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Thyroid cancer following scalp irradiation: a reanalysis accounting for uncertainty in dosimetry.

In the 1940s and 1950s, over 20,000 children in Israel were treated for tinea capitis (scalp ringworm) by irradiation to induce epilation. Follow-up studies showed that the radiation exposure was associated with the development of malignant thyroid neoplasms. Despite this clear evidence of an effect, the magnitude of the dose-response relationship is much less clear because of probable errors in individual estimates of dose to the thyroid gland. Such errors have the potential to bias dose-response estimation, a potential that was not widely appreciated at the time of the original analyses. We revisit this issue, describing in detail how errors in dosimetry might occur, and we develop a new dose-response model that takes the uncertainties of the dosimetry into account. Our model for the uncertainty in dosimetry is a complex and new variant of the classical multiplicative Berkson error model, having components of classical multiplicative measurement error as well as missing data. Analysis of the tinea capitis data suggests that measurement error in the dosimetry has only a negligible effect on dose-response estimation and inference as well as on the modifying effect of age at exposure.

Biometry↗

Quantification of physical and biological uncertainty in the simulation of the yield of a tropical crop using present-day and doubled CO2 climates.

The impacts of climate change on crop productivity are often assessed using simulations from a numerical climate model as an input to a crop simulation model. The precision of these predictions reflects the uncertainty in both models. We examined how uncertainty in a climate (HadAM3) and crop General Large-Area Model (GLAM) for annual crops model affects the mean and standard deviation of crop yield simulations in present and doubled carbon dioxide (CO2) climates by perturbation of parameters in each model. The climate sensitivity parameter (gamma, the equilibrium response of global mean surface temperature to doubled CO2) was used to define the control climate. Observed 1966-1989 mean yields of groundnut (Arachis hypogaea L.) in India were simulated well by the crop model using the control climate and climates with values of gamma near the control value. The simulations were used to measure the contribution to uncertainty of key crop and climate model parameters. The standard deviation of yield was more affected by perturbation of climate parameters than crop model parameters in both the present-day and doubled CO2 climates. Climate uncertainty was higher in the doubled CO2 climate than in the present-day climate. Crop transpiration efficiency was key to crop model uncertainty in both present-day and doubled CO2 climates. The response of crop development to mean temperature contributed little uncertainty in the present-day simulations but was among the largest contributors under doubled CO2. The ensemble methods used here to quantify physical and biological uncertainty offer a method to improve model estimates of the impacts of climate change.

Arachis↗

Uncertainty quantification in the health consequences of the boiling liquid expanding vapour explosion phenomenon.

A methodology for estimating the risk owing to the phenomenon of boiling liquid expanding vapour explosion (BLEVE) in the presence of uncertainties both in the model and in the parameters of the models is presented. BLEVE takes place when a tank containing liquefied petroleum gas (LPG) is exposed to fire and fails catastrophically. Two models have been used in the estimation of the intensity of thermal radiation from the resulting fireball, namely the solid-flame model assuming an emission power independent of the combustion mass and the point-source model that estimates the emissive power as a function of the combustion mass. Three measures of the BLEVE consequences, the intensity of thermal radiation, the dose of thermal radiation and the probability of loss of life as a result of the exposure to the thermal radiation and as a function of the distance from the center of the tank have been considered. Uncertainties in the exact values of the parameters of the models have been quantified and the resulting uncertainties in the three consequence measures have been assessed. A sensitivity analysis on the relative contribution of the uncertainty in each of the input variables to the uncertainties of the consequence measures has been performed. One conclusion is that the uncertainties in the probability of loss of life are mainly due to the uncertainties in the model of the physical phenomenon rather than to the uncertainties of the dose-response model.

Accidents, Occupational↗

Modeling macropore flow effects on pesticide leaching: inverse parameter estimation using microlysimeters.

Macropore flow is a key factor determining pesticide fate, but models accounting for this process need parameters that cannot be easily measured. This study was conducted to investigate the use of inverse techniques to estimate parameters controlling macropore flow and pesticide fate in the dual-permeability model MACRO. Undisturbed columns were sampled at three landscape positions (hilltop, slope, hollow) with contrasting texture and organic carbon content. Transient leaching experiments were performed for an anionic tracer and the herbicide MCPA (4-chloro-2methylphenoxy acetic acid) during a 4-mo period, first under natural rainfall, and then under controlled irrigation in the laboratory. The tracer breakthrough for the liner-textured soil from the hilltop showed strong evidence of macropore flow, resulting in a rapid leaching of MCPA, while leaching was minimal from the organic-rich hollow soil, since macropore flow was weaker and adsorption stronger. The MACRO model was linked to the inverse modeling program SUFI (Sequential Uncertainty Fitting) to enable calibration of nine key model parameters. Based on calculated model efficiencies, MACRO-SUFI gave generally good predictions of water movement and tracer and pesticide transport, although some errors were attributed to difficulties in simulating the effects of soil moisture on degradation and the timing of water outflows. Even after calibration, significant uncertainties remained for some key parameters controlling macropore flow. Nevertheless, the parameter estimates were significantly different between landscape positions and could also be related to basic soil properties. The posterior uncertainty ranges could probably be reduced with a more exhaustive sampling of the parameter space and improved experimental designs.

2-Methyl-4-chlorophenoxyacetic Acid↗

An integrated model for the analysis of pharmacokinetic data from microdialysis experiments.

PURPOSE: To develop an integrated model for microdialysis data that incorporates all data including the recovery measurements in one model, and to compare this model to a previous model and the results from a noncompartmental analysis. METHODS: The models were developed in NONMEM. The modes of analysis were compared with respect to parameter estimates, model structures, gained mechanistic insight, and practical aspects. RESULTS: Both modeling approaches resulted in similar model structures. The parameter estimates in blood and brain from the models and the results from the noncompartmental analysis were comparable. Using the integrated model all data, that is, the total arterial concentrations, the venous and brain dialysate concentrations, and the recovery measurements, were analyzed simultaneously. CONCLUSION: The theoretical benefits of the integrated model are related to the inclusion of the recovery in the model and the use of all collected data as it was observed. Thus, all data are described in a single model, corrections for the recovery and the protein binding are done within the model, and the dialysate observations are described by the integral over each collection interval. Thereby, the variability and the uncertainty in the model parameters are handled correctly to give more reliable parameter estimates.

Animals↗

Initial uptake kinetics in human skin exposed to dilute aqueous trichloroethylene in vitro.

In vitro uptake of 14C-labeled trichloroethylene (TCE) from dilute (approximately 5-ppb) aqueous solutions into human surgical skin was measured using accelerator mass spectrometry (AMS). We analyzed 105 breast-tissue samples obtained from three subjects, representing 27 separate exposure experiments conducted at approximately 20 degrees C for 0, 1, 5, 15, 30, or 60 min. The AMS data obtained positively correlate with (p approximately 0) and vary significantly nonlinearly with (p = 0.0094) exposure duration. These data are inconsistent (p approximately 0) with predictions made for TCE by a proposed U.S. Environmental Protection Agency (USEPA) dermal-exposure model, even when uncertainties in its recommended parameter values for TCE are considered, but are consistent (p = 0.17) with a 1-compartment model for exposed skin-surface tissue governed in vitro by a maximum effective permeability of K*p = 0.28 cm h-1 (+/- 7.0%) and a first-order rate constant of k1 = 1.2 h-1 (+/- 16%). The apparent compartment depth is estimated to be approximately 40-100 microns, i.e., to comprise much or all of the epidermis. In contrast, the USEPA model implies only negligible TCE penetration beyond SC during a 1-h exposure. The K*p estimate based on the 1-compartment model fit is consistent with estimates for TCE based on in vivo studies, which supports the hypothesis that the USEPA model underpredicts short-term dermal uptake of TCE from water. It is shown that for humans, this fit also implies that normalized total uptake of TCE from water by short-term dermal contact in vivo is predicted to be fK*p, where f is approximately 80% for longer normothermic exposures and approximately 95% during a brief hot shower or bath. This study illustrates the power of AMS to facilitate analyses of contaminant biodistribution and uptake kinetics at very low environmental concentrations.

Breast↗

Evaluation of uncertainty predictions and dose output for model-based dose calculations for megavoltage photon beams.

In many radiotherapy clinics an independent verification of the number of monitor units (MU) used to deliver the prescribed dose to the target volume is performed prior to the treatment start. Traditionally this has been done by using methods mainly based on empirical factors which, at least to some extent, try to separate the influence from input parameters such as field size, depth, distance, etc. The growing complexity of modern treatment techniques does however make this approach increasingly difficult, both in terms of practical application and in terms of the reliability of the results. In the present work the performance of a model-based approach, describing the influence from different input parameters through actual modeling of the physical effects, has been investigated in detail. The investigated model is based on two components related to megavoltage photon beams; one describing the exiting energy fluence per delivered MU, and a second component describing the dose deposition through a pencil kernel algorithm solely based on a measured beam quality index. Together with the output calculations, the basis of a method aiming to predict the inherent calculation uncertainties in individual treatment setups has been developed. This has all emerged from the intention of creating a clinical dose/MU verification tool that requires an absolute minimum of commissioned input data. This evaluation was focused on irregular field shapes and performed through comparison with output factors measured at 5, 10, and 20 cm depth in ten multileaf collimated fields on four different linear accelerators with varying multileaf collimator designs. The measurements were performed both in air and in water and the results of the two components of the model were evaluated separately and combined. When compared with the corresponding measurements the resulting deviations in the calculated output factors were in most cases smaller than 1% and in all cases smaller than 1.7%. The distribution describing the calculation errors in the total dose output has a mean value of -0.04% and a standard deviation of 0.47%. In the dose calculations a previously developed correction of the pencil kernel was applied that managed to contract the error distribution considerably. A detailed analysis of the predicted uncertainties versus the observed deviations suggests that the predictions indeed can be used as a basis for creating action levels and tracking dose calculation errors in homogeneous media.

Air↗

Data reconciliation with uncertain models

Data reconciliation has proven to be an effective technique for providing frequent, accurate and consistent "best estimates" of plant operation data. However, in almost all the proposed techniques until today, the mathematical model of the process has been considered as exact. In point of fact, this hypothesis is uncommon and frequently the models used are uncertain. This paper proposes a new technique of data reconciliation which is able to exploit the knowledge about the uncertainties of the model with regard to which the reconciliation is done. It leads to the solution of a classical quadratic optimisation problem subject to constraints. The originality of the proposed technique is to use penalty functions for solving this problem and to weight each constraint with regard to their uncertainties.

Journal Article↗

Biological modeling of 5-fluorouracil developmental toxicity.

A biologically-based dose-response (BBDR) model is a mathematical description of the biological events leading to expression of a toxic response. As an alternative to current approaches in non-cancer risk assessment, such models will reduce uncertainty in that they will provide a more comprehensive description of toxicity. We are involved in construction of a BBDR model for the developmental toxicity of 5-fluorouracil (5-FU) in the rat using multiple approaches. First, to identify critical events in the pathogenesis of 5-FU developmental toxicity, thymidylate synthetase (TS) inhibition and alterations in cell kinetics and growth were examined in embryos following maternal administration of 5-FU on day 14 of gestation. A dose-related decline in TS activity was observed within 1 h; however, maximal inhibition and recovery were similar at 10, 20 and 40 mg/kg. Dose-dependent cell cycle alterations were observed within 4 h after exposure and were maximal at 8 h. Hindlimb growth reduction was observed 24 h after exposure to 40 mg/kg, but not at lower doses. At term hindlimb defects were observed at doses above 30 mg/kg. An integrated dose-response model for hindlimb defects was derived from empirical relationships among these events. The resultant dose-response somewhat over-predicted the developmental toxicity of 5-FU, although results of a Monte Carlo simulation indicated that these data were not incompatible with model predictions. Overall, the results suggest that TS inhibition is a key component of the mechanism of 5-FU developmental toxicology, but the model does not capture all of the critical events in the induction of hindlimb defects. A preliminary mechanistic model for the inhibition of embryonic TS, DNA synthesis and cell cycle following maternal exposure to 5-FU, independently derived from literature data to further examine the potential role of this pathway in its developmental toxicity, predicted a dose-response for TS inhibition and DNA synthesis that closely reflected the observed patterns. These results further suggest that TS inhibition, resultant deficits in DNA synthesis and cell cycle perturbations represent a critical mechanistic pathway in the developmental toxicity of 5-FU.

Animals↗

Inverse solutions based on MEG and EEG applied to volume conductor analysis.

An inverse solution computer program, using a single current dipole in a selected volume conductor, calculates an equivalent dipole from a magneto- or electroencephalographic distribution. The program is used to evaluate several volume conductor models of the head by using one model when generating the distribution and another when calculating the equivalent dipole. Sources of errors in the equivalent dipole, namely uncertainties in the model parameters (e.g. conductivities) and noise in the MEG or EEG distribution, are investigated in the same way. A realistically shaped model of the head is introduced to investigate the extent to which sphere-shaped models can be used.

Adult↗

An interacting multiple model probabilistic data association filter for cavity boundary extraction from ultrasound images.

This paper presents a novel segmentation technique for extracting cavity contours from ultrasound images. The problem is first discretized by projecting equispaced radii from an arbitrary seed point inside the cavity toward its boundary. The distance of the cavity boundary from the seed point is modeled by the trajectory of a moving object. The motion of this moving object is assumed to be governed by a finite set of dynamical models subject to uncertainty. Candidate edge points obtained along each radius include the measurement of the object position and some false returns. The modeling approach enables us to use the interacting multiple model estimator along with a probabilistic data association filter, for contour extraction. The convergence rate of the method is very fast because it does not employ any numerical optimization. The robustness and accuracy of the method are demonstrated by segmenting contours from a series of ultrasound images. The results are validated through comparison with manual segmentations performed by an expert. An application of the method in segmenting bone contours from computed tomography images is also presented.

Algorithms↗

Air pollution statistics in policy applications.

This review of the role of air pollution statistics in environmental policy sets the UK current controls of sulfur emissions for health and environmental effects in a historical context. The use of critical loads and levels is discussed. The role of air pollution monitoring data in assessing achievement of a health effects air quality standard or predicting exceedance of a critical level or critical load on a national basis is reviewed with the level of monitoring and the interpolation of concentration data identified as important issues. The problems of spatial scale, the scarcity of data for model validation and the use of trends to identify model inadequacy are illustrated. The current statistical challenges in understanding air pollution processes and defining appropriate policies include quantification of uncertainty within complex models, problems of spatial scale and model validation, and development of monitoring strategies which balance the spatial (more sites) and temporal (better process understanding) aspects of the science alongside the balance between policy desire and monitoring practicality. An appropriate statistical goal is development of methodology to ensure appropriate derived data with sufficient accuracy are used for measuring policy achievement.

Air Pollution↗

Estimating internal dose due to ingestion of radionuclides from Nevada Test Site fallout.

The U.S. Department of Energy initiated the Radiation Exposure Review Project to provide a critical reexamination of radiation doses to people resulting from testing nuclear devices at the Nevada Test Site. One part of this effort focused on the dose resulting from the ingestion of contaminated food. The PATHWAY radionuclide transport model was developed to provide estimates of food concentrations for 20 radionuclides for each of 86 test events and 15 agricultural scenarios. These results were then used as input to the Human Ingestion model to provide dose estimates for individuals and populations in 9 western states. The model considered the life-style and age of the people, and accounted for the transport of milk between locations. Estimates of uncertainty were provided for all doses using Monte Carlo simulation techniques. Propagation of uncertainty between the PATHWAY model and the Human Ingestion model required the development of special strategies to ensure that the inherent correlations between concentrations of the radionuclides in foods were handled properly. In addition, the size of the input data base (60 megabytes), the number of cases to consider (over 30,000), and the number of Monte Carlo simulations (over 6 million) required the development of efficient and reliable methods of data access and storage while running simulations concurrently on up to 14 UNIX workstations. The problems encountered in this effort are likely to be typical of any dose reconstruction involving geographically heterogeneous environmental conditions. This paper documents the methods used to disaggregate the system to achieve computation efficiency, the methods used to propagate uncertainty through the model system, and the techniques used to manage data in a distributed computing environment. The radionuclide- and age-specific dose factors used in the analysis are also provided.

Environmental Exposure↗

Can increasing carbon dioxide cause climate change?

The realistic physical functioning of the greenhouse effect is reviewed, and the role of dynamic transport and water vapor is identified. Model errors and uncertainties are quantitatively compared with the forcing due to doubling CO2, and they are shown to be too large for reliable model evaluations of climate sensitivities. The possibility of directly measuring climate sensitivity is reviewed. A direct approach using satellite data to relate changes in globally averaged radiative flux changes at the top of the atmosphere to naturally occurring changes in global mean temperature is described. Indirect approaches to evaluating climate sensitivity involving the response to volcanic eruptions and Eocene climate change are also described. Finally, it is explained how, in principle, a climate that is insensitive to gross radiative forcing as produced by doubling CO2 might still be able to undergo major changes of the sort associated with ice ages and equable climates.

Journal Article↗

Geostatistical assessment and validation of uncertainty for three-dimensional dioxin data from sediments in an estuarine river.

Contaminated sediment management is an urgent environmental and regulatory issue worldwide. Because remediation is expensive, sound quantitative assessments of uncertainty aboutthe spatial distribution of contaminants are critical, butthey are hampered bythe physical complexity of sediment environments. This paper describes the use of geostatistical modeling approaches to quantify uncertainty of 2,3,7,8-tetrachlorodibenzo-p-dioxin concentrations in Passaic River (New Jersey) sediments and to incorporate this information in decision-making processes, such as delineation of contaminated areas and additional sampling needs. First, coordinate transformation and analysis of three-dimensional semivariograms were used to describe and modelthe directional variability accounting forthe meandering course of the river. Then, indicator kriging was employed to provide models of local uncertainty at unsampled locations without requiring a prior transform (e.g. log-normal) of concentrations. Cross-validation results show that the use of probability thresholds leads to more efficient delineation of contaminated areas than a classification based on the exceedence of regulatory thresholds by concentration estimates. Depending on whether additional sampling aims at reducing prediction errors or misclassification rates, the variance of local probability distributions or a measure of the expected closeness to the regulatory threshold can be used to locate candidate locations.

Decision Making↗

A quantitative model of the Escherichia coli 16 S RNA in the 30 S ribosomal subunit.

We use a computer-based protocol for automated structure refinement of large RNAs and ribonucleoproteins to propose a three-dimensional model for the Escherichia coli 16 S RNA in the 30 S ribosomal subunit along with the first quantitative estimates of the uncertainties in the model. Our models are based on the 16 S RNA secondary structure, the small angle neutron scatter map of 30 S proteins, tertiary RNA-RNA and RNA-protein contacts as suggested by cross-linking, chemical footprinting and other experimental studies, and electron microscopy data for the shape of the 30 S subunit and placement of 16 S RNA fragments, along with known motifs in RNA structure. In addition, some data on the interaction of the tRNAs/mRNA with the 16 S RNA were used to localize the active site. Since there are not enough structural data to derive a unique three-dimensional folding of the 16 S RNA, several different conformations can be generated to satisfy the experimental data. A set of seven models was refined to survey the range of acceptable conformations. These models were analyzed to deduce probable positions and orientations of the different helical segments that comprise the 16 S RNA in the Escherichia coli small subunit, and one consensus model from this set is presented here. An estimate of the reliability of our predicted structure is made using the variations between the models, and about 75% of 16 S RNA helical segments are localized to 15 A or less in their position in the small subunit. Our models show a distinct separation of the three major domains of the 16 S RNA. The 5' major domain and the central domain are clustered in the body of the 30 S subunit, whereas the 3' major domain is localized in the head of the subunit. Our modeling results are compared with models of the 16 S RNA proposed by other researchers, and are seen to be similar to the manually built models by Stern et al. and Brimacombe et al. with a few significant differences. The position of nucleotides implicated by footprinting and crosslinking data in tRNA and mRNA binding, and in subunit association are examined, and many of these sites are seen to lie along the 30 S subunit neck, cleft and the platform.

Base Sequence↗

A review of parameter values used to assess the transport of plutonium, uranium, and thorium in terrestrial food chains.

A general methodology of predicting the food chain transport of atmospherically deposited radionuclides is reviewed with an emphasis on variation in parameter values important for realistic behavioral characterization of environmental releases of plutonium, uranium, and thorium. Parameters important to generic simulations of food chain transport, given a known constant deposition onto vegetation, include: fractional interception of particulates by vegetation, vegetation density, effective half-life of contamination on vegetation, soil-to-plant transfer factors, consumption rates by cattle and man, and transfer of nuclides from forage to meat and from forage to milk. Variation in these parameters, which has been encountered in field studies, is summarized. A partial reduction in the variation of predicted concentrations of actinides in foods can be accomplished by more accurately determining critical parameter values like fractional interception of deposition by vegetation, vegetation biomass, and the effective half-life of contamination on vegetation. Field research describing the site dependency and time dependency of probability density functions for model parameter values is needed to make probabilistic predictions concerning Pu, U, and Th transport in food chains and to reduce the uncertainty associated with model predictions and generic assessments of environmental impact.

Biological Transport↗

Measuring decision sensitivity: a combined Monte Carlo-logistic regression approach.

Modeling of the uncertainty of multiple input variables for a complex decision problem complicates sensitivity analysis. A method of analysis comprising stochastic simulation of the model and logistic regression of the simulated dichotomous decision variable against all of the input variables yields a direct measure of the importance of input variables to the decision. This method is demonstrated on a previously analyzed clinical decision either to continue observation or to immediately treat with anticoagulants a woman presenting with deep vein thrombosis in the first trimester of pregnancy. A relative measure of the importance of each input variable in causing a change of decision is estimated by calculating the change in the log odds attributable to variation of each input variable over its range of uncertain values compared with the total change of log odds from variation of all input variables. This method is compared with alternative measures of input variable importance, and is found to be a simple yet powerful tool for gaining quantitative insight into the nuances of a decision model.

Analysis of Variance↗