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.

Geospatial cryptography: enabling researchers to access private, spatially referenced, human subjects data for cancer control and prevention.

As the volume, accuracy and precision of digital geographic information have increased, concerns regarding individual privacy and confidentiality have come to the forefront. Not only do these challenge a basic tenet underlying the advancement of science by posing substantial obstacles to the sharing of data to validate research results, but they are obstacles to conducting certain research projects in the first place. Geospatial cryptography involves the specification, design, implementation and application of cryptographic techniques to address privacy, confidentiality and security concerns for geographically referenced data. This article defines geospatial cryptography and demonstrates its application in cancer control and surveillance. Four use cases are considered: (1) national-level de-duplication among state or province-based cancer registries; (2) sharing of confidential data across cancer registries to support case aggregation across administrative geographies; (3) secure data linkage; and (4) cancer cluster investigation and surveillance. A secure multi-party system for geospatial cryptography is developed. Solutions under geospatial cryptography are presented and computation time is calculated. As services provided by cancer registries to the research community, de-duplication, case aggregation across administrative geographies and secure data linkage are often time-consuming and in some instances precluded by confidentiality and security concerns. Geospatial cryptography provides secure solutions that hold significant promise for addressing these concerns and for accelerating the pace of research with human subjects data residing in our nation's cancer registries. Pursuit of the research directions posed herein conceivably would lead to a geospatially encrypted geographic information system (GEGIS) designed specifically to promote the sharing and spatial analysis of confidential data. Geospatial cryptography holds substantial promise for accelerating the pace of research with spatially referenced human subjects data.

How geostatistics can help you find lead and galvanized water service lines: The case of Flint, MI.

In the aftermath of Flint drinking water crisis, most US cities have been scrambling to locate all lead service lines (LSLs) in their water supply systems. This information, which is most often inaccurate or lacking, is critical to assess compliance with the Lead and Copper Rule and to plan the replacement of lead and galvanized service lines (GSLs) as currently under way in Flint. This paper presents the first geospatial approach to predict the likelihood that a home has a LSL or GSL based on neighboring field data (i.e., house inspection) and secondary information (i.e., construction year and city records). The methodology is applied to the City of Flint where 3254 homes have been inspected by the Michigan Department of Environmental Quality to identify service line material. GSLs and LSLs were mostly observed in houses built prior to 1934 and during World War II, respectively. City records led to the over-identification of LSLs, likely because old records were not updated as these lines were being replaced. Indicator semivariograms indicated that both types of service line are spatially clustered with a range of 1.4km for LSLs and 2.8km for GSLs. This spatial autocorrelation was integrated with secondary data using residual indicator kriging to predict the probability of finding each type of material at the tax parcel level. Cross-validation analysis using Receiver Operating Characteristic (ROC) Curves demonstrated the greater accuracy of the kriging model relative to the current approach targeting houses built in the forties; in particular as more field data become available. Anticipated rates of false positives and percentages of detection were computed for different sampling strategies. This approach is flexible enough to accommodate additional sources of information, such as local code and regulatory changes, historical permit records, maintenance and operation records, or customer self-reporting.

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.

The drinking water contamination crisis in Flint: Modeling temporal trends of lead level since returning to Detroit water system.

Since Flint returned to its pre-crisis source of drinking water close to 25,000 water samples have been collected and tested for lead and copper in >10,000 residences. This paper presents the first analysis and time trend modeling of lead data, providing new insights about the impact of this intervention. The analysis started with geocoding all water lead levels (WLL) measured during an 11-month period following the return to the Detroit water supply. Each data was allocated to the corresponding tax parcel unit and linked to secondary datasets, such as the composition of service lines, year built, or census tract poverty level. Only data collected on residential parcels within the City limits were used in the analysis. One key feature of 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 (non-sentinel sites), and (ii) State-controlled sampling where data were collected bi-weekly at selected sites after training of residents by technical teams (sentinel sites). Temporal trends modeled from these two datasets were found to be statistically different with fewer sentinel data exceeding WLL thresholds ranging from 10 to 50µg/L. Even after adjusting for housing characteristics the odds ratio (OR) of measuring WLL above 15µg/L at non-sentinel sites is significantly >1 (OR=1.480) and it increases with the threshold (OR=2.055 for 50µg/L). Joinpoint regression showed that the city-wide percentage of WLL data above 15µg/L displayed four successive trends since the return to Detroit Water System. Despite the recent improvement in water quality, the culprit for differences between sampling programs needs to be identified as it impacts exposure assessment and might influence whether there is compliance or not with the Lead and Copper Rule.

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.

Spatial analysis of drug poisoning deaths in the American West, particularly Utah.

BACKGROUND: Most states in the Western US have high rates of drug poisoning death (DPD), especially New Mexico, Nevada, Arizona and Utah (UT). This seems paradoxical in UT where illicit drug use, smoking and drinking rates are low. To investigate this, spatial analysis of county level DPD data and other relevant factors in the Western US and UT was undertaken. METHODS: Poisson kriging was used to smooth the DPD data, populate data gaps and improve the reliability of rates recorded in sparsely populated counties. Links between DPD and economic, environmental, health, lifestyle, and demographic factors were investigated at four scales using multiple linear regression. LDS church membership and altitude, factors not previously considered, were included. Spatial change in the strength and sign of relationships was investigated using geographically weighted regression and significant DPD clusters were identified using the Local Moran's I. RESULTS: Economic factors, like the sharp social gradient between rural and urban areas were important to DPD throughout the west. Higher DPD rates were also found in areas of higher elevation and the desert rural areas in the south. The unique characteristics of DPD in UT in terms of health and lifestyle factors, as well as the demographic structure of DPD in the most LDS populous states (UT, Idaho, Wyoming), suggest that high DPD in heavily LDS areas are predominantly prescription opioid related whereas in other Western states a larger proportion of DPD might come from illicit drugs. CONCLUSION: Drug policies need to be adapted to the geographical differences in the dominant type of drug causing death. Educational materials need to be marketed to the demographic groups at greatest risk and take into account differences in population characteristics between and within States. Some suggestions about how such adaptations can be made are given and future research needs outlined.

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.

Impact of Comorbidities on Prostate Cancer Stage at Diagnosis in Florida.

To examine the association of major types of comorbidity with late-stage prostate cancer, a random sample of 11,083 men diagnosed with prostate cancer during 2002-2007 was taken from the Florida Cancer Data System. Individual-level covariates included demographics, primary insurance payer, and comorbidity following the Elixhauser Index. Socioeconomic variables were extracted from Census 2000 data and merged to the individual level data. Provider-to-case ratio at county level was alsocomputed. Multilevel logistic regression was used to assess associations between these factors and late-stage diagnosis of prostate cancer. Higher odds of late-stage diagnosis was significantly related to presence of comorbidities, being unmarried, current smoker, uninsured, and diagnosed in not-for-profit hospitals. The study reported that the presence of certain comorbidities, specifically 10 out of the 45, was associated with late-stage prostate cancer diagnosis. Eight out of 10 significant comorbid conditions were associated with greater risk of being diagnosed at late-stage prostate cancer. On the other hand, men who had chronic pulmonary disease, and solid tumor without metastasis, were less likely to be diagnosed with late-stage prostate cancer. Late-stage diagnosis was associated with comorbidity, which is often associated with increased health care utilization. The association of comorbidity with late-stage prostate cancer diagnosis suggests that individuals with significant comorbidity should be offered routine screening for prostate cancer rather than focusing only on managing symptomatic health problems.

Impact of Age, Race and Socio-economic Status on Temporal Trends in Late-Stage Prostate Cancer Diagnosis in Florida.

Individual-level data from the Florida Cancer Data System (1981-2007) were analysed to explore temporal trends of prostate cancer late-stage diagnosis, and how they vary based on race, income and age. Annual census-tract rates were computed for two races (white and black) and two age categories (40-65, >65) before being aggregated according to census tract median household incomes. Joinpoint regression and a new disparity statistic were applied to model temporal trends and detect potential racial and socio-economic differences. Multi-dimensional scaling was used as an innovative way to visualize similarities among temporal trends in a 2-D space. Analysis of time-series indicated that late-stage diagnosis was generally more prevalent among blacks, for age category 40-64 compared to older patients covered by Medicare, and among classes of lower socio-economic status. Joinpoint regression also showed that the rate of decline in late-stage diagnosis was similar among older patients. For younger patients, the decline occurred at a faster pace for blacks with rates becoming similar to whites in the late 90s, in particular for higher incomes. Both races displayed distinct spatial patterns with higher rates of late-stage diagnosis in the Florida Panhandle for whites whereas high rates clustered in South-eastern Florida for blacks.

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.

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.

Factors associated with overall survival prostate cancer in Florida: a multilevel analysis.

OBJECTIVE: To investigate individual and contextual factors contributing to overall prostate cancer (PCa) survival in Florida. METHODS: A random sample of 6,457 PCa cases diagnosed between 10/1/2001 and 12/31/2007 was extracted from Florida Cancer Data System. Comorbidity was computed following Elixhauser Index. Survival probability curve was generated using Kaplan-Meier method. The Wei, Lin, and Weissfel model was used for the multivariate analysis. RESULTS: Older age at diagnosis was associated with shorter time to death. Current smokers had a higher hazard rate than non-current smokers. Higher hazard of overall mortality was associated with being diagnosed with advanced stage compared with localized stage and having poorly-differentiated tumor compared with well-moderately differentiated tumor. No definitive treatment, radiation alone, and hormone alone were significantly associated with elevated hazard rate compared with surgery. Fifteen comorbidities were significantly associated with shorter time-to-death. CONCLUSIONS: Effective control of comorbidity in PCa patients should help improve life expectancy and lead to prolonged survival.

Multilevel Factors Associated With Overall Mortality for Men Diagnosed With Prostate Cancer in Florida.

To identify individual and contextual factors contributing to overall mortality among men diagnosed with prostate cancer in Florida, a random sample of patients (between October 1, 2001, and December 31, 2007) was taken from the Florida Cancer Data System. Patient's demographic and clinical information were obtained from the Florida Cancer Data System. Comorbidity was computed following the Elixhauser Index method. Census-tract-level socioeconomic status and farm house presence were extracted from Census 2000 and linked to patient data. The ratio of urologists and radiation oncologists to prostate cancer cases at the county level was computed. Multilevel logistic regression was conducted to identify significance of individuals and contextual factors in relation to overall mortality. A total of 18,042 patients were identified, among whom 2,363 died. No racial difference was found in our study. Being older at diagnosis, unmarried, current smoker, uninsured, diagnosed at late stage, with undifferentiated, poorly differentiated, or unknown tumor grade were significantly associated with higher odds of overall mortality. Living in a low-income area was significantly associated with higher odds of mortality (p = .0404). After adjusting for age, stage, and tumor grade, patients who received hormonal, combination of radiation with hormone therapy, and no definitive treatment had higher odds of mortality compared with those who underwent surgery only. A large number of comorbidities were associated with higher odds of mortality. Although disease-specific mortality was not examined, our findings suggest the importance of careful considerations of patient sociodemographic characteristics and their coexisting conditions in treatment decision making, which in turn affects mortality.

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.

Use of treatment information from a state central cancer registry in prostate cancer research.

A method was developed to categorize prostate cancer treatments for epidemiologic and outcomes studies. A total of 60,497 prostate cancer cases from the Florida Cancer Data System diagnosed between 2001 and 2007 were used. The classification has the following properties. First, the treatments classified in the same group are clinically comparable and capture all prostate cancer treatments or combinations of treatments (exhaustive classification). Second, the grouping was set up in a way that each patient is captured in only 1 treatment category without leaving out any patient due to treatment type (mutually exclusive categories). The prostate cancer cases were initially categorized into 14 combinations of treatment, which were then collapsed into 8 broader groups in order to maintain a large sample size for all groups, with treatments remaining clinically comparable within a group.

Construction of a comorbidity index for prostate cancer patients linking state cancer registry with inpatient and outpatient data.

INTRODUCTION: Identifying clinically relevant comorbid conditions might lead to effective control of prostate cancer- specific risk factors and provide opportunities to improve patient care and outcomes. There are challenges in assessing comorbidity using linked databases such as statewide hospital administrative data and state cancer registry. The objective was to compile a comprehensive list of clinically relevant comorbid conditions for patients with prostate cancer using registry and statewide diagnosis databases. METHODS: Florida Cancer Data System cases were linked with the inpatient/ outpatient diagnosis information. The Elixhauser Comorbidity Index was used as a reference. Conditions not captured by Elixhauser were identified, and grouped into clinically meaningful categories. Descriptive analysis was performed on comorbidity conditions and major study population variables. Associations of comorbidity with selected demographic and disease characteristics were examined. RESULTS: Twenty-nine Elixhauser and 16 additional categories were examined within the 1 record per patient data set. Statistically significant association was found between comorbidity with race, stage, and age. Blacks had a higher mean number of conditions compared to whites. A higher proportion of blacks had at least 1 comorbid condition compared to whites. Additional conditions identified by this research capture more comorbidities for white men. Distinct trends towards larger number of comorbidities with older age at diagnosis and advanced disease stage were observed. CONCLUSIONS: The Elixhauser Comorbidity Index captured the majority of comorbidities in the study population while the additional conditions identified by this research add more information. This study offers important insights into the challenges and process to identify relevant comorbidities for prostate cancer patients.

A comparison of multiple indicator kriging and area-to-point Poisson kriging for mapping patterns of herbivore species abundance in Kruger National Park, South Africa.

Kruger National Park (KNP), South Africa, provides protected habitats for the unique animals of the African savannah. For the past 40 years, annual aerial surveys of herbivores have been conducted to aid management decisions based on (1) the spatial distribution of species throughout the park and (2) total species populations in a year. The surveys are extremely time consuming and costly. For many years, the whole park was surveyed, but in 1998 a transect survey approach was adopted. This is cheaper and less time consuming but leaves gaps in the data spatially. Also the distance method currently employed by the park only gives estimates of total species populations but not their spatial distribution. We compare the ability of multiple indicator kriging and area-to-point Poisson kriging to accurately map species distribution in the park. A leave-one-out cross-validation approach indicates that multiple indicator kriging makes poor estimates of the number of animals, particularly the few large counts, as the indicator variograms for such high thresholds are pure nugget. Poisson kriging was applied to the prediction of two types of abundance data: spatial density and proportion of a given species. Both Poisson approaches had standardized mean absolute errors (St. MAEs) of animal counts at least an order of magnitude lower than multiple indicator kriging. The spatial density, Poisson approach (1), gave the lowest St. MAEs for the most abundant species and the proportion, Poisson approach (2), did for the least abundant species. Incorporating environmental data into Poisson approach (2) further reduced St. MAEs.

The impact of place and time on the proportion of late-stage diagnosis: the case of prostate cancer in Florida, 1981-2007.

A suite of techniques is introduced for the exploratory spatial data analysis of geographical disparities in time series of health outcomes, including 3D display in a combined time and geography space, binomial kriging for noise filtering, space-time boundary analysis to detect significant differences between adjacent geographical units, and spatially-weighted cluster analysis to group units with similar temporal trends. The approach is used to explore how time series of annual county-level proportions of late-stage prostate cancer diagnosis differ across Florida. The state-average proportion of late-stage diagnosis decreased 50% since 1981. This drop started in the early 1990s when prostate-specific antigen (PSA) test became widely available and several parts of Florida underwent fast urbanization. Boundary analysis revealed geographical disparities in the impact of the screening procedure, in particular as it began available. The gap among counties is narrowing with time, except for the Big Bend region where the decline is much slower.