancer diagnosed at late-stages and ultimately eliminate health disparities.

Space-Time Distribution of Trichloroethylene Groundwater Concentrations: Geostatistical Modeling and Visualization.

This paper describes a geostatistical approach to model and visualize the space-time distribution of groundwater contaminants. It is illustrated using data from one of the world's largest plume of trichloroethylene (TCE) contamination, extending over 23 km2, which has polluted drinking water wells in northern Michigan. A total of 613 TCE concentrations were recorded at 36 wells between May 2003 and October 2018. To account for the non-stationarity of the spatial covariance, the data were first projected in a new space using multidimensional scaling. During this spatial deformation the domain is stretched in regions of relatively lower spatial correlation (i.e., higher spatial dispersion), while being contracted in regions of higher spatial correlation. The range of temporal autocorrelation is 43 months, while the spatial range is 11 km. The sample semivariogram was fitted using three different types of non-separable space-time models, and their prediction performance was compared using cross-validation. The sum-metric and product-sum semivariogram models performed equally well, with a mean absolute error of prediction corresponding to 23% of the mean TCE concentration. The observations were then interpolated every 6 months to the nodes of a 150 m spacing grid covering the study area and results were visualized using a three-dimensional space-time cube. This display highlights how TCE concentrations increased over time in the northern part of the study area, as the plume is flowing to the so-called Chain of Lakes.

Disaggregation of Green Space Access, Walkability, and Behavioral Risk Factor Data for Precise Estimation of Local Population Characteristics.

BACKGROUND: Social and Environmental Determinants of Health (SEDH) provide us with a conceptual framework to gain insights into possible associations among different human behaviors and the corresponding health outcomes that take place often in and around complex built environments. Developing better built environments requires an understanding of those aspects of a community that are most likely to have a measurable impact on the target SEDH. Yet data on local characteristics at suitable spatial scales are often unavailable. We aim to address this issue by application of different data disaggregation methods. METHODS: We applied different approaches to data disaggregation to obtain small area estimates of key behavioral risk factors, as well as geospatial measures of green space access and walkability for each zip code of Allegheny County in southwestern Pennsylvania. RESULTS: Tables and maps of local characteristics revealed their overall spatial distribution along with disparities therein across the county. While the top ranked zip codes by behavioral estimates generally have higher than the county's median individual income, this does not lead them to have higher than its median green space access or walkability. CONCLUSION: We demonstrated the utility of data disaggregation for addressing complex questions involving community-specific behavioral attributes and built environments with precision and rigor, which is especially useful for a diverse population. Thus, different types of data, when comparable at a common local scale, can provide key integrative insights for researchers and policymakers.

Analysis of geographical disparities in temporal trends of health outcomes using space-time joinpoint regression.

Analyzing temporal trends in health outcomes can provide a more comprehensive picture of the burden of a disease like cancer and generate new insights about the impact of various interventions. In the United States such an analysis is increasingly conducted using joinpoint regression outside a spatial framework, which overlooks the existence of significant variation among U.S. counties and states with regard to the incidence of cancer. This paper presents several innovative ways to account for space in joinpoint regression: (1) prior filtering of noise in the data by binomial kriging and use of the kriging variance as measure of reliability in weighted least-square regression, (2) detection of significant boundaries between adjacent counties based on tests of parallelism of time trends and confidence intervals of annual percent change of rates, and (3) creation of spatially compact groups of counties with similar temporal trends through the application of hierarchical cluster analysis to the results of boundary analysis. The approach is illustrated using time series of proportions of prostate cancer late-stage cases diagnosed yearly in every county of Florida since 1980s. The annual percent change (APC) in late-stage diagnosis and the onset years for significant declines vary greatly across Florida. Most counties with non-significant average APC are located in the north-western part of Florida, known as the Panhandle, which is more rural than other parts of Florida. The number of significant boundaries peaked in the early 1990s when prostate-specific antigen (PSA) test became widely available, a temporal trend that suggests the existence of geographical disparities in the implementation and/or impact of the new screening procedure, in particular as it began available.

Geospatial model of composition of water service lines in Flint, Michigan: Validation using excavation data and a new compositional geostatistical approach.

Following the Flint drinking water crisis, a service line (SL) replacement program was implemented to replace lead SLs and galvanized SLs connecting residences to Flint's water system, leading to the excavation and inspection over a 5-year period (2016-2020) of a total of 26,750 lines, representing close to 50% of all tax parcels in the City of Flint. These recent data were used to validate an earlier geospatial model created by residual indicator kriging (IK) to predict the probability that a home has a lead, galvanized, or copper private-side SL based on neighboring house inspections (i.e., 3254 homes visited in 2017) and secondary information (i.e., built year and city records on SL composition). Receiver operating characteristic curves indicated an average frequency of detection (i.e., area under the curve [AUC]) of 0.9 for copper and galvanized material and 0.6 for lead service lines. Predicting the composition of SL at unmonitored residences by IK, however, can result in negative probabilities of occurrence and probabilities that do not sum to 1. These limitations were overcome by adopting simplicial IK, whereby data undergo a logratio transform before the geospatial analysis. This first application of a compositional approach to SL data improved the detection of lead SLs (AUC = 0.8 vs. 0.6) while providing coherent predictions. Incorporating secondary information, in particular using standardized cokriging and a new rescaled cross-semivariogram estimator introduced to correct for geographical clustering of house inspections, increased the accuracy of the prediction.

Comparison of Soft Indicator and Poisson Kriging for the Noise-Filtering and Downscaling of Areal Data: Application to Daily COVID-19 Incidence Rates.

This paper addresses two common challenges in analyzing spatial epidemiological data, specifically disease incidence rates recorded over small areas: filtering noise caused by small local population sizes and deriving estimates at different spatial scales. Geostatistical techniques, including Poisson kriging (PK), have been used to address these issues by accounting for spatial correlation patterns and neighboring observations in smoothing and changing spatial support. However, PK has a limitation in that it can generate unrealistic rates that are either negative or greater than 100%. To overcome this limitation, an alternative method that relies on soft indicator kriging (IK) is presented. The performance of this method is compared to PK using daily COVID-19 incidence rates recorded in 2020-2021 for each of the 581 municipalities in Belgium. Both approaches are used to derive noise-filtered incidence rates for four different dates of the pandemic at the municipality level and at the nodes of a 1 km spacing grid covering the country. The IK approach has several attractive features: (1) the lack of negative kriging estimates, (2) the smaller smoothing effect, and (3) the better agreement with observed municipality-level rates after aggregation, in particular when the original rate was zero.

Disaggregation of legacy soil data using area to point kriging for mapping soil organic carbon at the regional scale.

Legacy data in the form of soil maps, which often have typical property measurements associated with each polygon, can be an important source of information for digital soil mapping (DSM). Methods of disaggregating such information and using it for quantitative estimation of soil properties by methods such as regression kriging (RK) are needed. Several disaggregation processes have been investigated; preferred methods include those which include consideration of scorpan factors and those which are mass preserving (pycnophylactic) making transitions between different scales of investigation more theoretically sound. Area to point kriging (AtoP kriging) is pycnophylactic and here we investigate its merits for disaggregating legacy data from soil polygon maps. Area to point regression kriging (AtoP RK) which incorporates ancillary data into the disaggre-gation process was also applied. The AtoP kriging and AtoP RK approaches do not involve collection of new soil measurements and are compared with disaggregation by simple rasterization. Of the disaggregation methods investigated, AtoP RK gave the most accurate predictions of soil organic carbon (SOC) concentrations (smaller mean absolute errors (MAEs) of cross-validation) for disaggregation of soil polygon data across the whole of Northern Ireland. Legacy soil polygon data disaggregated by AtoP kriging and simple rasterization were used in a RK framework for estimating soil organic carbon (SOC) concentrations across the whole of Northern Ireland, using soil sample data from the Tellus survey of Northern Ireland and with other covariates (altitude and airborne radiometric potassium). This allowed direct comparison with previous analysis of the Tellus survey data. Incorporating the legacy data, whether from simple rasterization of the polygons or AtoP kriging, substantially reduced the MAEs of RK compared with previous analyses of the Tellus data. However, using legacy data disaggregated by AtoP kriging in RK resulted in a greater reduction in MAEs. A jack-knife procedure was also performed to determine a suitable number of additional soil samples that would need to be collected for RK of SOC for the whole of Northern Ireland depending on the availability of ancillary data. We recommend i) if only legacy soil polygon map data are available, they should be disaggregated using AtoP kriging, ii) if ancillary data are also available legacy data should be disaggregated using AtoP RK and iii) if new soil measurements are available in addition to ancillary and legacy soil map data, the legacy soil map data should be first disaggregated using AtoP kriging and these data used along with ancillary data as the fixed effects for RK of the new soil measurements.

Geographical, temporal and racial disparities in late-stage prostate cancer incidence across Florida: a multiscale joinpoint regression analysis.

BACKGROUND: Although prostate cancer-related incidence and mortality have declined recently, striking racial/ethnic differences persist in the United States. Visualizing and modelling temporal trends of prostate cancer late-stage incidence, and how they vary according to geographic locations and race, should help explaining such disparities. Joinpoint regression is increasingly used to identify the timing and extent of changes in time series of health outcomes. Yet, most analyses of temporal trends are aspatial and conducted at the national level or for a single cancer registry. METHODS: Time series (1981-2007) of annual proportions of prostate cancer late-stage cases were analyzed for non-Hispanic Whites and non-Hispanic Blacks in each county of Florida. Noise in the data was first filtered by binomial kriging and results were modelled using joinpoint regression. A similar analysis was also conducted at the state level and for groups of metropolitan and non-metropolitan counties. Significant racial differences were detected using tests of parallelism and coincidence of time trends. A new disparity statistic was introduced to measure spatial and temporal changes in the frequency of racial disparities. RESULTS: State-level percentage of late-stage diagnosis decreased 50% since 1981; a decline that accelerated in the 90's when Prostate Specific Antigen (PSA) screening was introduced. Analysis at the metropolitan and non-metropolitan levels revealed that the frequency of late-stage diagnosis increased recently in urban areas, and this trend was significant for white males. The annual rate of decrease in late-stage diagnosis and the onset years for significant declines varied greatly among counties and racial groups. Most counties with non-significant average annual percent change (AAPC) were located in the Florida Panhandle for white males, whereas they clustered in South-eastern Florida for black males. The new disparity statistic indicated that the spatial extent of racial disparities reached a peak in 1990 because of an early decline in frequency of late-stage diagnosis observed for black males. CONCLUSIONS: Analyzing temporal trends in cancer incidence and mortality rates outside a spatial framework is unsatisfactory, since it leads one to overlook significant geographical variation which can potentially generate new insights about the impact of various interventions. Differences observed among nested geographies in Florida show how the modifiable areal unit problem (MAUP) also impacts the analysis of temporal changes.

Lifetime exposure to arsenic in drinking water and bladder cancer: a population-based case-control study in Michigan, USA.

OBJECTIVE: Arsenic in drinking water has been linked with the risk of urinary bladder cancer, but the dose-response relationships for arsenic exposures below 100 microg/L remain equivocal. We conducted a population-based case-control study in southeastern Michigan, USA, where approximately 230,000 people were exposed to arsenic concentrations between 10 and 100 microg/L. METHODS: This study included 411 bladder cancer cases diagnosed between 2000 and 2004, and 566 controls recruited during the same period. Individual lifetime exposure profiles were reconstructed, and residential water source histories, water consumption practices, and water arsenic measurements or modeled estimates were determined at all residences. Arsenic exposure was estimated for 99% of participants' person-years. RESULTS: Overall, an increase in bladder cancer risk was not found for time-weighted average lifetime arsenic exposure >10 microg/L when compared with a reference group exposed to <1 microg/L (odds ratio (OR) = 1.10; 95% confidence interval (CI): 0.65, 1.86). Among ever-smokers, risks from arsenic exposure >10 microg/L were similarly not elevated when compared to the reference group (OR = 0.94; 95% CI: 0.50, 1.78). CONCLUSIONS: We did not find persuasive evidence of an association between low-level arsenic exposure and bladder cancer. Selecting the appropriate exposure metric needs to be thoughtfully considered when investigating risk from low-level arsenic exposure.

Identification of racial disparities in breast cancer mortality: does scale matter?

BACKGROUND: This paper investigates the impact of geographic scale (census tract, zip code, and county) on the detection of disparities in breast cancer mortality among three ethnic groups in Texas (period 1995-2005). Racial disparities were quantified using both relative (RR) and absolute (RD) statistics that account for the population size and correct for unreliable rates typically observed for minority groups and smaller geographic units. Results were then correlated with socio-economic status measured by the percentage of habitants living below the poverty level. RESULTS: African-American and Hispanic women generally experience higher mortality than White non-Hispanics, and these differences are especially significant in the southeast metropolitan areas and southwest border of Texas. The proportion and location of significant racial disparities however changed depending on the type of statistic (RR versus RD) and the geographic level. The largest proportion of significant results was observed for the RD statistic and census tract data. Geographic regions with significant racial disparities for African-Americans and Hispanics frequently had a poverty rate above 10.00%. CONCLUSIONS: This study investigates both relative and absolute racial disparities in breast cancer mortality between White non-Hispanic and African-American/Hispanic women at the census tract, zip code and county levels. Analysis at the census tract level generally led to a larger proportion of geographical units experiencing significantly higher mortality rates for minority groups, although results varied depending on the use of the relative versus absolute statistics. Additional research is needed before general conclusions can be formulated regarding the choice of optimal geographic regions for the detection of racial disparities.

Geostatistical modeling of the spatial distribution of sediment oxygen demand within a Coastal Plain blackwater watershed.

Blackwater streams are found throughout the Coastal Plain of the southeastern United States and are characterized by a series of instream floodplain swamps that play a critical role in determining the water quality of these systems. Within the state of Georgia, many of these streams are listed in violation of the state's dissolved oxygen (DO) standard. Previous work has shown that sediment oxygen demand (SOD) is elevated in instream floodplain swamps and due to these areas of intense oxygen demand, these locations play a major role in determining the oxygen balance of the watershed as a whole. This work also showed SOD rates to be positively correlated with the concentration of total organic carbon. This study builds on previous work by using geostatistics and Sequential Gaussian Simulation to investigate the patchiness and distribution of total organic carbon (TOC) at the reach scale. This was achieved by interpolating TOC observations and simulated SOD rates based on a linear regression. Additionally, this study identifies areas within the stream system prone to high SOD at representative 3rd and 5th order locations. Results show that SOD was spatially correlated with the differences in distribution of TOC at both locations and that these differences in distribution are likely a result of the differing hydrologic regime and watershed position. Mapping of floodplain soils at the watershed scale shows that areas of organic sediment are widespread and become more prevalent in higher order streams. DO dynamics within blackwater systems are a complicated mix of natural and anthropogenic influences, but this paper illustrates the importance of instream swamps in enhancing SOD at the watershed scale. Moreover, our study illustrates the influence of instream swamps on oxygen demand while providing support that many of these systems are naturally low in DO.

Spatial cluster analysis of early stage breast cancer: a method for public health practice using cancer registry data.

OBJECTIVES: Cancer registries are increasingly mapping residences of patients at time of diagnosis, however, an accepted protocol for spatial analysis of these data is lacking. We undertook a public health practice-research partnership to develop a strategy for detecting spatial clusters of early stage breast cancer using registry data. METHODS: Spatial patterns of early stage breast cancer throughout Michigan were analyzed comparing several scales of spatial support, and different clustering algorithms. RESULTS: Analyses relying on point data identified spatial clusters not detected using data aggregated into census block groups, census tracts, or legislative districts. Further, using point data, Cuzick-Edwards' nearest neighbor test identified clusters not detected by the SaTScan spatial scan statistic. Regression and simulation analyses lent credibility to these findings. CONCLUSIONS: In these cluster analyses of early stage breast cancer in Michigan, spatial analyses of point data are more sensitive than analyses relying on data aggregated into polygons, and the Cuzick-Edwards' test is more sensitive than the SaTScan spatial scan statistic, with acceptable Type I error. Cuzick-Edwards' test also enables presentation of results in a manner easily communicated to public health practitioners. The approach outlined here should help cancer registries conduct and communicate results of geographic analyses.

Second-Phase Sampling Designs for Non-Stationary Spatial Variables.

In spatial sampling, once initial samples of the primary variable have been collected, it is possible to take additional measurements, an approach known as second-phase sampling. Additional samples are usually collected away from observation locations, or where the kriging variance is maximum. However, the kriging variance (also known as prediction error variance) is independent of data values and computed under the assumption of stationary spatial process, which is often violated in practice. In this paper, we weight the kriging variance with another criterion, giving greater sampling importance to locations exhibiting significant spatial roughness that is computed by a spatial moving average window. Additional samples are allocated using a simulated annealing procedure since the weighted objective function is non-linear. A case study using an exhaustive remote sensing image illustrates the procedure. Combinations of first-phase systematic and nested sampling designs (or patterns) of varying densities are generated, while the location of additional observations is guided in a way which optimizes the proposed objective function. The true pixel value at the new points is extracted, the semivariogram model updated, and the image reconstructed. Second-phase sampling patterns optimizing the proposed criterion lead to predictions closer to the true image than when using the kriging variance as the main criterion. This improvement is stronger when there is a low density of first-phase samples, and decreases however as the initial density increases.

Geostatistical prediction of water lead levels in Flint, Michigan: A multivariate approach.

Despite several environmental crises, little research has been conducted on citywide geospatial modeling of water lead levels (WLL) in public distribution systems. This paper presents the first application of multivariate geostatistics to lead in drinking water within a distribution system, specifically in Flint, Michigan. One of the key features of the Flint data is their collection through two different sampling initiatives: (i) voluntary or homeowner-driven sampling whereby concerned citizens decided to acquire a testing kit and conduct sampling on their own (10,717 sites), and (ii) State-administered sampling where data were collected bi-weekly at 809 selected sites after training of residents by technical teams (sentinel sites). These two datasets were first averaged over the 41-week sampling period and each tax parcel to attenuate sampling fluctuations and create a set of 420 tax parcels sampled by both protocols. Both variables displayed a correlation of 0.62 while their direct and cross-semivariograms showed substantial nugget effect and a long range of 7.5 km. WLLs recorded at sentinel sites and deemed more reliable by city officials were then interpolated using cokriging to account for the more densely sampled voluntary data and information on service line composition (lead, other, or unknown) available for each of 51,045 residential tax parcels. Cross-validation demonstrated the greater prediction accuracy of the multivariate geostatistical approach relative to kriging and inverse square distance weighting interpolation using only sentinel data. This general procedure is applicable to other cities with aging infrastructure where lead in drinking water is a concern.

How does Poisson kriging compare to the popular BYM model for mapping disease risks?

BACKGROUND: Geostatistical techniques are now available to account for spatially varying population sizes and spatial patterns in the mapping of disease rates. At first glance, Poisson kriging represents an attractive alternative to increasingly popular Bayesian spatial models in that: 1) it is easier to implement and less CPU intensive, and 2) it accounts for the size and shape of geographical units, avoiding the limitations of conditional auto-regressive (CAR) models commonly used in Bayesian algorithms while allowing for the creation of isopleth risk maps. Both approaches, however, have never been compared in simulation studies, and there is a need to better understand their merits in terms of accuracy and precision of disease risk estimates. RESULTS: Besag, York and Mollie's (BYM) model and Poisson kriging (point and area-to-area implementations) were applied to age-adjusted lung and cervix cancer mortality rates recorded for white females in two contrasted county geographies: 1) state of Indiana that consists of 92 counties of fairly similar size and shape, and 2) four states in the Western US (Arizona, California, Nevada and Utah) forming a set of 118 counties that are vastly different geographical units. The spatial support (i.e. point versus area) has a much smaller impact on the results than the statistical methodology (i.e. geostatistical versus Bayesian models). Differences between methods are particularly pronounced in the Western US dataset: BYM model yields smoother risk surface and prediction variance that changes mainly as a function of the predicted risk, while the Poisson kriging variance increases in large sparsely populated counties. Simulation studies showed that the geostatistical approach yields smaller prediction errors, more precise and accurate probability intervals, and allows a better discrimination between counties with high and low mortality risks. The benefit of area-to-area Poisson kriging increases as the county geography becomes more heterogeneous and when data beyond the adjacent counties are used in the estimation. The trade-off cost for the easier implementation of point Poisson kriging is slightly larger kriging variances, which reduces the precision of the model of uncertainty. CONCLUSION: Bayesian spatial models are increasingly used by public health officials to map mortality risk from observed rates, a preliminary step towards the identification of areas of excess. More attention should however be paid to the spatial and distributional assumptions underlying the popular BYM model. Poisson kriging offers more flexibility in modeling the spatial structure of the risk and generates less smoothing, reducing the likelihood of missing areas of high risk.

A comparative analysis of aspatial statistics for detecting racial disparities in cancer mortality rates.

BACKGROUND: Our progress towards the goal of eliminating racial health disparities requires methods for assessing the existence, magnitude, and statistical significance of health disparities. In comparing disease rates, we must account for the unreliability of rates computed for small minority populations and within sparsely populated areas. Furthermore, as the number of geographic units under study increases, we also must account for multiple testing to assure we do not misclassify disparities as present when they actually are not (false positive). To date and to our knowledge, none of the methodologies in current use simultaneously address all of these important needs. And few, if any studies have undertaken a systematic comparison of methods to identify those that are statistically robust and reliable. RESULTS: We introduced six test statistics for quantifying absolute and relative differences between cancer rates measured in distinct groups (i.e. race or ethnicity). These alternative measures were illustrated using age-adjusted prostate and lung cancer mortality rates for white and black males in 688 counties of the Southeastern US (1970-1994). Statistical performance, including power and proportion of false positives, was investigated in simulation studies that mimic different scenarios for the magnitude and frequency of disparities. Two test statistics, which are based on the difference and ratio of rates, consistently outperformed the other measures. Corrections for multiple testing actually increased misclassification compared with the unadjusted tests and are not recommended. One-tailed tests allowed the researcher to consider a priori hypotheses beyond the basic test that the two rates are different. CONCLUSION: The assessment of significant racial disparities across geographic areas is an important tool in guiding cancer control practices, and public health officials must consider the problems of small population size and multiple comparison, and should conduct disparity analyses using both absolute (difference, RD statistic) and relative (ratio, RR statistic) measures. Simple test statistics to assess the significance of rate difference and rate ratio perform well, and their unadjusted p-values provide a realistic assessment of the proportion of type I errors (i.e. disparities wrongly declared significant).

Monitoring the aftermath of Flint drinking water contamination crisis: Another case of sampling bias?

The delay in reporting high levels of lead in Flint drinking water, following the city's switch to the Flint River as its water supply, was partially caused by the biased selection of sampling sites away from the lead pipe network. Since Flint returned to its pre-crisis source of drinking water, the State has been monitoring water lead levels (WLL) at selected "sentinel" sites. In a first phase that lasted two months, 739 residences were sampled, most of them bi-weekly, to determine the general health of the distribution system and to track temporal changes in lead levels. During the same period, water samples were also collected through a voluntary program whereby concerned citizens received free testing kits and conducted sampling on their own. State officials relied on the former data to demonstrate the steady improvement in water quality. A recent analysis of data collected by voluntary sampling revealed, however, an opposite trend with lead levels increasing over time. This paper looks at potential sampling bias to explain such differences. Although houses with higher WLL were more likely to be sampled repeatedly, voluntary sampling turned out to reproduce fairly well the main characteristics (i.e. presence of lead service lines (LSL), construction year) of Flint housing stock. State-controlled sampling was less representative; e.g., sentinel sites with LSL were mostly built between 1935 and 1950 in lower poverty areas, which might hamper our ability to disentangle the effects of LSL and premise plumbing (lead fixtures and pipes present within old houses) on WLL. Also, there was no sentinel site with LSL in two of the most impoverished wards, including where the percentage of children with elevated blood lead levels tripled following the switch in water supply. Correcting for sampling bias narrowed the gap between sampling programs, yet overall temporal trends are still opposite.