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PubMed1994

Propagation of uncertainty in risk assessments: the need to distinguish between uncertainty due to lack of knowledge and uncertainty due to variability.

In quantitative uncertainty analysis, it is essential to define rigorously the endpoint or target of the assessment. Two distinctly different approaches using Monte Carlo methods are discussed: (1) the end point is a fixed but unknown value (e.g., the maximally exposed individual, the average individual, or a specific individual) or (2) the end point is an unknown distribution of values (e.g., the variability of exposures among unspecified individuals in the population). In the first case, values are sampled at random from distributions representing various "degrees of belief" about the unknown "fixed" values of the parameters to produce a distribution of model results. The distribution of model results represents a subjective confidence statement about the true but unknown assessment end point. The important input parameters are those that contribute most to the spread in the distribution of the model results. In the second case, Monte Carlo calculations are performed in two dimensions producing numerous alternative representations of the true but unknown distribution. These alternative distributions permit subject confidence statements to be made from two perspectives: (1) for the individual exposure occurring at a specified fractile of the distribution or (2) for the fractile of the distribution associated with a specified level of individual exposure. The relative importance of input parameters will depend on the fractile or exposure level of interest. The quantification of uncertainty for the simulation of a true but unknown distribution of values represents the state-of-the-art in assessment modeling.

Humans↗

PubMed2003

The Guide to expression of uncertainty in measurement approach for estimating uncertainty: an appraisal.

BACKGROUND: The aim of the Guide to Expression of Uncertainty in Measurement (GUM) is to harmonize the different practices for estimating and reporting uncertainty of measurement. Although there are clear advantages in having a common approach for evaluating uncertainty, application of the GUM approach to chemistry measurements is not straightforward. In the above commentary, Krouwer suggests that the GUM approach should not be applied to diagnostic assays, because (a) the quality of diagnostic assays is to low, and (b) the GUM uncertainty intervals are too narrow to predict the outliers that occasionally trouble these methods. METHODS: Some of the examples presented by Krouwer are reviewed. Sodium measurements are modeled mathematically to illustrate the GUM approach to uncertainty. A standardized uncertainty evaluation process is presented. RESULTS: Modeling of sodium measurements demonstrates how the GUM uncertainty interval reflects the treatment of a bias: The width of the uncertainty interval varied depending on whether a correction for a calibrator lot bias was applied, but in both cases it was consistent with the distribution of measurement results. Expanding the uncertainty interval to include outliers runs counter to the definition of uncertainty. Used appropriately, the GUM uncertainty can be helpful in detecting outliers. In standardizing the uncertainty evaluation, the importance of the analytical imprecision and traceability was emphasized. It is problematic that manufacturers of commercial assays rarely inform about the uncertainty of the values assigned to the calibrators. As demonstrated by an example, external quality-assurance data may be used to estimate this uncertainty. CONCLUSIONS: The GUM uncertainty should be applied to measurements in laboratory medicine because it may actually support the forces that drive the work on improving the quality of measurement procedures. However, it is important that the GUM approach is made more manageable by standardizing the uncertainty evaluation procedure as much as possible. It is essential to focus on the traceability and uncertainty of calibrators and reagents supplied by manufacturers of assays. Information about uncertainty is necessary in the evaluation of the uncertainty associated with manufacturers' measurement procedures, and in general it may force manufacturers to increase their efforts in improving the metrologic and analytical quality of their products.

Calibration↗

PubMed2006

Uncertainty in liquid chromatographic analysis of pharmaceutical product: influence of various uncertainty sources.

An ISO GUM measurement uncertainty estimation procedure was developed for a liquid-chromatographic drug quality control method-assay of simvastatin in drug formulation. In quantification of uncertainty components several practical approaches for including difficult-to-estimate uncertainty sources (such as uncertainty due to peak integration, uncertainty due to nonlinearity of the calibration curve, etc.) have been presented. Detailed analysis of contributions of the various uncertainty sources was carried out. The results were calculated based on different definitions of the measurand and it was demonstrated that unequivocal definition of the measurand is essential in order to get rigorous uncertainty estimate. Two different calibration methods - single-point (1P) and five-point (5P) - were used and the obtained uncertainties and uncertainty budgets were compared. Results calculated using 1P and 5P calibrations agree very well. The uncertainty estimate for 1P is only slightly larger than with 5P calibration.

Calibration↗

PubMed2005

Model uncertainty--parameter uncertainty versus conceptual models.

Uncertainties in model structures have been recognised often to be the main source of uncertainty in predictive model simulations. Despite this knowledge, uncertainty studies are traditionally limited to a single deterministic model and the uncertainty addressed by a parameter uncertainty study. The extent to which a parameter uncertainty study may encompass model structure errors in a groundwater model is studied in a case study. Three groundwater models were constructed on the basis of three different hydrogeological interpretations. Each of the models was calibrated inversely against groundwater heads and streamflows. A parameter uncertainty analysis was carried out for each of the three conceptual models by Monte Carlo simulations. A comparison of the predictive uncertainties for the three conceptual models showed large differences between the uncertainty intervals. Most discrepancies were observed for data types not used in the model calibration. Thus uncertainties in the conceptual models become of increasing importance when predictive simulations consider data types that are extrapolates from the data types used for calibration.

Denmark↗

PubMed2003

Critique of the Guide to the expression of uncertainty in measurement method of estimating and reporting uncertainty in diagnostic assays.

BACKGROUND: The Guide to the Expression of Uncertainty in Measurement (GUM) provides instructions for constructing uncertainty intervals for a measurement. This method is usually reserved for reference materials, but GUM has been recently proposed as a way to express uncertainty for commercial diagnostic assays. METHODS: Using the official GUM standard and published applications of GUM to commercial diagnostic assays, I undertook an analysis to evaluate whether applying GUM to commercial diagnostic assays is warranted. RESULTS: Certain important assays, such as troponin I, would not be candidates for GUM because troponin I is not a well-defined physical quantity. Unlike definitive methods, in which efforts are taken to detect and eliminate all systematic error sources, commercial assays often trade off features such as ease of use and cost with accuracy and allow systematic errors to be present as long as the overall accuracy meets the medical need goal. Laboratories are hindered in preparing GUM models because the knowledge required to specify some systematic errors is often available only to manufacturers. Some non-GUM methods to estimate uncertainty rely on observed data, which include both known and unknown sources of error. The occurrence of large, unknown errors for assays in routine use (e.g., outliers) is not unusual because diagnostic assays must be chemically specific in the presence of thousands of potentially interfering substances. There is no provision in GUM to deal with unexplained outliers, which may lead to uncertainty intervals that are not wide enough. Some clinicians assume that diagnostic assay results have little uncertainty. This situation may be made worse by including an uncertainty interval, which implies certification. CONCLUSIONS: Evaluations for accuracy (total analytical error) based on describing the distribution of result differences between commercial assays and reference methods indicate that some assays have a few results with large differences (e.g., outliers). This leads to a wide accuracy interval (total analytical error limits). It is unlikely that GUM would be able to predict these wide intervals, especially because there is little or no provision for outlier treatment in GUM. Presenting too narrow GUM uncertainty intervals to clinicians would be misleading. The modeling used by practitioners of the GUM method is potentially useful in improving quality, but commercial diagnostic assays are not ready for GUM uncertainty statements.

Clinical Laboratory Techniques↗

PubMedDate not supplied

Uncertainty and appraisal of uncertainty in women with rheumatoid arthritis.

This study examined relationships among length of illness, degree of uncertainty, and appraisal of uncertainty in women with rheumatoid arthritis. Twenty-three subjects completed the Mishel Uncertainty in Illness Scale and an Appraisal Scale. No association was found between length of illness and uncertainty or its appraisal, but uncertainty was significantly correlated with appraisal of uncertainty as danger. High uncertainty was predictive of appraisal of uncertainty as danger. Nurses who are aware of uncertainty experienced by their patients may be better able to recognize and support the individual's coping efforts.

Adaptation, Psychological↗

PubMed2000

Incorporating model uncertainties along with data uncertainties in microbial risk assessment.

Much research on food safety has been conducted since the National Food Safety Initiative of 1997. Risk assessment plays an important role in food safety practices and programs, and various dose-response models for estimating microbial risks have been investigated. Several dose-response models can provide reasonably good fits to the data in the experimental dose range, but yield risk estimates that differ by orders of magnitude in the low-dose range. Hence, model uncertainty can be just important as data uncertainty (experimental variation) in risk assessment. Although it is common in risk assessment to account for data uncertainty, it is uncommon to account for model uncertainties. In this paper we incorporate data uncertainties with confidence limits and model uncertainties with a weighted average of an estimate from each of various models. A numerical tool to compute the maximum likelihood estimates and confidence limits is addressed. The proposed method for incorporating model uncertainties is illustrated with real data sets.

Colony Count, Microbial↗

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↗

PubMed2002

Propagation of the uncertainties of sample position to the uncertainty of the counting efficiency in gamma-ray spectrometry.

The uncertainties generated by inaccurate positioning of homogeneous cylindrical samples are propagated into the uncertainty of the counting efficiency. In this work general expressions describing the uncertainty of the counting efficiency in terms of the sample and detector properties are derived. The uncertainty of the counting efficiency generated by the uncertainty of the sample-detector distance is evaluated using the point detector concept. The uncertainty generated by the displacement of the symmetry axes of the sample and the detector is evaluated using the empirical radial dependence of the efficiency for point sources. Results are presented for some counting geometries resembling counting conditions frequently used in actual measurements. The results of the evaluations are compared to experimentally measured results and are briefly discussed.

Journal Article↗

PubMed1999

Risk assessment--the mother of all uncertainties. Disciplinary perspectives on uncertainty in risk assessment.

Uncertainty in the detection and evaluation of chemical hazards to health leads to challenges when conducting risk assessments. Some of the uncertainty has to do with data, some with incomplete understanding of processes, and some with the most fundamental ways of viewing the questions. True variability--across space, in time, or among individuals--complicates the search for understanding many important aspects of risk. A few statistical and toxicologic tools are available to assess uncertainty. Three methods of classifying uncertainty are briefly discussed. In addition, our disciplinary background may influence how we view and discuss variability and uncertainty. We rarely know as much as we think we do (and not just in risk assessment). Great uncertainty is likely to remain an important part of risk assessment for some decades to come.

Environmental Health↗

PubMed2001

Impact of dose-distribution uncertainties on rectal ntcp modeling. I: Uncertainty estimates.

A trial of nonescalated conformal versus conventional radiotherapy treatment of prostate cancer has been carried out at the Royal Marsden NHS Trust (RMH) and Institute of Cancer Research (ICR), demonstrating a significant reduction in the rate of rectal bleeding reported for patients treated using the conformal technique. The relationship between planned rectal dose-distributions and incidences of bleeding has been analyzed, showing that the rate of bleeding falls significantly as the extent of the rectal wall receiving a planned dose-level of more than 57 Gy is reduced. Dose-distributions delivered to the rectal wall over the course of radiotherapy treatment inevitably differ from planned distributions, due to sources of uncertainty such as patient setup error, rectal wall movement and variation in the absolute rectal wall surface area. In this paper estimates of the differences between planned and treated rectal dose-distribution parameters are obtained for the RMH/ICR nonescalated conformal technique, working from a distribution of setup errors observed during the RMH/ICR trial, movement data supplied by Lebesque and colleagues derived from repeat CT scans, and estimates of rectal circumference variations extracted from the literature. Setup errors and wall movement are found to cause only limited systematic differences between mean treated and planned rectal dose-distribution parameter values, but introduce considerable uncertainties into the treated values of some dose-distribution parameters: setup errors lead to 22% and 9% relative uncertainties in the highly dosed fraction of the rectal wall and the wall average dose, respectively, with wall movement leading to 21% and 9% relative uncertainties. Estimates obtained from the literature of the uncertainty in the absolute surface area of the distensible rectal wall are of the order of 13%-18%. In a subsequent paper the impact of these uncertainties on analyses of the relationship between incidences of bleeding and planned rectal dose-distributions is explored.

Dose-Response Relationship, Radiation↗

PubMed2006

Dissociating uncertainty responses and reinforcement signals in the comparative study of uncertainty monitoring.

Although researchers are exploring animals' capacity for monitoring their states of uncertainty, the use of some paradigms allows the criticism that animals map avoidance responses to error-causing stimuli not because of uncertainty monitored but because of feedback signals and stimulus aversion. The authors addressed this criticism with an uncertainty-monitoring task in which participants completed blocks of trials with feedback deferred so that they could not associate reinforcement signals to particular stimuli or stimulus-response pairs. Humans and 1 of 2 monkeys were able to make cognitive, decisional uncertainty responses that were independent of feedback or reinforcement history within a task. This finding unifies the comparative literature on uncertainty monitoring. The dissociation of performance from reinforcement has theoretical implications, and the deferred-feedback technique has many applications.

Adolescent↗

PubMed2001

Impact of dose-distribution uncertainties on rectal ntcp modeling. II: Uncertainty implications.

A trial of nonescalated conformal versus conventional radiotherapy treatment of prostate cancer has been carried out at the Royal Marsden NHS Trust (RMH) and Institute of Cancer Research (ICR), demonstrating a significant reduction in the rate of rectal bleeding reported for patients treated using the conformal technique. The rate of bleeding has been shown to fall significantly as the extent of rectal wall receiving a planned dose-level in excess of 57 Gy is reduced. Dose-distributions delivered to the rectal wall over the course of radiotherapy treatment inevitably differ from planned distributions. In a previous paper estimates were obtained of the uncertainties in some planned rectal dose-distribution parameters generated by patient setup error, rectal wall movement and the variable degree of rectal wall distension. Here these uncertainties are combined to obtain estimates of the total planning uncertainties in rectal dose-distribution parameters thought likely, on the basis of mechanistic biological modeling, to correlate strongly with the complication rate. Working from these totaled uncertainty values, together with values of patient-to-patient and technique-to-technique differences in planned dose-distribution parameters, it can be inferred that the rectal dose-distribution uncertainties: (i) Have only a marginal impact on fits of a normal tissue complication probability (ntcp) model to RMH/ICR dose-distribution and grade 1, 2, 3 bleeding data (slightly flattening observed volume-response curves); (ii) only slightly reduce the power of a 2 x 100 patient trial of conformal versus conventional prostate radiotherapy to detect a significantly lower rate of grade 1,2,3 rectal bleeding amongst conformally treated patients; (iii) do not diminish the information content of individual planned patient dose-distribution data to the point where the fitting of technique-averaged data would provide as sensitive a test of the existence of a volume effect as the fitting of individual patient data.

Humans↗

PubMed2002

Uncertainty in cost-effectiveness analysis. Probabilistic uncertainty analysis and stochastic league tables.

Interest is growing in the application of standard statistical inferential techniques to the calculation of cost-effectiveness ratios (CER), but individual level data will not be available in many cases because it is very difficult to undertake prospective controlled trials of many public health interventions. We propose the application of probabilistic uncertainty analysis using Monte Carlo simulations, in combination with nonparametric bootstrapping techniques where appropriate. This paper also discusses how decision makers should interpret the CER of interventions where uncertainty intervals overlap. We show how the incorporation of uncertainty around costs and effects of interventions into a stochastic league table provides additional information to decision makers for priority setting. Stochastic league tables inform decision makers about the probability that a specific intervention would be included in the optimal mix of interventions for different resource levels, given the uncertainty surrounding the interventions.

Cost-Benefit Analysis↗

PubMed2001

Propagation of uncertainties in sample properties to the uncertainty of the counting efficiency in gamma-ray spectrometry.

Explicit expressions are derived describing the variance of the counting efficiency for a homogeneous cylindrical sample, placed coaxially on the detector's symmetry axis, in terms of the variances of the sample properties thickness, density and composition. In the derivation, the emission of gamma-rays parallel to the sample axis and the efficiency for an area source proportional to the solid angle subtended by the source from the effective point of interaction of the gamma-rays within the detector crystal are assumed. For the uncertainties of the mass attenuation coefficients, as well as for the uncertainties of concentrations of admixtures to the sample matrix, constant relative uncertainties are assumed.

Journal Article↗

PubMed2005

Combined effects of uncertainty and organizational justice on employee health: testing the uncertainty management model of fairness judgments among Finnish public sector employees.

We examined whether the combination of uncertainty (lack of work-time control, and negative changes at work) and organizational justice (i.e., justice of decision-making procedures and interpersonal treatment at work) contributes to sickness absence. A total of 7083 male and 24,317 female Finnish public sector employees completed questionnaires designed to assess organizational justice, workload and other factors. Hierarchical regression showed that after adjustment for age, income, and health behaviors low procedural and interactional justice were related to long sickness absence spells. In accordance with the uncertainty management model, these associations were dependent on experienced work-time control and perceived changes at work.

Adult↗

PubMed1977

Prior time uncertainty reduction of foreperiod duration under two different levels of event uncertainty in schizophrenia.

Schizophrenic and alcoholic Ss judged stimulus durations of .50 and .55 seconds. Stimulus was 1, 3 or 5 dark dots and was preceded by variable foreperiod duration of 1, 3 or 5 seconds. Judgment of stimulus duration was found to be a monotonically increasing function of foreperiod duration. When pitch of sound was correlated with foreperiod duration so that it functioned as prior information, such monotonic function was eliminated for schizophrenics only when the numerosity of dots was constant from trial to trial. The effect of prior information as to foreperiod duration was negligible for both schizophrenics and alcoholics when the numerosity of dots was variable from trial to trial. Uniqueness of schizophrenia was shown to be associated with prior time uncertainty reduction of foreperiod duration in the context of minimal event uncertainty of stimulus.

Acoustic Stimulation↗

PubMed1977

Prior time uncertainty reduction of foreperiod duration under two different levels of event uncertainty in process and reactive schizophrenia.

Process and reactive schizophrenic Ss judged stimulus durations of .50 and .55 seconds. Stimulus was 1, 3 or 5 dark dots and was preceded by variable foreperiod duration of 1, 3 or 5 seconds. Judgment of stimulus duration was found to be a monotonically increasing function of foreperiod duration. When pitch of the auditory warning signal was correlated with foreperiod duration so that it functioned as prior time information, such monotonic function was eliminated for process schizophrenics only when the numerosity of dots was constant from trial to trial. The effect of prior time information that concerned foreperiod duration was negligible for both process and reactive schizophrenics when the numerosity of dots was variable from trial to trial. Uniqueness of process schizophrenia was shown to be associated with prior time uncertainty reduction of foreperiod duration in the context of minimal event uncertainty of stimulus.

Adult↗