Statistical uncertainty assessment

COMPOUNDING OF ERRORS. Data collected in an experiment seldom involves a single operation, a single adjustment, or a single experimental determination. For example, in studies of an enzyme-catalyzed reaction, one must separately prepare stock solutions of enzyme and substrate, one must then mix these and other components to arrive at desired assay concentrations, followed by spectrophotometric determinations of reaction rates. A Lowry determination of protein or enzyme concentration has its own error, as does the spectrophotometric determination of ATP that is based on a known molar absorptivity. All operations are subject to error, and the error for the entire set of operations performed in the course of an experiment is said to involve the compounding of errors. In some circumstances, the experimenter may want to conduct an error analysis to assess the contributions of statistical uncertainties arising in component operations to the error of the entire set of operations. Knowledge of standard deviations from component operations can also be utilized to estimate the overall experimental error. 

UCL takes into account measurement uncertainty in the study used to estimate the dose-response relationship, such as the statistical uncertainty in the number of tumors at each administered dose, but it does not take into account other uncertainties, such as the relevance of animal data to humans. It is important to emphasize that UCL gives an indication of how well the model fits the data at the high doses where data are available, but it does not indicate how well the model reflects the true response at low doses. The reason for this is that the bounding procedure used is highly conservative. Use of UCL has become a routine practice in dose-response assessments for chemicals that cause stochastic effects even though a best estimate (MLE) also is available (Crump, 1996 Crump et al., 1976). Occasionally, EPA will use MLE of the dose-response relationship obtained from the model if human epidemiologic data, rather than animal data, are used to estimate risks at low doses. MLEs have been used nearly universally in estimating stochastic responses due to radiation exposure. 

The relative importance of the statistical uncertainty and the uncertainties of the boundary positions can be assessed from Table 1, where the quantities contributing... 

Because most risk assessments include major uncertainties, it is important that biological and statistical uncertainties be described in the risk characterization. The assessment should identify the components of the risk assessment process that involve the greatest degree of uncertainty. 

The chemical potential of gas phase is underestimated by 57 to 15%, while the liquid phase data, still underestimated, are reproduced within -10%. Also the temperature dependence of dielectric constant is well reproduced, although the large statistical uncertainty reported prevents a definite assessment of this issue. This is apparent at 25 C, where also equilibration problems might be present, as suggested by the difference observed between results obtained with zero and calculated average total dipole moment for the simulation cell. 

Therefore, we distinguish three categories of risks for a practicable and rational risk evaluation (see Fig. 1) the normal area, the intermediate area, and the intolerable area (area of permission) (cf. also Piechowski, 1994). The normal area is characterized by relatively low statistical uncertainty, rather low probability of occurrence, rather low extent of damage, high certainty of assessment, low persistency and ubiquity of risk consequences, and low irreversibility of risk consequences, and the risks iUso have low complexity or empirically proven adequacy. In this case the objective risk dimensions almost correspond to the scientific risk evaluation. For risks in the normal area we follow the recommendations of decision-making analysts who take a neutral risk attitude as a starting point for collective binding decisions. 

Type A standard uncertainty assessing is the adoption of a set of measured data for statistical analysis, with methods of the experimental standard deviation characterizing uncertainty. Single experimental standard deviation of measurements data commonly uses the Bessel formula to calculate ... 

Successful application of the classical control systems have been appreciated in industrial and engineering solutions. However, there remains still uncertainties to a certain extend that cannot be modeled by the classical approaches, and therefore, uncertainty assessment methodologies are necessary. On this regard for many years probabilistic, statistical and stochastic approaches and methods have been exploited to the farthest extend with effective impacts of linguistic concepts. Due to the lack of verbal information content, at times main knowledge could not be appended to the whole system. On the other hand their inclusion in the system brings further dimensions and additions which may be unmanageable to solve with certainty. In this respect, for the last three decades and especially... 

In an illustrative example assume that a test method cannot be readily improved. The number of measurements n is then optimised to reduce the statistical uncertainty and minimise expected total costs related to a specified reference period. The optimum number of measurements can be assessed as ... 

Statistical inference. The broad problem of statistical inference is to provide measures of the uncertainty of conclusions drawn from experimental data. This area uses the theoiy of probabihty, enabhng scientists to assess the reliability of their conclusions in terms of probabihty statements. 

Uncertainty on tlie other hand, represents lack of knowledge about factors such as adverse effects or contaminant levels which may be reduced with additional study. Generally, risk assessments carry several categories of uncertainly, and each merits consideration. Measurement micertainty refers to tlie usual eiTor tliat accompanies scientific measurements—standard statistical teclmiques can often be used to express measurement micertainty. A substantial aniomit of uncertainty is often inlierent in enviromiiental sampling, and assessments should address tliese micertainties. There are likewise uncertainties associated with tlie use of scientific models, e.g., dose-response models, and models of environmental fate and transport. Evaluation of model uncertainty would consider tlie scientific basis for the model and available empirical validation. 

Risk assessment pertains to characterization of the probability of adverse health effects occurring as a result of human exposure. Recent trends in risk assessment have encouraged the use of realistic exposure scenarios, the totality of available data, and the uncertainty in the data, as well as their quality, in arriving at a best estimate of the risk to exposed populations. The use of "worst case" and even other single point values is an extremely conservative approach and does not offer realistic characterization of risk. Even the use of arithmetic mean values obtained under maximum use conditions may be considered to be conservative and not descriptive of the range of exposures experienced by workers. Use of the entirety of data is more scientific and statistically defensible and would provide a distribution of plausible values. 

In assessing animal data, careful attention must be paid to the quality of the data, the incidence of spontaneous tumors in the control population, consistency if more than one study is available, and statistical validity. If the exposure route and experimental regimen employed do not agree with the most likely mode(s) of human exposure (e.g., intramuscular injection), the data must be interpreted cautiously. Consideration should be given to data on metabolism of the compound by the animal species tested, as compared with metabolism in humans if this information is known. If only in vitro data are available, only qualitative estimates may be possible because of uncertainties regarding the association between in vitro results and human or animal effects. The availability of associated pharmacokinetic data, however, may allow development of a rough quantitative estimate. 

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