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Geostatistics offers two fundamental contributions to environmental contaminant exposure assessment: (1) a group of methods to quantitatively describe the spatial distribution of a pollutant and (2) the ability to improve estimates of the exposure point concentration by exploiting the geospatial information present in the data. The second contribution is particularly valuable when exposure estimates must be derived from small data sets, which is often the case in environmental risk assessment. This article addresses two topics related to the use of geostatistics in human and ecological risk assessments performed at hazardous waste sites: (1) the importance of assessing model assumptions when using geostatistics and (2) the use of geostatistics to improve estimates of the exposure point concentration (EPC) in the limited data scenario. The latter topic is approached here by comparing design‐based estimators that are familiar to environmental risk assessors (e.g., Land's method) with geostatistics, a model‐based estimator. In this report, we summarize the basics of spatial weighting of sample data, kriging, and geostatistical simulation. We then explore the two topics identified above in a case study, using soil lead concentration data from a Superfund site (a skeet and trap range). We also describe several areas where research is needed to advance the use of geostatistics in environmental risk assessment.

Concerning the characterisation or classification of municipalities a wide range of different approaches exists. Usually some historical, functional, and/or political indicators are used for such a classification. These indicators are usually structured simple, referring to inhabitant size, political importance, configuration of available infrastructure like hospitals and schools, places of work, or the like. However, an application field, where a quite specific, meaningful, and comprehensible classification for each municipality is of fundamental interest, is the local financial adjustment between communities on the same hierarchical administrative level. Which municipality delivers gladly more money than it is forced to do by law, or which community renounces voluntarily external support? Therefore, well elaborated indicators are needed to define the amount of money which has to be transferred, generally spoken, from rich communities to the poorer ones. However, it is obvious that a pure redistribution of revenues between financially strong and financially weak communities, which would lead in principle to a more or less equal financial configuration of the communities, is not sufficient for a fair system of financial adjustment. Such a redistribution system would not consider the different financial loads of the budgets of different types of communes. These varying financial loads for varying types of commues can be characterised by the following two concepts: 'costs of width' and 'costs of density'. The 'costs of width' are explained mainly by geographical reasons for peripheral and/or mountainous communities with low population density, which implies specific financial load for the particular community. By contrast, 'costs of density' are explained by disproportional high socio-demographic burdens and high costs of infrastructure in central and urban communities. Meaningful indicators for such a financially oriented classification of municipalities need detailed investigations, to be silent completely of that these indicators also need political acceptance, in the end. This paper presents a study carried out for the Canton of Zurich, Switzerland, which made part of the cantonal revision of the system of inter-communal financial adjustment. The aim was to provide means for a cantonal regulation on how the financial adjustment between the communities should be regulated. Therefore, socio-demographic and geographic indicators have been evaluated in order to find rules to reflect the financial load of the municipal budgets. The heuristically driven statistical modelling has been carried out using multiple regression. Besides the presentation of the technical approach, this paper discusses the analysed indicators in the perspective of regional policy and territorial justice.

This paper gives an overview of space–time variability in agriculture and the environment. Analysis is based upon geostatistics in the framework of linear regression theory. Common procedures for spatial data are extended towards the space–time domain. Several practical studies are presented. The first study describes the use of REML to estimate semi‐variogram models within the presence of trends. The second study describes the use of probability maps in an environmental statistical study. The third study describes the use of geostatistics in modelling the development of a disease in cabbage. Studies are evaluated using quadratic scoring rules.

The definive version is avalaible at: http://www.springerlink.com/content/0920-4741/ ; This paper presents the results of the interpolation of annual precipitation over a regular grid performed in Aragón (Spain). The main objective was the quantification of the improvement in estimation uncertainty by including elevation in the interpolation and by using base 10 logarithms of both annual precipitation and elevation versus the original values. Long-term annual precipitation (APRE) was available at 182 weather stations. Elevation above sea level (ELEV) was available at those stations and at 1913 additional points over a regular 5 km grid. The spatial variability of APRE, ELEV and their base 10 logarithms (LAPRE and LELEV, respectively), and the spatial correlation between APRE and ELEV, APRE and LELEV, LAPRE and ELEV, and LAPRE and LELEV were described by gaussian direct- and cross-semivariogram models with nugget effects. Geostatistical interpolation methods, ordinary kriging and cokriging, were used to estimate APRE and LAPRE at the 1913 additional elevation points. Estimates of LAPRE were transformed back to APRE values. Cokriging estimates were in general higher than kriging ones, mainly at points of high elevation. The average percent difference among cokriging and kriging estimates was 9–12%. Cokriging estimates obtained with the different sample data sets were in general terms similar. However, at points of high elevation, cokriging with ELEV as the auxiliary variable seemed to overestimate annual precipitation. Estimation error standard deviations (EESD) also were computed in each interpolation point. For all points, the EESD obtained using LAPRE values were lower than those obtained using APRE values, being the average percent differences of –38 to –42%. Likewise, for all interpolation points, cokriging EESD were lower than kriging ones. Using LAPRE and LELEV values, the average percent difference among cokriging and kriging EESD was –11.0%, with minimum and maximum percent differences of –6.7 and –35.8%, respectively. ; This research was funded by the Ministerio de Educaci6n y Ciencia, Government of Spain, through the project CICYT-514 and a grant to the author. ; Peer reviewed

Geostatistics is the main technique used to efficiently determine spatial variability. The objective of this study was to evaluate the applicability of the principles of geostatistics in the use of semivariograms elaborated through parametric monitoring and the assumption automatically made by software in the map preparation of soil chemical attributes. Available phosphorus (P), potassium (K+), calcium (Ca2+), magnesium (Mg2+), base saturation (V%), sulfur (SO42-), and pH were compared from the soil chemical attributes of 60 samples of a Typical Oxisol collected at a 0-20 cm depth and a distance of 300 m between the points. The maps were compared using error matrices and evaluated by the Global Accuracy (GA), Kappa (K), and Tau (T) indexes. The parameterized semivariograms and the automatic software model assumption did not present a high coincidence for the available P and Mg2+, making it necessary to adjust the semivariogram variables in the spatial analysis as a function of the outliers, sum of squares of residuals, coefficient of determination, and cross-validation to better represent the variability of the data and thus avoid distortions of the sample point range that would affect the adequate representativeness of the attributes, which contrasts with the automatic model generated by the software.

Background Most Ministries of Health across Africa invest substantial resources in some form of health management information system (HMIS) to coordinate the routine acquisition and compilation of monthly treatment and attendance records from health facilities nationwide. Despite the expense of these systems, poor data coverage means they are rarely, if ever, used to generate reliable evidence for decision makers. One critical weakness across Africa is the current lack of capacity to effectively monitor patterns of service use through time so that the impacts of changes in policy or service delivery can be evaluated. Here, we present a new approach that, for the first time, allows national changes in health service use during a time of major health policy change to be tracked reliably using imperfect data from a national HMIS. Methods Monthly attendance records were obtained from the Kenyan HMIS for 1 271 government-run and 402 faith-based outpatient facilities nationwide between 1996 and 2004. A space-time geostatistical model was used to compensate for the large proportion of missing records caused by non-reporting health facilities, allowing robust estimation of monthly and annual use of services by outpatients during this period. Results We were able to reconstruct robust time series of mean levels of outpatient utilisation of health facilities at the national level and for all six major provinces in Kenya. These plots revealed reliably for the first time a period of steady nationwide decline in the use of health facilities in Kenya between 1996 and 2002, followed by a dramatic increase from 2003. This pattern was consistent across different causes of attendance and was observed independently in each province. Conclusion The methodological approach presented can compensate for missing records in health information systems to provide robust estimates of national patterns of outpatient service use. This represents the first such use of HMIS data and contributes to the resurrection of these hugely expensive but ...

Background: Most Ministries of Health across Africa invest substantial resouces in some form of health management information system (HMIS) to coordinate the routine acquisition and compilation of monthly treatment and attendance records from health facilities nationwide. Despite the expense of these systems, poor data coverage means they are rarely, if ever, used to generate reliable evidence for decision makers. One critical weakness across Africa is the current lack of capacity to effectively monitor patterns of service use through time so that the impacts of changes in policy or service delivery can be evaluated. Here, we present a new approach that, for the first time, allows national changes in health service use during a time of major health policy change to be tracked reliably using imperfect data from a national HMIS. Methods: Monthly attendance records were obtained from the Kenyan HMIS for 1 271 government-run and 402 faith-based outpatient facilities nationwide between 1996 and 2004. A space-time geostatistical model was used to compensate for the large proportion of missing records caused by non-reporting health facilities, allowing robust estimation of monthly and annual use of services by outpatients during this period. Results: We were able to reconstruct robust time series of mean levels of outpatient utilisation of health facilities at the national level and for all six major provinces in Kenya. These plots revealed reliably for the first time a period of steady nationwide decline in the use of health facilities in Kenya between 1996 and 2002, followed by a dramatic increase from 2003. This pattern was consistent across different causes of attendance and was observed independently in each province. Conclusion: The methodological approach presented can compensate for missing records in health information systems to provide robust estimates of national patterns of outpatient service use. This represents the first such use of HMIS data and contributes to the resurrection of these hugely expensive ...

Abstract Background Most Ministries of Health across Africa invest substantial resources in some form of health management information system (HMIS) to coordinate the routine acquisition and compilation of monthly treatment and attendance records from health facilities nationwide. Despite the expense of these systems, poor data coverage means they are rarely, if ever, used to generate reliable evidence for decision makers. One critical weakness across Africa is the current lack of capacity to effectively monitor patterns of service use through time so that the impacts of changes in policy or service delivery can be evaluated. Here, we present a new approach that, for the first time, allows national changes in health service use during a time of major health policy change to be tracked reliably using imperfect data from a national HMIS. Methods Monthly attendance records were obtained from the Kenyan HMIS for 1 271 government-run and 402 faith-based outpatient facilities nationwide between 1996 and 2004. A space-time geostatistical model was used to compensate for the large proportion of missing records caused by non-reporting health facilities, allowing robust estimation of monthly and annual use of services by outpatients during this period. Results We were able to reconstruct robust time series of mean levels of outpatient utilisation of health facilities at the national level and for all six major provinces in Kenya. These plots revealed reliably for the first time a period of steady nationwide decline in the use of health facilities in Kenya between 1996 and 2002, followed by a dramatic increase from 2003. This pattern was consistent across different causes of attendance and was observed independently in each province. Conclusion The methodological approach presented can compensate for missing records in health information systems to provide robust estimates of national patterns of outpatient service use. This represents the first such use of HMIS data and contributes to the resurrection of these hugely expensive but underused systems as national monitoring tools. Applying this approach to Kenya has yielded output with immediate potential to enhance the capacity of decision makers in monitoring nationwide patterns of service use and assessing the impact of changes in health policy and service delivery.

BACKGROUND: Most Ministries of Health across Africa invest substantial resources in some form of health management information system (HMIS) to coordinate the routine acquisition and compilation of monthly treatment and attendance records from health facilities nationwide. Despite the expense of these systems, poor data coverage means they are rarely, if ever, used to generate reliable evidence for decision makers. One critical weakness across Africa is the current lack of capacity to effectively monitor patterns of service use through time so that the impacts of changes in policy or service delivery can be evaluated. Here, we present a new approach that, for the first time, allows national changes in health service use during a time of major health policy change to be tracked reliably using imperfect data from a national HMIS. METHODS: Monthly attendance records were obtained from the Kenyan HMIS for 1 271 government-run and 402 faith-based outpatient facilities nationwide between 1996 and 2004. A space-time geostatistical model was used to compensate for the large proportion of missing records caused by non-reporting health facilities, allowing robust estimation of monthly and annual use of services by outpatients during this period. RESULTS: We were able to reconstruct robust time series of mean levels of outpatient utilisation of health facilities at the national level and for all six major provinces in Kenya. These plots revealed reliably for the first time a period of steady nationwide decline in the use of health facilities in Kenya between 1996 and 2002, followed by a dramatic increase from 2003. This pattern was consistent across different causes of attendance and was observed independently in each province. CONCLUSION: The methodological approach presented can compensate for missing records in health information systems to provide robust estimates of national patterns of outpatient service use. This represents the first such use of HMIS data and contributes to the resurrection of these hugely expensive but underused systems as national monitoring tools. Applying this approach to Kenya has yielded output with immediate potential to enhance the capacity of decision makers in monitoring nationwide patterns of service use and assessing the impact of changes in health policy and service delivery.