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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↗
PubMed2005

Uncertainty, imprecision, and the precautionary principle in climate change assessment.

Statistical decision theory can provide useful support for climate change decisions made under conditions of uncertainty. However, the probability distributions used to calculate expected costs in decision theory are themselves subject to uncertainty, disagreement, or ambiguity in their specification. This imprecision can be described using sets of probability measures, from which upper and lower bounds on expectations can be calculated. However, many representations, or classes, of probability measures are possible. We describe six of the more useful classes and demonstrate how each may be used to represent climate change uncertainties. When expected costs are specified by bounds, rather than precise values, the conventional decision criterion of minimum expected cost is insufficient to reach a unique decision. Alternative criteria are required, and the criterion of minimum upper expected cost may be desirable because it is consistent with the precautionary principle. Using simple climate and economics models as an example, we determine the carbon dioxide emissions levels that have minimum upper expected cost for each of the selected classes. There can be wide differences in these emissions levels and their associated costs, emphasizing the need for care when selecting an appropriate class.

Air Pollution↗
PubMed2006

Estimation of daily bisphenol a intake of Japanese individuals with emphasis on uncertainty and variability.

The purpose of this study was to comprehensively assess the exposure of Japanese individuals to bisphenol A (BPA) with emphasis on uncertainty and variability in available information. The uncertainty and variability in parameters were numerically analyzed using Monte Carlo simulation. The uncertainty in the functional relationship between sources and exposure was treated by comparing two approaches: one was to aggregate ingestion and inhalation through all possible exposure pathways and the other was to estimate the intake from urinary excretion by backward calculation. For individuals aged 6 months or above, food was the most significant source of intake. The alteration of the method used in inactivating the inside surface of drink cans slightly contributed to the decrease in daily intake. By the backward calculation approach based on urinary excretion, 95% confidence intervals for the daily intake for high-exposure populations were estimated to be 0.037-0.064 microg/kg/day for males and 0.043-0.075 microg/kg/day for females. Even conservatively estimated daily intakes were lower than the EU's temporary tolerable daily intake (TDI) of 10 microg/kg/day as well as the U.S. Environmental Protection Agency (US EPA)'s reference dose (RfD) of 50 microg/kg/day. Thus, it is unlikely that humans, including infants and young children, are at unacceptable risk from possible BPA exposure.

Adolescent↗
PubMed2006

Uncertainty, decision-making and trust: lessons from the MMR controversy.

Uncertainty about the likelihood of a particular child coming to harm is a chief concern for parents making decisions about the MMR vaccine, but little attention has been given to the ways that parents cope with this uncertainty. Social science frameworks may help practitioners to understand parental decision making and its implications for community practice. In focus groups and interviews involving 87 parents, three distinct strategies for dealing with uncertainty emerged: reducing complexity through trust, compromise strategies that embrace ambivalence and identifying vulnerable groups. Community practitioners should seek to understand how parents may be using these strategies in order to appropriately tailor their information provision and foster trusting relationships in the communities they serve.

Attitude to Health↗
PubMed1998

Confidence intervals or surfaces? Uncertainty on the cost-effectiveness plane.

Although cost-effectiveness analysis is not new, it is only recently that economic analysis has been conducted alongside clinical trials. Whereas in the past economic analysts most often used sensitivity analysis to examine the implications of uncertainty for their results, the existence of patient-level data on costs and effects opens up the possibility of statistical analysis of uncertainty. Unfortunately, ratio statistics can cause problems for standard statistical methods of confidence interval estimation. The recent health economics literature contains a number of suggestions for estimating confidence limits for ratios. In this paper, we begin by reviewing the different methods of confidence interval estimation with a view to providing guidance concerning the most appropriate method. We go on to argue that the focus on confidence interval estimation for cost-effectiveness ratios in the recent literature has been concerned more with problems of estimation than with problems of decision-making. We argue that decision-makers are most likely to be interested in one-sided tests of hypothesis and that confidence surfaces are better suited to such tests than confidence intervals. This approach is consistent with decision-making on the cost-effectiveness plane and with the cost-effectiveness acceptability curve approach to presenting uncertainty due to sampling variation in stochastic cost-effectiveness analyses.

Confidence Intervals↗
PubMed1997

Uncertainty in hydrogeological modelling.

Hydrogeological models are built to predict groundwater flow and the fate of contaminants in the subsurface. After the crucial step of building a conceptual model that includes the processes that should be accounted for, parameter values must be assigned to the components of the model. Measured values of these parameters are available only at a few locations, as is the case for transmissivity, hydraulic conductivity or porosity. Therefore, before making predictions about the movement of contaminants in the aquifer, it is necessary to predict the parameter values at unsampled locations. Given the spatial heterogeneity of the parameters involved, this prediction is always uncertain. Model parameter uncertainty propagates to flow-response variables and further to transport predictions. Parameter uncertainty can be modelled using stochastic methods. Stochastic simulation is used for the generation of alternative spatial realizations of the parameter values, which are then used as input to groundwater flow and mass transport models to obtain frequency distributions of the response variables, e.g. flow velocities, arrival times or concentration levels. These frequency distributions help in making risk-qualified decisions. In order to make these frequency distributions as precise and accurate as possible, it is necessary to incorporate all relevant information in the parameter uncertainty model, i.e. it is necessary to condition the parameter realizations to all direct and indirect information. With this aim, new techniques have recently been developed in hydrogeological modelling. One such technique, for the generation of conductivity realizations conditioned to conductivity, piezometric head and geophysical data, is the self-calibrated method.

Calibration↗
PubMed2005

Uncertainty analysis of penicillin V production using Monte Carlo simulation.

Uncertainty and variability affect economic and environmental performance in the production of biotechnology and pharmaceutical products. However, commercial process simulation software typically provides analysis that assumes deterministic rather than stochastic process parameters and thus is not capable of dealing with the complexities created by variance that arise in the decision-making process. Using the production of penicillin V as a case study, this article shows how uncertainty can be quantified and evaluated. The first step is construction of a process model, as well as analysis of its cost structure and environmental impact. The second step is identification of uncertain variables and determination of their probability distributions based on available process and literature data. Finally, Monte Carlo simulations are run to see how these uncertainties propagate through the model and affect key economic and environmental outcomes. Thus, the overall variation of these objective functions are quantified, the technical, supply chain, and market parameters that contribute most to the existing variance are identified and the differences between economic and ecological evaluation are analyzed. In our case study analysis, we show that final penicillin and biomass concentrations in the fermenter have the highest contribution to variance for both unit production cost and environmental impact. The penicillin selling price dominates return on investment variance as well as the variance for other revenue-dependent parameters.

Fermentation↗
PubMed1984

Perceived uncertainty and stress in illness.

A structural model was proposed to explain the stress resulting from hospitalization for a medical problem. Perceived uncertainty about symptoms, treatment, and outcome was examined as a major predictor of stress. Other variables proposed in the model included seriousness of illness, age, education, and recency of rehospitalization. Testing of the model with hospitalized medical patients indicated support for the relationship of uncertainty to stress. Uncertainty also had the predicted mediating role between seriousness of illness and stress. The only other variable supporting the proposed model was age which related inversely to stress. Much of the unexplained variance in the model is attributed to the heterogeneity of diagnoses in the sample. Suggestions for future testing of the model are presented.

Adult↗
PubMed1987

Estimation of uncertainties in X-ray refinement results by use of perturbed structures.

The uncertainties in the refined parameters for a 1.5-A X-ray structure of carbon-monoxy (FeII) myoglobin are estimated by combining energy minimization with least-squares refinement against the X-ray data. The energy minimizations, done without reference to the X-ray data, provide perturbed structures which are used to restart conventional X-ray refinement. The resulting refined structures have the same, or better, R-factor and stereochemical parameters as the original X-ray structure, but deviate from it by 0.13 A rms for the backbone atoms and 0.31 A rms for the sidechain atoms. Atoms interacting with a disordered sidechain, Arg 45 CD3, are observed to have larger positional uncertainties. The uncertainty in the B-factors, within the isotropic harmonic motion approximation, is estimated to be 15%. The resulting X-ray structures are more consistent with the energy parameters used in simulations.

Arginine↗
PubMed2005

Uncertainty of inductively coupled plasma mass spectrometry based measurements: an application to the analysis of urinary barium, cesium, antimony and tungsten.

The wide use of barium (Ba), cesium (Cs), antimony (Sb) and tungsten (W) in many industrial and agricultural fields causes the increased release of these metals into the environment, laying the basis for health risk. To assess the exposure for the general population, the development of adequate and reliable analytical techniques becomes compulsory. This study refers to the quantification of urinary Ba, Cs, Sb and W levels by both quadrupole (Q) and sector field (SF) inductively coupled plasma mass spectrometry (ICP-MS). The two procedures were compared for their performances and their measurement uncertainties. The limits of detection were (Q and SF) 23.0 and 5.21 ng L(-1) for Ba; 21.1 and 7.52 ng L(-1) for Cs; 1.09 and 0.43 ng L(-1) for Sb; and 0.36 and 0.49 ng L(-1) for W. The trueness was better than 93.3% and the precision less than 12% for both techniques. Relative expanded uncertainties of the analytical procedures, at the median levels found in the general population, were below 5% for all the elements with both ICP-MS techniques. The uncertainties related to the calibration and repeatability were the parameters most influencing the final analytical performance. The urinary median values observed in healthy subjects from central Italy were 1146, 4301, 60.8 and 48.5 ng L(-1) for Ba, Cs, Sb and W, respectively.

Adult↗
PubMed2005

Uncertainties associated with incidence estimates of HIV/AIDS diagnoses adjusted for reporting delay and risk redistribution.

Reporting delay occurs frequently in the case surveillance of a disease such as HIV/AIDS. To evaluate the current trend of incidence, it is important to consider incidence estimates adjusted for reporting delays and the uncertainty associated with this adjustment. For a surveillance system in which cases are reported monthly, there is no straightforward method for constructing the confidence interval estimators for annual incidence or incidence for a period longer than a month. This is because the monthly incidence estimators are not independent and the correlations among them are not available. Furthermore, to estimate the incidence for a specific risk, or exposure, group (e.g. men who have sex with men), we also have to consider the uncertainty associated with the counts from cases reported without an identified risk. Cases with no reported risk are assigned proportionally to each risk group on the basis of experience with cases reported initially with no reported risk but reported later with an identified risk. In this article, we introduce a method for combining the uncertainties associated with both reporting delay and risk redistribution. An estimator for the covariance between two incidence estimators is also provided so that we can make pairwise comparisons and discover any significant changes in incidence over time. Results are applied to evaluating the current trends in AIDS incidence among men who have sex with men in the United States.

Acquired Immunodeficiency Syndrome↗
PubMed1999

Strength of evidence, judged probability, and choice under uncertainty.

This paper traces, within subjects, the relationship between assessed strength of evidence, judgments of probability, and decisions under uncertainty. The investigation relies on the theoretical framework provided by support theory (Tversky & Koehler, 1994; Rottenstreich & Tversky, 1997), a nonextensional model of judgment under uncertainty. Fans of professional basketball (N = 50) judged the probability that each of eight teams, four divisions, and two conferences would win the National Basketball Association championship. Additionally, participants rated the relative strength of each team, judged the probability that a given team would win the championship assuming a particular pairing in the finals, priced prospects contingent on the winner of the championship, and made choices between chance prospects. The data conformed to the major tenets of support theory, and the predicted relationships between assessed strength of evidence, hypothetical support, judged probabilities, and choices under uncertainty also held quite well.

Adult↗
PubMed2001

A tool for comparison of PET and fMRI methods: calculation of the uncertainty in the location of an activation site in a PET image.

A technique for calculating the uncertainty in the location of an activation site in a PET image, without performing repeated measures, is presented. With the development of new fMRI methods for measuring cerebral hemodynamics, demonstration of the efficacy of these techniques will be critical to establish clinical utility. Comparisons with PET are a powerful tool for validating these new fMRI techniques. In addition to the fact that PET techniques are well-established methods for making physiological measurements in vivo, PET methods are also free of the geometric distortions and nonuniform signal-to-noise artifacts (due to signal dropout) common in fMRI techniques. Comparisons reported previously have been limited by the large number of trials acquired in single-subject fMRI studies and the small number of trials in a PET study (due to the radiation dose to the patient or the interscan delays for tracer decay). Our method calculates both the center of mass (CM) of a predefined region of interest and the uncertainty in the location of the CM using the preimage PET data (sinograms). Results of phantom studies demonstrate that our method is an unbiased measurement equivalent to that of repeated measures with a large number of images. Extension of this technique to estimate the uncertainty in the location of an activation site in a PET statistical parametric map will permit precise rigorous comparisons of PET and fMRI methods in single subjects without the constraints imposed by the relatively small number of PET measurements.

Brain Mapping↗
PubMed1999

Are societal judgments being incorporated into the uncertainty factors used in toxicological risk assessment?

The aim of this paper is to show that the uncertainty factors used in toxic risk assessment to develop exposure standards do contain societal judgments as well as technical judgments. The process generally used today originated in the 1950s, when a deterministic approach to risk was the norm. Technical judgments are required concerning the nature and the quality of the evidence used in the risk assessment. Judgments taken are essentially cautious. This caution may not matter when measured exposure is significantly below the standard and may be accepted when exposure occurs only following an approval process based on "gate keeping." More sophisticated judgments are required when actual exposure may exceed this type of standard or when risk needs to be compared with benefit. These circumstances can occur with patient exposure to human medicines and with occupational exposure to chemicals. Under these circumstances more explicitly considered societal judgments concerning what constitute "broadly acceptable" and "tolerable" risk criteria, and hence what are appropriate uncertainty factors, are required. The outcomes of those societal judgments are likely to vary according to the circumstances surrounding the exposure and have led to smaller uncertainty factors being considered appropriate for occupational exposure, when compared with widespread public exposure.

Humans↗
PubMed2001

Physiological-model-based derivation of the adult and child pharmacokinetic intraspecies uncertainty factors for volatile organic compounds.

The intraspecies uncertainty factor (UF(HH)=10x) is used in the determination of the reference dose or reference concentration and accounts for the pharmacokinetic and pharmacodynamic heterogeneity within the human population. The Food Quality Protection Act of 1996 mandated the use of an additional uncertainty factor (UF(HC)=10x) to take into account potential pre- and postnatal toxicity and lack of completeness of the data with respect to exposure and toxicity to children. There is no conclusive experimental or theoretical justification to support or refute the magnitude of the UF(HH) and UF(HC) nor any conclusive evidence to suggest that a factor of 100 is needed to account for intrahuman variability. This study presents a new chemical-specific method for estimating the pharmacokinetic (PK) component of the interspecies uncertainty factor (UF(HH-PK) and UF(HC-PK)) for volatile organic compounds (VOCs). The approach utilizes validated physiological-based pharmacokinetic (PBPK) models and simplified physiological-model-based algebraic equations to translate ambient exposure concentration to tissue dose in adults and children the ratio of which is the UF(HH-PK) and UF(HC-PK). The results suggest that: (i) the UF(HH-PK) and UF(HC-PK) are chemical specific; (ii) for the chemicals used in this study there is no significant difference between UF(HH-PK) and UF(HC-PK); (iii) the magnitude of UF(HH-PK) and UF(HC-PK) varies between 0.033 and 2.85 with respect to tissue and blood concentrations; (iv) the body weight, the rate of ventilation, the fraction of cardiac output flowing to the liver, the blood : air partition coefficient, and the hepatic extraction ratio are the only parameters that play a critical role in the variability of tissue and blood doses within species; and (v) the magnitude of the UF(HH-PK) and UF(HC-PK) obtained with the simplified steady-state equations is essentially the same with that obtained with PBPK models. Overall, this study suggests that no adult-children differences in the parent chemical concentrations of the VOCs are likely to be observed during inhalation exposures. The physiological-model-based approaches used in the present study to estimate the UF(HH-PK) and UF(HC-PK) provide a scientific basis for their magnitude. They can replace the currently used empirical default approaches to provide chemical-specific UF(HH-PK) in future risk assessments.

Adolescent↗
PubMed2006

Uncertainty in diffusion tensor based fibre tracking.

BACKGROUND: Diffusion tensor imaging and related fibre tracking techniques have the potential to identify major white matter tracts afflicted by an individual pathology or tracts at risk for a given surgical approach. However, the reliability of these techniques is known to be limited by image distortions, image noise, low spatial resolution, and the problem of identifying crossing fibres. This paper intends to bridge the gap between the requirements of neurosurgical applications and basic research on fibre tracking uncertainty. METHOD: We acquired echo planar diffusion tensor data from both 1.5 T and 3.0 T scanners. For fibre tracking, an extended deflection-based algorithm is employed with enhanced robustness to impaired fibre integrity such as caused by diffuse or infiltrating pathological processes. Moreover, we present a method to assess and visualize the uncertainty of fibre reconstructions based on variational complex Gaussian noise, which provides an alternative to the bootstrap method. We compare fibre tracking results with and without variational noise as well as with artificially decreased image resolution and signal-to-noise. FINDINGS: Using our fibre tracking technique, we found a high robustness to decreased image resolution and signal-to-noise. Still, the effects of image quality on the tracking result will depend on the employed fibre tracking algorithm and must be handled with care, especially when being used for neurosurgical planning or resection guidance. An advantage of the variational noise approach over the bootstrap technique is that it is applicable to any given set of diffusion tensor images. CONCLUSIONS: We conclude that the presented approach allows for investigating the uncertainty of diffusion tensor imaging based fibre tracking and might offer a perspective to overcome the problem of size underestimation observed by existing techniques.

Adult↗
PubMed1991

Energy filters, motion uncertainty, and motion sensitive cells in the visual cortex: a mathematical analysis.

Energy filters are tuned to space-time frequency orientations. In order to compute velocity it is necessary to use a collection of filters, each tuned to a different space-time frequency. Here we analyze, in a probabilistic framework, the properties of the motion uncertainty. Its lower bound, which can be explicitly computed through the Cramér-Rao inequality, will have different values depending on the filter parameters. We show for the Gabor filter that, in order to minimize the motion uncertainty, the spatial and temporal filter sizes cannot be arbitrarily chosen; they are only allowed to vary over a limited range of values such that the temporal filter bandwidth is larger than the spatial bandwidth. This property is shared by motion sensitive cells in the primary visual cortex of the cat, which are known to be direction selective and are tuned to space-time frequency orientations. We conjecture that these cells have larger temporal bandwidth relative to their spatial bandwidth because they compute velocity with maximum efficiency, that is, with a minimum motion uncertainty.

Animals↗
PubMed1992

Uncertainty, appraisal and quality of life.

This study evaluates the influence of different factors in the adaptation process activated by uncertainty in illness on health-related quality of life. The sample included 100 women (mean age = 52.1 years) receiving treatment for newly diagnosed (M = 5.1 months) gynaecological cancer (38 cervical, 26 ovarian, 24 endometrial, 7 uterine, 4 vulvar, and 1 vaginal). Stepwise regression analyses identified mood states, ambiguity about illness-wellness state, danger-focused appraisal and mastery as key predictors of four health-related quality of life scores. The variance accounted for by those variables is reflected in cumulative multiple R2 of 0.56 for total quality of life score, 0.57 for psychosocial well-being, 0.235 for physical well-being and 0.25 for disease/symptom distress. These variances do not reflect the contribution of age, time since diagnosis, metastasis and stage of cancer which were forced to enter the regression equation first. The latter set of variables accounted for a smaller portion of the variance in health-related quality of life (R2 = 0.03-0.195). Coping strategy did not predict health-related quality of life. These findings provide beginning support for conceptualizing health-related quality of life as the outcome of an adaptation process explained by the uncertainty in illness theory. However, uncertainty in illness theory may not be sufficient to predict quality of life outcomes. Future research should consider the addition of discrepancy theory to guide the selection or development of a health-related quality of life measure, to account for the perceived discrepancy between actual experience and expected well-being.

Adaptation, Psychological↗