ON THE USE OF NON-EUCLIDEAN ISOTROPY IN GEOSTATISTICS

This paper investigates the use of non-Euclidean distances to characterize isotropic spatial dependence for geostatistical related applications. A simple example is provided to demonstrate there are no guarantees that existing covariogram and variogram functions remain valid (i.e.\ positive definite or conditionally negative definite) when used with a non-Euclidean distance measure. Furthermore, satisfying the conditions of a metric is not sufficient to ensure the distance measure can be used with existing functions. Current literature is not clear on these topics. There are certain distance measures that when used with existing covariogram and variogram functions remain valid, an issue that is explored. No new theorems are provided, rather links between existing theorems and definitions related to the concepts of isometric embedding, conditionally negative definiteness, and positive definiteness are used to demonstrate classes of valid norm dependent isotropic covariogram and variogram functions, results most of which have yet to appear in mainstream geostatistical literature or application. These classes of functions extend the well known classes by adding a parameter to define the distance norm. In practice, this distance parameter can be set a priori to represent, for example, the Euclidean distance, or kept as a parameter to allow the data to choose the distance norm. Applications of the latter are provided for demonstration

Geographical clustering of prostate cancer grade and stage at diagnosis, before and after adjustment for risk factors

BACKGROUND: Spatial variation in patterns of disease outcomes is often explored with techniques such as cluster detection analysis. In other types of investigations, geographically varying individual or community level characteristics are often used as independent predictors in statistical models which also attempt to explain variation in disease outcomes. However, there is a lack of research which combines geographically referenced exploratory analysis with multilevel models. We used a spatial scan statistic approach, in combination with predicted block group-level disease patterns from multilevel models, to examine geographic variation in prostate cancer grade and stage at diagnosis. RESULTS: We examined data from 20928 Maryland men with incident prostate cancer reported to the Maryland Cancer Registry during 1992–1997. Initial cluster detection analyses, prior to adjustment, indicated that there were four statistically significant clusters of high and low rates of each outcome (later stage at diagnosis and higher histologic grade of tumor) for prostate cancer cases in Maryland during 1992–1997. After adjustment for individual case attributes, including age, race, year of diagnosis, patterns of clusters changed for both outcomes. Additional adjustment for Census block group and county-level socioeconomic measures changed the cluster patterns further. CONCLUSIONS: These findings provide evidence that, in locations where adjustment changed patterns of clusters, the adjustment factors may be contributing causes of the original clusters. In addition, clusters identified after adjusting for individual and area-level predictors indicate area of unexplained variation, and merit further small-area investigations

Using Imputation to Provide Location Information for Nongeocoded Addresses

Background: The importance of geography as a source of variation in health research continues to receive sustained attention in the literature. The inclusion of geographic information in such research often begins by adding data to a map which is predicated by some knowledge of location. A precise level of spatial information is conventionally achieved through geocoding, the geographic information system (GIS) process of translating mailing address information to coordinates on a map. The geocoding process is not without its limitations, though, since there is always a percentage of addresses which cannot be converted successfully (nongeocodable). This raises concerns regarding bias since traditionally the practice has been to exclude nongeocoded data records from analysis. Methodology/Principal: Findings In this manuscript we develop and evaluate a set of imputation strategies for dealing with missing spatial information from nongeocoded addresses. The strategies are developed assuming a known zip code with increasing use of collateral information, namely the spatial distribution of the population at risk. Strategies are evaluated using prostate cancer data obtained from the Maryland Cancer Registry. We consider total case enumerations at the Census county, tract, and block group level as the outcome of interest when applying and evaluating the methods. Multiple imputation is used to provide estimated total case counts based on complete data (geocodes plus imputed nongeocodes) with a measure of uncertainty. Results indicate that the imputation strategy based on using available population-based age, gender, and race information performed the best overall at the county, tract, and block group levels. Conclusions/Significance: The procedure allows for the potentially biased and likely under reported outcome, case enumerations based on only the geocoded records, to be presented with a statistically adjusted count (imputed count) with a measure of uncertainty that are based on all the case data, the geocodes and imputed nongeocodes. Similar strategies can be applied in other analysis settings

Estimating Indoor PM2.5 and CO Concentrations in Households in Southern Nepal: The Nepal Cookstove Intervention Trials

High concentrations of household air pollution (HAP) due to biomass fuel usage with unvented, insufficient combustion devices are thought to be an important health risk factor in South Asia population. To better characterize the indoor concentrations of particulate matter (PM2.5) and carbon monoxide (CO), and to understand their impact on health in rural southern Nepal, this study analyzed daily monitoring data collected with DataRAM pDR-1000 and LASCAR CO data logger in 2980 households using traditional biomass cookstove indoor through the Nepal Cookstove Intervention Trial–Phase I between March 2010 and October 2011. Daily average PM2.5 and CO concentrations collected in area near stove were 1,376 (95% CI, 1,331–1,423) μg/m3 and 10.9 (10.5–11.3) parts per million (ppm) among households with traditional cookstoves. The 95th percentile, hours above 100μg/m3 for PM2.5 or 6ppm for CO, and hours above 1000μg/m3 for PM2.5 or 9ppm for CO were also reported. An algorithm was developed to differentiate stove-influenced (SI) periods from non-stove-influenced (non-SI) periods in monitoring data. Average stove-influenced concentrations were 3,469 (3,350–3,588) μg/m3 for PM2.5 and 21.8 (21.1–22.6) ppm for CO. Dry season significantly increased PM2.5concentration in all metrics; wood was the cleanest fuel for PM2.5 and CO, while adding dung into the fuel increased concentrations of both pollutants. For studies in rural southern Nepal, CO concentration is not a viable surrogate for PM2.5 concentrations based on the low correlation between these measures. In sum, this study filled a gap in knowledge on HAP in rural Nepal using traditional cookstoves and revealed very high concentrations in these households

Evaluation of Methicillin-Resistant Staphylococcus aureus Carriage and High Livestock Production Areas in North Carolina through Active Case Finding at a Tertiary Care Hospital

: Recent reports from the Netherlands document the emergence of novel multilocus sequence typing (MLST) types (e.g., ST-398) of methicillin-resistant Staphylococcus aureus (MRSA) in livestock, particularly swine. In Eastern North Carolina (NC), one of the densest pig farming areas in the United States, as many as 14% of MRSA isolates from active case finding in our medical center have no matches in a repetitive sequence-based polymerase chain reaction (rep-PCR) library. The current study was designed to determine if these non-matched MRSA (NM-MRSA) were geographically associated with exposure to pig farming in Eastern NC. While residential proximity to farm waste lagoons lacked association with NM-MRSA in a logistic regression model, a spatial cluster was identified in the county with highest pig density. Using MLST, we found a heterogeneous distribution of strain types comprising the NM-MRSA isolates from the most pig dense regions, including ST-5 and ST-398. Our study raises the warning that patients in Eastern NC harbor livestock associated MRSA strains are not easily identifiable by rep-PCR. Future MRSA studies in livestock dense areas in the U.S. should investigate further the role of pig–human interactions

Spatial and Temporal Changes in Household Structure Locations Using High-Resolution Satellite Imagery for Population Assessment: An Analysis in Southern Zambia, 2006-2011

Satellite imagery is increasingly available at high spatial resolution and can be used for various purposes in public health research and programme implementation. Comparing a census generated from two satellite images of the same region in rural southern Zambia obtained four and a half years apart identified patterns of household locations and change over time. The length of time that a satellite image-based census is accurate determines its utility. Households were enumerated manually from satellite images obtained in 2006 and 2011 of the same area. Spatial statistics were used to describe clustering, cluster detection, and spatial variation in the location of households. A total of 3821 household locations were enumerated in 2006 and 4256 in 2011, a net change of 435 houses (11.4% increase). Comparison of the images indicated that 971 (25.4%) structures were added and 536 (14.0%) removed. Further analysis suggested similar household clustering in the two images and no substantial difference in concentration of households across the study area. Cluster detection analysis identified a small area where significantly more household structures were removed than expected; however, the amount of change was of limited practical significance. These findings suggest that random sampling of households for study participation would not induce geographic bias if based on a 4.5-year-old image in this region. Application of spatial statistical methods provides insights into the population distribution changes between two time periods and can be helpful in assessing the accuracy of satellite imagery

Humidity and gravimetric equivalency adjustments for nephelometer-based particulate matter measurements of emissions from solid biomass fuel in cookstoves

Great uncertainty exists around indoor biomass burning exposure-disease relationships due to lack of detailed exposure data in large health outcome studies. Passive nephelometers can be used to estimate high particulate matter (PM) concentrations during cooking in low resource environments. Since passive nephelometers do not have a collection filter they are not subject to sampler overload. Nephelometric concentration readings can be biased due to particle growth in high humid environments and differences in compositional and size dependent aerosol characteristics. This paper explores relative humidity (RH) and gravimetric equivalency adjustment approaches to be used for the pDR-1000 used to assess indoor PM concentrations for a cookstove intervention trial in Nepal. Three approaches to humidity adjustment performed equivalently (similar root mean squared error). For gravimetric conversion, the new linear regression equation with log-transformed variables performed better than the traditional linear equation. In addition, gravimetric conversion equations utilizing a spline or quadratic term were examined. We propose a humidity adjustment equation encompassing the entire RH range instead of adjusting for RH above an arbitrary 60% threshold. Furthermore, we propose new integrated RH and gravimetric conversion methods because they have one response variable (gravimetric PM2.5 concentration), do not contain an RH threshold, and is straightforward