Extrapolation variability

Uncertainty factors are intended to account for animal-to-human extrapolation, variability within the human population, use of a... 

As with any constitutive theory, the particular forms of the constitutive functions must be constructed, and their parameters (material properties) must be evaluated for the particular materials whose response is to be predicted. In principle, they are to be evaluated from experimental data. Even when experimental data are available, it is often difficult to determine the functional forms of the constitutive functions, because data may be sparse or unavailable in important portions of the parameter space of interest. Micromechanical models of material deformation may be helpful in suggesting functional forms. Internal state variables are particularly useful in this regard, since they may often be connected directly to averages of micromechanical quantities. Often, forms of the constitutive functions are chosen for their mathematical or computational simplicity. When deformations are large, extrapolation of functions borrowed from small deformation theories can produce surprising and sometimes unfortunate results, due to the strong nonlinearities inherent in the kinematics of large deformations. The construction of adequate constitutive functions and their evaluation for particular... 

Bridgman had strong views on the importance of empirical research, influenced as little as possible by theory, and this helped him test the influence of numerous variables that lesser mortals failed to heed. He kept clear of quantum mechanics and dislocation theory, for instance. He became deeply ensconced in the philosophy of physics research for instance, he published a famous book on dimensional analysis, and another on the logic of modern physics . When he sought to extrapolate his ideas into the domain of social science, he found himself embroiled in harsh disputes this has happened to a number of eminent scientists, for instance, J.D. Bernal. Walter s book goes into this aspect of Bridgman s life in detail. 

Lk(a) is the interpolation funetion and L i (a) its derivative. Their detailed deseription and evaluation proeedure ean be found in Riee and Do (1995). The value of state variable X, within an element is extrapolated to find its magnitudes at the end through equation 9.25. The balanee between feed and erystallizing streams is represented by equation 9.26. 

A UF of 10 is used when extrapolating from animals to humans. This factor is intended to account for the intcrspccies variability between humans and other mammals. 

It is partly because of the variable effect of hydrogen (giving both softening and hardening, according to the nature of the slip) that the extrapolation of model experiments on very pure iron to predict the behaviour of commercial materials is so difficult. It is further hindered by the ability of dissolved hydrogen to modify the dislocation structure of a straining material. 

The LC50 refers to the wastewater concentration which results in 50 percent mortality under the test conditions (see text). It is an extrapolated value with varying confidence limits. In the work summarized here confidence limits were quite variable and often could not be calculated due to insufficient data points. Nevertheless the data satisfies the primary intent of the tests as a screening tool. 

An intermediate-duration oral MRL of 0.0007 mg/kg/day was derived for methyl parathion based on the observation of electrophysiological effects in the central and peripheral nervous systems of male rats exposed to methyl parathion through gavage administration of 0.22 mg/kg/day to the dams on days 5-15 of gestation and days 2-28 of lactation, followed by direct administration of the same dose to the male pups for 8 weeks. More marked effects occurred at the two higher doses, 0.44 and 0.88 mg/kg/day. The effects were dose-related, and were statistically significant at all three dose levels. The MRL was derived by dividing the LOAEL from this study (0.22 mg/kg/day) by an uncertainty factor of 300 (3 for a minimal LOAEL, 10 for extrapolation from animals to humans, and 10 for human variability). 

Used to derive an intermediate oral MRL of0.0007 mg/kg/day dose divided by an uncertainty factor of300 (10 for extrapolation from animals to humans, 10 for human variability, and 3 for a minimal LOAEL). 

It follows that for a special value of one parameter, the observed value of y is independent of the second parameter. This happens at Ii= a2/ai2 or I2 = -ai/ai2 any of these values determines y= a -aia2/ai2, the so called isoparametrical point. The argument can evidently be extended to more than two independently variable parameters. Experimental evidence is scarce. In the field of extrathermodynamic relationships, i.e., when j and 2 are kinds of a constants, eq. (84) was derived by Miller (237) and the isoparametrical point was called the isokinetic point (170). Most of the available examples originate from this area (9), but it is difficult to attribute to the isoparametrical point a definite value and even to obtain a significant proof that a is different from zero (9, 170). It can happen—probably still more frequently than with the isokinetic temperature—that it is merely a product of extrapolation without any immediate physical meaning. 

Figure 3.10. The relationship between the three coefficients A, B, and C for the curves shown in Figure 3.9 the quadratic and the linear coefficients are tightly linked. The intercept suffers from higher variability because it carries the extrapolation penalty discussed in Section 2.2.5 and Figure 2.8.

The chronic-duration oral MRL was derived based on the observation of increased serum levels of alkaline phosphatase (an indicator of hepatotoxicity) in dogs consuming 0.6 mg/kg/day for 1 year (Hoechst 1989c). The choice of this end point is supported by the observation of hydropic hepatic cells in rats that consumed 5 mg/kg/day for 2 years (EMC 1959b). The chronic-duration MRL of 0.002 mg/kg/day was derived by dividing the NOAEL for elevated serum alkaline phosphatase (0.18 mg/kg/day) by an uncertainty factor of 100 (10 for extrapolating from animals to humans, and 10 for human variability). 

Alternatively, some studies used expert opinion to extrapolate the effectiveness of donepezil over a longer period (Neumann et al, 1999 O Brien et al, 1999). However, it is recognized that expert opinion can be the weakest source of evidence, which introduces considerable uncertainty into the analysis and interpretation of the results. In addition, the cost-effectiveness of acetylcholinesterase inhibitors depends heavily on the distribution of the cohort of patients across different severity states. O Brien s team found that the results of their model were very sensitive to this variable. In this context, the correct... 

Used to derived an intermediate-duration inhalation Minimal Risk Level (MRL) of 0.1 ppm for trichloroethylene 50 ppm adjusted tor duration (5/7 days x 8 hr/d) and species-specific ratio of daiiy inhalation volume (m /day)/body weight(kg) ratio for rat (0.23/2.17) to human (20/70) to 44.2 ppm, divided by an uncertainty factor of 300 (10 for using a LOAEL, 3 tor extrapolation from animals to humans, and 10 tor human variability) = 0.147 ppm, rounded to 0.1 ppm. 

NOAEL (no-observed-adverse-effect level) is defined as the highest dose at which no adverse effects are observed in the most susceptible animal species. The NOAEL is used as a basis for setting human safety standards for acceptable daily intakes (ADIs), taking into account uncertainty factors for extrapolation from animals to humans and inter-individual variabilities of humans. The adequacy of any margin of safety or margin of exposure must consider the nature and quality of the available hazard identification and dose-response data and the reliability and relevance of the exposure estimations. In some cases, no adverse endpoint can be identified such as for many naturally occurring compounds that are widespread in foods. In that case, an ADI Not Specified is assigned. ... 

---