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PubMed2001

Variable selection and Bayesian model averaging in case-control studies.

Covariate and confounder selection in case-control studies is often carried out using a statistical variable selection method, such as a two-step method or a stepwise method in logistic regression. Inference is then carried out conditionally on the selected model, but this ignores the model uncertainty implicit in the variable selection process, and so may underestimate uncertainty about relative risks. We report on a simulation study designed to be similar to actual case-control studies. This shows that p-values computed after variable selection can greatly overstate the strength of conclusions. For example, for our simulated case-control studies with 1000 subjects, of variables declared to be 'significant' with p-values between 0.01 and 0.05, only 49 per cent actually were risk factors when stepwise variable selection was used. We propose Bayesian model averaging as a formal way of taking account of model uncertainty in case-control studies. This yields an easily interpreted summary, the posterior probability that a variable is a risk factor, and our simulation study indicates this to be reasonably well calibrated in the situations simulated. The methods are applied and compared in the context of a case-control study of cervical cancer.

Analysis of Variance↗
PubMed2004

Stochastic modelling of landfill leachate and biogas production incorporating waste heterogeneity. Model formulation and uncertainty analysis.

A mathematical model simulating the hydrological and biochemical processes occurring in landfilled waste is presented and demonstrated. The model combines biochemical and hydrological models into an integrated representation of the landfill environment. Waste decomposition is modelled using traditional biochemical waste decomposition pathways combined with a simplified methodology for representing the rate of decomposition. Water flow through the waste is represented using a statistical velocity model capable of representing the effects of waste heterogeneity on leachate flow through the waste. Given the limitations in data capture from landfill sites, significant emphasis is placed on improving parameter identification and reducing parameter requirements. A sensitivity analysis is performed, highlighting the model's response to changes in input variables. A model test run is also presented, demonstrating the model capabilities. A parameter perturbation model sensitivity analysis was also performed. This has been able to show that although the model is sensitive to certain key parameters, its overall intuitive response provides a good basis for making reasonable predictions of the future state of the landfill system. Finally, due to the high uncertainty associated with landfill data, a tool for handling input data uncertainty is incorporated in the model's structure. It is concluded that the model can be used as a reasonable tool for modelling landfill processes and that further work should be undertaken to assess the model's performance.

Biodegradation, Environmental↗
PubMed2005

An integrated methodology for recording uncertainties about environmental data.

Understanding the limitations of environmental data is essential both for managing environmental systems effectively and for encouraging the responsible use of scientific research when knowledge is limited and priorities are varied. Using a combination of quantitative and qualitative techniques for assessing probabilities, and acknowledging the importance of scenarios where probabilities cannot be determined, an integrated methodology is presented for handling uncertainties about environmental data. The methodology is based on a fourfold distinction between the empirical quality of data (and the ancillary information, such as 'scale', required to interpret this), the sources of uncertainty in data, the 'fitness for use' of the data, and the quality or 'goodness' of an uncertainty model.

Environmental Monitoring↗
PubMed2006

Role of geographic information system (GIS) in watershed simulation by WinVAST model.

The uncertainty of modeling input will increase the simulation error, and this situation always happens in a model without user-friendly interface. WinVAST model, developed by the University of Virginia in 2003, treats an entire multi-catchment by a tree-view structure. Its extra computer programs can connect geographic information system (GIS). Model users can prepare all the necessary information in ArcGIS. Extracting information from GIS interface can not only decrease the inconvenience of data input, but also lower the uncertainty due to data preparation. The Daiyuku Creek and Qupoliao Creek in the Fei-tsui reservoir watershed in Northern Taiwan provided the setting for the case study reported herein. The required information, including slope, stream length, subbasin area, soil type and land-use condition, for WinVAST model should be prepared in a Microsoft Access database, which is the project file of WinVAST with extension mdb. In ArcGIS interface, when the soil layer, land-use layer, and Digital Elevation Model (DEM) map are prepared, all the watershed information can be created as well. This study compared the simulation results from automatically generated input and manual input. The results show that the relative simulation error resulting from the rough process of data input can be around 30% in runoff simulation, and even reach 70% in non-point source pollution (NPSP) simulation. It could conclude that GIS technology is significant for predicting watershed responses by WinVAST model, because it can efficiently reduce the uncertainty induced by input errors.

Computer Simulation↗
PubMed2001

Reliability of optimal control strategies for photochemical air pollution.

This study illustrates how consideration of modeling uncertainties can affect optimal control strategies for urban ozone. Control strategies are investigated for illustrative cases of air parcel trajectories ending at Azusa, CA, and Riverside, CA, on August 28, 1987. The control strategies are designed to achieve a specified air quality target with a given reliability, considering uncertainties in the California Institute of Technology's trajectory model and its inputs, including uncertainties in emissions and in the SAPRC-97 chemical mechanism. A decoupled stochastic optimization scheme is used to solve the chance-constrained programming problem. Least-cost control strategies derived using nominal model inputs and parameter values have low reliability for some target O3 concentrations when uncertainties are taken into account. For the case considered, reducing volatile organic compound (VOC) emissions from motor vehicles is identified as the least-cost approach to meeting O3 targets at Azusa. However, the optimal control strategies for Riverside depend on the target O3 concentrations and the level of reliability required. Consideration of model uncertainty is found to shift the focus from VOC controls to nitrogen oxide controls for the Riverside trajectory.

Air Pollution↗
PubMed1989

Evaluation of uncertainty in input parameters to pharmacokinetic models and the resulting uncertainty in output.

Physiologically-based pharmacokinetic (PBPK) models may be used to predict the concentrations of parent chemical or metabolites in tissues, resulting from specified chemical exposures. An important application of PBPK modeling is in assessment of carcinogenic risks to humans, based on animal data. The parameters of a PBPK model may include metabolic parameters, blood/air and tissue/blood partition coefficients, and physiological parameters, such as organ weights and blood flow rates. Uncertainty in estimates of these parameters results in uncertainty regarding tissue concentrations and resulting risks. Data are reviewed relevant to the quantification of these uncertainties, for a PBPK model-based risk assessment for tetrachloroethylene. Probability distributions are developed to express uncertainty in model parameters, and uncertainties are propagated by a sequence of operations that simulates processes recognized as contributing to estimates of human risk. Distributions of PBPK model output and human risk estimates are used to characterize uncertainty resulting from uncertainty in model parameters.

Animals↗
PubMed2001

An overview of human exposure modeling activities at the USEPA's National Exposure Research Laboratory.

The computational modeling of human exposure to environmental pollutants is one of the primary activities of the US Environmental Protection Agency (USEPA)s National Exposure Research Laboratory (NERL). Assessment of human exposures is a critical part of the overall risk assessment paradigm. In exposure assessment, we analyze the source-to-dose sequence of processes, in which pollutants are released from sources into the environment, where they may move through multiple environmental media, and to human receptors via multiple pathways. Exposure occurs at the environment-human interface, where pollutants are contacted in the course of human activities. Exposure may result in a dose, by which chemicals enter the body through multiple portals of entry, primarily inhalation, ingestion, and dermal absorption. Within the body, absorbed pollutants are distributed to, metabolized within, and eliminated from various organs and tissues, where they may cause toxicologic responses or adverse health effects. The NERL's modeling efforts are directed at improving our understanding of this sequence of processes, by characterizing the various factors influencing exposures and dose, and their associated variabilities and uncertainties. Modeling at the NERL is one of three essential programmatic elements, along with measurements and methods development. These are pursued interactively to advance our understanding of exposure-related processes. Exposure models are developed and run using the best currently available measurement data to simulate and predict population exposure and dose distributions, and to identify the most important factors and their variabilities and uncertainties. This knowledge is then used to guide the development of improved methods and measurements needed to obtain better data to improve the assessment and reduce critical uncertainties. These models and measurement results are tools that can be used in risk assessments and in risk management decisions in order to reduce harmful exposures. Current areas of the NERL's exposure modeling emphasis include: Pollutant concentrations in ambient (outdoor) air using the Third Generation Air Quality Modeling System's Community Multiscale Air Quality model (Models-3/CMAQ); Air flow and pollutant concentrations at local and microenvironmental scales using computational fluid dynamics (CFD); Human inhalation exposure to airborne particulate matter, air toxics, and multipathway exposure to pesticides, using the Stochastic Human Exposure and Dose Simulation (SHEDS) model; Human and ecological exposure and risk assessments of hazardous waste sites using Framework for Risk Analysis in Multimedia Environmental Systems--Multimedia, Multipathway, Multireceptor Risk Assessment (FRAMES-3MRA), one of many software programs available from the NERL's Center for Exposure Assessment Modeling (CEAM); Physiologically based pharmacokinetic (PBPK) modeling of pesticides and volatile organic compounds (VOCs) in the Exposure-Related Dose-Estimating Model (ERDEM). A brief historical overview of the NERL's evolution of human exposure models is presented, with examples of the present state-of-the-science represented by SHEDS and FRAMES-3MRA.

Air Pollutants↗
PubMed1996

On the interpretation of certainty factors in expert systems.

Despite the strong theoretical foundation the Bayesian probabilistic approach to model uncertainty in medicine meets many difficulties at the implementation step. One of these difficulties is related to a large amount of conditional probabilities to be assessed and in many cases this task was recognised to be practically insoluble. The MYCIN certainty factors model is a widely distributed pragmatical approach for modeling reasoning under uncertainty that substantially simplifies the problem, at the sacrifice of theoretical soundness. One can determine certainty factors as a function of prior and posterior probability. However, this approach is only consistent with the modularity axiom for certainty factors for tree-structure inference networks, which is rarely true for practical applications. In this paper we abandon the requirement of a direct probabilistic interpretation of certainty factors and build a model of propagation of uncertainty in terms of absolute belief and belief updates. We describe our model for propagating uncertainty in terms of matrix multiplication with specifically defined addition and multiplication which correspond to parallel and sequential combinations of certainty factors. It is possible to define these operations in such a manner that they form a field, and therefore to obtain some useful properties. Finally we present a method of determining certainty factors from statistical data using nonlinear regression and illustrate it with a leukemia diagnostics problem.

Artificial Intelligence↗
PubMed2005

Bayesian model averaging: development of an improved multi-class, gene selection and classification tool for microarray data.

MOTIVATION: Selecting a small number of relevant genes for accurate classification of samples is essential for the development of diagnostic tests. We present the Bayesian model averaging (BMA) method for gene selection and classification of microarray data. Typical gene selection and classification procedures ignore model uncertainty and use a single set of relevant genes (model) to predict the class. BMA accounts for the uncertainty about the best set to choose by averaging over multiple models (sets of potentially overlapping relevant genes). RESULTS: We have shown that BMA selects smaller numbers of relevant genes (compared with other methods) and achieves a high prediction accuracy on three microarray datasets. Our BMA algorithm is applicable to microarray datasets with any number of classes, and outputs posterior probabilities for the selected genes and models. Our selected models typically consist of only a few genes. The combination of high accuracy, small numbers of genes and posterior probabilities for the predictions should make BMA a powerful tool for developing diagnostics from expression data. AVAILABILITY: The source codes and datasets used are available from our Supplementary website.

Algorithms↗
PubMed1995

EEG dipole localization bounds and MAP algorithms for head models with parameter uncertainties.

The Cramer-Rao bound for unbiased dipole location estimation is derived under the assumption of a general head model parameterized by deterministic and stochastic parameters. The expression thus characterizes fundamental limits on EEG dipole localization performance due to the effects of both model uncertainty and statistical measurements noise. Expressions are derived for the cases of multivariate Gaussian and gamma distribution priors, and examples are given to illustrate the derived bounds when the radii and conductivities of a four-concentric sphere head model are allowed to be random. The joint MAP estimate of location/model parameters is then examined as a means of achieving robustness to deviations from an ideal head model. Random variations in both the multiple sphere radii and the layer conductivities are shown, via the stochastic Cramer-Rao bounds and Monte Carlo simulation of the MAP estimator, to have the most impact on localization performance in high SNR regions, where finite sample effects are not the limiting factors. This corresponds most often to spatial regions that are close to the scalp electrodes.

Algorithms↗
PubMed2004

Experimental validation of a nonparametric probabilistic model of nonhomogeneous uncertainties for dynamical systems.

The paper deals with an experimental validation of a nonparametric probabilistic model of nonhomogeneous uncertainties for dynamical systems. The theory used, recently introduced, allows model uncertainties and data uncertainties to be simultaneously taken into account. An experiment devoted to this validation was specifically developed. The experimental model is constituted of two simple dural rectangular plates connected together with a complex joint. In the mean mechanical model, the complex joint, which is constituted of two additional plates attached with 40 screw-bolts, is modeled by a homogeneous orthotropic continuous plate with constant thickness, as usual. Consequently, the mean model introduces a region (the joint) which has a high level of uncertainties. The objective of the paper is to present the experiment and the comparisons of the theoretical prediction with the experiments.

Journal Article↗
PubMedDate not supplied

Modeling aggregate exposures to glycol ethers from use of commercial floor products.

Computer modeling of aggregate exposure provides the capability to estimate the range of doses that can occur from product use and to understand the relative importance of different routes of exposure. This paper presents an assessment of aggregate occupational exposure to two glycol ethers used as solvents in floor maintenance products for industrial and institutional facilities, using a simulation tool named PROMISE. Three commercial floor-care products were assumed to be applied in sequence--a floor stripper, then a floor cleaner, and lastly a protective coating. The glycol ethers modeled were ethylene glycol butyl ether (EGBE) in the floor stripper and in the floor cleaner, and dipropylene glycol methyl ether (DPGME) in the coating. Modeling uncertainty was assessed through a comparison of the PROMISE inhalation exposure estimates with those from an independent model (MCCEM), and parameter uncertainty was investigated using PROMISE software's Monte Carlo simulation capabilities. Modeling results indicated that inhalation is the dominant exposure route. The predicted average air concentration and inhalation dose from PROMISE agreed with the second model (MCCEM) within 10%. Monte Carlo simulation indicated that the upper end of the aggregate-dose distribution for the scenario was more than 50% higher than the value of the point estimate. The modeled 8-h TWA concentrations for EGBE and DPGME were lower than the corresponding permissible exposure limits American Conference of Governmental Industrial Hygienists (ACGIH) Threshold Limit Values (TLV) by at least a factor of 20, indicating that under the assumed conditions workplace exposures to glycol ethers are below levels of concern.

Adult↗
PubMed2004

Uncertainty analysis in dissolved oxygen modeling in streams.

Uncertainty analysis in surface water quality modeling is an important issue. This paper presents a method based on the first-order reliability method (FORM) to assess the exceedance probability of a target dissolved oxygen concentration in a stream, using a Streeter-Phelps prototype model. Basic uncertainty in the input parameters is considered by representing them as random variables with prescribed probability distributions. Results obtained from FORM analysis compared well with those of the Monte Carlo simulation method. The analysis also presents the stochastic sensitivity of the probabilistic outcome in the form of uncertainty importance factors, and shows how they change with changing simulation time. Furthermore, a parametric sensitivity analysis was conducted to show the effect of selection of different probability distribution functions for the three most important parameters on the design point, exceedance probability, and importance factors.

Models, Theoretical↗
PubMed2002

Critical issues in benchmark calculations from continuous data.

The benchmark dose (BMD) is a dose that causes a specified low level of additional risk and is estimated using a statistical dose-response analysis. Regulatory agencies are using a statistical lower bound on the BMD in the place of the NOAEL for establishing exposure limits. However, there are still several issues regarding the BMD for which no clear consensus has emerged, particularly with respect to calculation of BMD from continuous response data. These include: (1) how to define the BMD from continuous data so that they are comparable to BMD derived from binary data, (2) what dose-response models and levels of additional risk should be used to calculate the BMD. The "hybrid" approach (Gaylor and Slikker, 1990; Crump, 1995) expresses the BMD from continuous data in terms that are directly comparable to those obtained using binary data. Several features of the hybrid approach are examined, with the emphasis on application to epidemiological data. The effect on the BMD of converting continuous data to binary form is quantified. Model uncertainty is explored, and the need for controlling this uncertainty by restricting the class of allowable models is demonstrated. Control data, which are often not available in epidemiological studies, are shown to have a limited effect upon the BMD so long as the model for the mean response is linear or convex. Such models are also biologically plausible, at least at low doses. Based on these and other considerations, suggestions are made for selecting a model for applying the hybrid approach and for selecting the level of additional risk on which to base the BMD.

Algorithms↗
PubMed2005

Measurement of the Cabibbo-Kobayashi-Maskawa angle gamma in B+/--->D*K+/- decays with a Dalitz analysis of D-->K0(S)pi-pi+.

We report on a measurement of the Cabibbo-Kobayashi-Maskawa CP-violating phase gamma through a Dalitz analysis of neutral D decays to K0(S)pi-pi+ in the processes B+/- -->D*K+/-, D*-->Dpi0, Dgamma. Using a sample of 227 x 10(6) BB pairs collected by the BABAR detector, we measure the amplitude ratios r(B)=0.12+/-0.03+/-0.04 and r*(B)=0.17+/-0.10+/-0.03+/-0.03, the relative strong phases delta(B)=(104+/-45(+17+16)(-21-24))degrees and delta*(B)=(-64+/-41(+14)(-12)+/-15) degrees between the amplitudes A(B- -->D*0K-) and A(B- -->D*0)K-), and gamma=(70+/-31(+12+14)(-10-11))degrees. The first error is statistical, the second is the experimental systematic uncertainty, and the third reflects the Dalitz model uncertainty. The results for the strong and weak phases have a twofold ambiguity.

Journal Article↗
PubMed2003

Risk estimates for deterministic health effects of inhaled weapons grade plutonium.

Risk estimates for deterministic effects of inhaled weapons-grade plutonium (WG Pu) are needed to evaluate potential serious harm to (1) U.S. Department of Energy nuclear workers from accidental or other work-place releases of WG Pu; and (2) the public from terrorist actions resulting in the release of WG Pu to the environment. Deterministic health effects (the most serious radiobiological consequences to humans) can arise when large amounts of WG Pu are taken into the body. Inhalation is considered the most likely route of intake during work-place accidents or during a nuclear terrorism incident releasing WG Pu to the environment. Our current knowledge about radiation-related harm is insufficient for generating precise estimates of risk for a given WG Pu exposure scenario. This relates largely to uncertainties associated with currently available risk and dosimetry models. Thus, rather than generating point estimates of risk, distributions that account for variability/uncertainty are needed to properly characterize potential harm to humans from a given WG Pu exposure scenario. In this manuscript, we generate and summarize risk distributions for deterministic radiation effects in the lungs of nuclear workers from inhaled WG Pu particles (standard isotopic mix). These distributions were developed using NUREG/CR-4214 risk models and time-dependent, dose conversion factor data based on Publication 30 of the International Commission on Radiological Protection. Dose conversion factors based on ICRP Publication 30 are more relevant to deterministic effects than are the dose conversion factors based on ICRP Publication 66, which relate to targets for stochastic effects. Risk distributions that account for NUREG/CR-4214 parameter and model uncertainties were generated using the Monte Carlo method. Risks were evaluated for both lethality (from radiation pneumonitis) and morbidity (due to radiation-induced respiratory dysfunction) and were found to depend strongly on absorbed-dose-rate history (which depends on WG Pu solubility). The results obtained were compared to new data from animal and epidemiological studies. Our findings suggest that NUREG/CR-4214 models for assessing lethality risk from inhaled radionuclides may need some modest revision in light the new data. However, for assessing morbidity risks, major revisions may be needed.

Administration, Inhalation↗
PubMed2003

A Bayesian A-optimal and model robust design criterion.

Suppose that the true model underlying a set of data is one of a finite set of candidate models, and that parameter estimation for this model is of primary interest. With this goal, optimal design must depend on a loss function across all possible models. A common method that accounts for model uncertainty is to average the loss over all models; this is the basis of what is known as Läuter's criterion. We generalize Läuter's criterion and show that it can be placed in a Bayesian decision theoretic framework, by extending the definition of Bayesian A-optimality. We use this generalized A-optimality to find optimal design points in an environmental safety setting. In estimating the smallest detectable trace limit in a water contamination problem, we obtain optimal designs that are quite different from those suggested by standard A-optimality.

Bayes Theorem↗