Extrapolation Practice uncertainty

Aside from the fundamentals, the principal compromise to the accuracy of extrapolations and interpolations is the interaction of the model parameters with the database parameters (e.g., tray efficiency and phase eqiiilibria). Compromises in the model development due to the uncertainties in the data base will manifest themselves when the model is used to describe other operating conditions. A model with these interactions may describe the operating conditions upon which it is based but be of little value at operating conditions or equipment constraints different from the foundation. Therefore, it is good practice to test any model predictions against measurements at other operating conditions. 

Baird et al. (1996) suggested a probabilistic alternative to the practice used by the US-EPA to derive RfDs from a NOAEL and application of UFs. The probabilistic approach expresses the human population threshold for a given substance as a probability distribution of values, rather than a single RfD value, taking into account the major sources of scientific uncertainty in such estimates. The approach was illustrated by using much of the same data that US-EPA used to justify their RfD procedure. For the four key extrapolations that were considered necessary to define the human population threshold based on animal data (interspecies, interindividual, LOAEL-to-NOAEL, and subchronic-to-chronic), the proposed approach used available data to define a probability distribution of each adjustment factor, rather than using available data to define point estimates of UFs. 

The Risk Characterization Handbook (US-EPA 2000) is thus a practical guide in how to perform the risk characterization. However, the Handbook does not include any detailed information on the practices employed in the risk assessment itself, including use of uncertainty factors and use of default and extrapolation assumptions in the risk characterization step. This information and practices are provided in the US-EPA staff paper from 2004 titled An Examination of EPA Risk Assessment Principles and Practices (US-EPA 2004). 

Extrapolation between the population and community levels of biological organization and between community and ecosystem levels may be greatly confounded by the occurrence of contaminant-induced indirect interactions between organisms, leading to a high level of uncertainty in model predictions. In practice, the most... 

Areas of uncertainty, future directions, and the resulting research needs are summarized in Chapter 8, and a Glossary of terms is provided in Chapter 9. This is followed by the last chapter, 10, a stand-alone document that offers practical guidance suitable to several levels of users, from those in the laboratory to those making the risk management decisions. This chapter is less detailed in discussing extrapolation... 

For food allergens, validated animal models for dose-response assessment are not available and human studies (double-blind placebo-controlled food challenges [DBPCFCs]) are the standard way to establish thresholds. It is practically impossible to establish the real population thresholds this way. Such population threshold can be estimated, but this is associated with major statistical and other uncertainties of low dose-extrapolation and patient recruitment and selection. As a matter of fact, uncertainties are of such order of magnitude that a reliable estimate of population thresholds is currently not possible. The result of the dose-response assessment can also be described as a threshold distribution rather than a single population threshold. Such distribution can effectively be used in probabilistic modeling as a tool in quantitative risk assessment (see Section 15.2.5)... 

The accurate calculation of thermodynamic properties for construction of a table or diagram is an exacting task, seldom required of an engineer. However engineers do make practical use of thermodynamic properties, and an understand ing of the methods used for their calculation leads to an appreciation that some, uncertainty is associated with every property value. There are two major reasons for inaccuracy. First, the experimental data are difficult to measure and are subject to error. Moreover, data are frequently incomplete, and are extended by interpolation and extrapolation. Second, even when reliable PVT data are available, a loss of accuracy occurs in the differentiation process required in the calculation of derived properties. This accounts for the fact that data of a high order of accuracy are required to produce enthalpy and entropy values suitable for engineering calculations. 

A frequent complication is that several simultaneous equilibria must be considered (Section 3-1). Our objective is to simplify mathematical operations by suitable approximations, without loss of chemical precision. An experienced chemist with sound chemical instinct usually can handle several solution equilibria correctly. Frequently, the greatest uncertainty in equilibrium calculations is imposed not so much by the necessity to approximate as by the existence of equilibria that are unsuspected or for which quantitative data for equilibrium constants are not available. Many calculations can be based on concentrations rather than activities, a procedure justifiable on the practical grounds that values of equilibrium constants are obtained by determining equilibrium concentrations at finite ionic strengths and that extrapolated values at zero ionic strength are unavailable. Often the thermodynamic values based on activities may be less useful than the practical values determined under conditions comparable to those under which the values are used. Similarly, thermodynamically significant standard electrode potentials may be of less immediate value than formal potentials measured under actual conditions. 

Methods for toxicological safety assessments are multiple and varied - some are more reliable than others, some more radical than others, but all are important. Their nature greatly depends on their endpoints, namely, the degree of practical safety they attempt to attain. Unfortunately, the true validity of these methods can only be assessed retrospectively, that is to say, by the record of cases of health impairment they were able to prevent over a reasonable period of time. Because of this and the uncertainty inherent in any extrapolation technique, the final products expressed in numerical form can only be considered as opinions. Some important toxicological opinions presented in numerical form are the LD50 the quantitative risk assessments, the threshold limit values (TLV), and the acceptable daily intakes (ADIs). 

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