Taking Account of Variability

It is therefore important to take account of variability and uncertainty in risk assessment. The question is, how ... 

Equation 5.4 is the basis of a more detailed and fundamental study of the swelling process achieved through the study of resin-water vapour sorption isotherms obtained isopiestically i.e. at equal total pressures and equal resin water content). The isopiestic vapour pressure technique takes account of variable activity of the water in the resin (and therefore IT) by allowing the resin to come to equilibrium with water vapour at different partial vapour pressures P. It is assumed that two resins of the same structural type, but with different degrees of crosslinking, have the same water activity at the same equivalent water content. At equilibrium between resin and vapour phases the water activity in resins (1) and (2) are given by ... 

Considering and examining all available evidence on exposure, hazard, and risk in an interdisciplinary manner, to take account of variability as well as direct and indirect, cumulative, and interactive effects. 

Monitoring programmes will need to take account of variability in contaminant concentrations in time and space (including depth) within a water body. A sufficient number of samples should be taken and analysed to adequately characterise such variability and to generate meaningful results with proper confidence. 

Thus, by substitution in this equation for the peak areas from the chromatogram, the relative response factors, derived from the calibration analysis, and the concentration of the internal standard added to the sample, the concentration of the components in the sample can be calculated. Since this method involves ratios of peak areas rather than absolute values, it should be noted that the precision of analysis is not dependent on the injection of an accurately known amount of sample. However, the accuracy does depend on the accurate measurement of peak area. Assay and quantitation by the internal standard is often the preferred method as it takes account of variable compound response and removes potential errors due to variation in sample injection. The 80 and 200 mg% (mg per 100 ml) standard solutions are used to confirm the linearity of response over this concentration range. 

An empirical relationship has been obtained between hardness and the weight fraction of hard ceramics in a matrix of PMMA. In further, more refined studies it would be preferable to seek a more general relationship which takes account of variables such as the hardness and density of the ceramic. Further studies are also needed to elucidate the role of the polymeric matrix. The present indications are that this is not a sensitive variable, at least in the case of glassy polymers which have reasonable mechanical integrity. For example, similar results were obtained for proprietary materials even though they have matrices which differ considerably from PMMA e.g. copolymers of BIS-GMA. Most of these materials contain less than 60 wt-% ceramic and therefore such similarity is an insensitive test (c.f. Fig. 2). However, recently a proprietary material has been reported to contain 80 wt-% of a strontium glass and to have a Knoop hardness of 82 these data fit the curve for PMMA. Incidentally, it was also reported that this harder material has improved wear resistance (6). 

Using (7.30), one can easily perform integration, required by (7.27). Substituting the result into (7.26), taking account of initial condition (7.28) we have the following matrix equation relative to the Fourier-transformed variables dq ((o)... 

Peaks are identified from absolute or relative retention times by comparison with data from previously run standards stored in RAM or in libraries on disk. To take account of the variability of retention times from successive runs, retention time windows are used. These are defined as being /R x% for a standard, the unknown being positively identified if its retention time falls within the specified range. The size of the window can be varied by the user to conform with the degree of certainty required. Reference peaks can be selected for the calculation of relative retention times or as internal standards in quantitative analysis (pp. 9, 114). 

Equations (c), (equality constraints. The other relations were modified to form two inequality constraints each, so as to take account of the uncertainty that existed in their formulation. The dl and du values fisted in Table E14.3B allow for deviations from the expected values of the associated variables. 

As mentioned previously, the assessment of hazard and risk to humans from exposure to chemical substances is generally based on the extrapolation from data obtained in smdies with experimental animals. In the absence of comparative data in humans, a basic assumption for toxicological risk assessment is that effects observed in laboratory animals are relevant for humans, i.e., would also be expressed in humans. In assessing the risk to humans, an assessment factor is applied to take account of uncertainties in the differences in sensitivity to the test substance between the species, i.e., to account for interspecies variability (Section 5.3). If data are available from more than one species or strain, the hazard and risk assessment is generally based on the most susceptible of these except where data strongly indicate that a particular species is more similar to man than the others with respect to toxicokinetics and/or toxicodynamics. Two main aspects of toxicity, toxicokinetics and toxicodynamics, account for the namre and extent of differences between species in their sensitivity to xenobiotics this is addressed in detail in Chapter 5. 

A good clinical trial is designed to take account of the variability in response (either efficacy or adverse event) that is expected when a new active drug is tested. This response depends on an individual s genetic make-up, and on a number of environmental factors, such as disease state, other drugs and age. The size of the trial and the selection of study subjects are carefully determined to reduce the variability in response to a minimum (i.e. to maximise the sensitivity of the trial) so that the trial endpoints can be determined with as much certainty as possible. 

Screening assessments incorporate variability and uncertainty implicitly, by using worst-case assumptions and safety factors. As mentioned earlier, these have rarely been based on a quantitative analysis and may not take account of the full range of uncertainties, so in principle they should be reviewed to determine whether they provide adequate margins of safety. 

In a first step the scaling of intrinsic clearances determined in rat hepatocytes was compared to in vivo clearance. When taking account of non-linearity, the estimated hepatic metabolic clearance values were in reasonable agreement with observed total clearances, which ranged from 7 to 35 mL/min/kg, and it was considered reasonable to estimate the expected clearances in human by a similar scaling of human hepatocyte data. The error around the mean predicted human clearance was based on the variability seen in different batches of human hepatocytes. 

It is, moreover, frequently the case that the activity of acquiring consumption (labour), and therefore the time devoted to it (fe), may in themselves give rise to satisfactions or annoyances or distress. In order to take account of this in our analysis, we must add ta to the range of variables of the function u. Let us call the corresponding derived function ua. All the previous discussions and results then remain valid if we add ujuc to c whenever we come across it. 

The second factor is designed to take account of the genetic variability of consumers likely to consume these drug residues, which is much wider than the genetic variability of the laboratory animals used in the toxicological study. The safety factor value of 100 can be increased to take account of the severity of the toxic effect observed and/or to offset shortcomings in the toxicological study. 

After values of the variables 1) and Vp called tear variables, are specified, Eqs. (182)ff become a linear set in the x9 variables. Initial estimates of the vapor flows are made by assuming constant molal overflow modified by taking account of external inputs and outputs, and those of the temperatures by assuming a linear gradient between estimated top and bottom temperatures. Initially, also, the Kji are taken as ideal values, independent of composition, and for later iterations the compositions derived from the preceding one may be used to evaluate corrected values of With appropriate substitutions,... 

This system of equations allows us to take account of the flow in the frontal zone and the influence of the fountain effect on the distributions of variables in the main stream zone. The equations for this rather complicated model can be solved numerically by computer. Comparison of the calculations with experimental data shows that the maximum deviations of the predicted values from the experimental points do not exceed 15 % (Fig. 4.60). 

Tariffs are import taxes levied at the border. They generally have two purposes protecting local industry and providing revenues for the government. Especially for less developed countries, tariffs are an important source of tax income. Tariffs can take different forms. Specific tariffs are flat rates on particular products (e.g., 200 EUR per ton). Variable tariffs take account of changes between domestic and world market prices (e.g., agricultural tariffs in the European Union). The most common form of tariffs is to calculate a percentage of the price of the imported product (ad valorem). 

For the establishment of the realistic limit, one has to take account of the rates of processes in which mass, heat, momentum, and chemical energy are transferred. In this so-called finite-time, finite-size thermodynamics, it is usually possible to establish optimal conditions for operating the process, namely, with a minimum, but nonzero, entropy generation and loss of work. Such optima seem to be characterized by a universal principle equiparti-tioning of the process s driving forces in time and space. The optima may eventually be shifted by including economic and environmental parameters such as fixed and variable costs and emissions. For this aspect, we refer to Chapter 13. 

Minimizatation of (2) with respect to the variables mi and rn2, taking account of the limits of their variation, yields the following solutions for the sublattice magnetizations at different intensities of the magnetic field ... 

It is sometimes said that, were it not for mutations, we would run out of genetic variability and thus cut off any possibility of future human evolution. Such statements do not take account of the extremely low rate at which... 

The prioritization of QSAR models for validation is likely to take account of regulatory needs. The selection of QSARs could also take into account the mechanistic basis of the QSAR. In the case of QSARs, this would involve a qualitative assessment of the relevance of descriptor variables to the endpoint being modeled. A strong mechanistic basis could be regarded as a desirable criterion, rather than an essential criterion, since mechanistic relevance cannot always be established this is especially the case since the fundamental processes underlying the expression of biological endpoints are often unknown. 

In the pot-cores used in inductors (see Section 9.5.1) for LC filter circuits, the fields are low enough for /T and tan i)m to vary only gradually with the field and the ratio (tan <5m)//T is sensibly constant. These cores are designed with small gaps of variable width so that their effective permeability can be adjusted in accordance with Eq. (9.12). If /tr 3> 1 Eq. (9.12) can be expressed in complex form to take account of losses and rearranged to give... 

---