Extrapolation bias

In risk assessment it is necessary to do extensive extrapolations. In human toxicology, we must extrapolate to man from experiments done on animals such as rats, guinea pigs, and hamsters. Even experiments performed on cells and bacteria are used in the assessment, which makes extrapolation even more extensive. In ecotoxicology we must extrapolate from one or few organisms, such as the most popular test organisms (e.g., the crayfish Daph-nia magna, the earthworm Eisenia fetida, or the collembolan Folsomia Candida) to all species in the environment. We must also extrapolate from laboratory experiments to the field situation. 

We must almost always extrapolate from experiments carried out with high concentrations in a short time frame to real situations with low concentrations and long-term exposure. 

---

Because the technical barriers previously outhned increase uncertainty in the data, plant-performance analysts must approach the data analysis with an unprejudiced eye. Significant technical judgment is required to evaluate each measurement and its uncertainty with respec t to the intended purpose, the model development, and the conclusions. If there is any bias on the analysts part, it is likely that this bias will be built into the subsequent model and parameter estimates. Since engineers rely upon the model to extrapolate from current operation, the bias can be amplified and lead to decisions that are inaccurate, unwarranted, and potentially dangerous. 

The presence of errors within the underlying database fudher degrades the accuracy and precision of the parameter e.stimate. If the database contains bias, this will translate into bias in the parameter estimates. In the flash example referenced above, including reasonable database uncertainty in the phase equilibria increases me 95 percent confidence interval to 14. As the database uncertainty increases, the uncertainty in the resultant parameter estimate increases as shown by the trend line represented in Fig. 30-24. Failure to account for the database uncertainty results in poor extrapolations to other operating conditions. 

Ihe implementation of the Resource Conservation and Recovery Act (RCRA) and the Comprehensive Environmental Response, Compensation, and Liability Act (Superfund) has underscored a number of the weaknesses in our capabilities to measure the chemical characteristics of wastes. We are now being called upon to identify and quantify with unprecedented sensitivity hundreds of chemicals found in many types of materials within waste sites, near discharges of hazardous contaminants, and in the surrounding environments. Extrapolations from a limited number of measurements must indicate the general environmental conditions near waste sites. The measurements have to be made faster and cheaper than ever before, with the precision and bias of each measurement fully documented. Thus, the technical challenges facing the monitoring community are substantial. 

Data analysis and interpretation (i.e. extrapolation to the target patient population) Different formulas are used to correct duration of the QT interval for heart rate some formulas may overcorrect at high heart rates and undercorrect at low heart rates (e.g. Bazett s formula) consider that with some formulas (e.g. Bazetf s) a QTc increase of 4-5 ms may result from measurement bias Need for an individualized correction formula... 

Gouy-Chapman, Stern, and triple layer). Methods which have been used for determining thermodynamic constants from experimental data for surface hydrolysis reactions are examined critically. One method of linear extrapolation of the logarithm of the activity quotient to zero surface charge is shown to bias the values which are obtained for the intrinsic acidity constants of the diprotic surface groups. The advantages of a simple model based on monoprotic surface groups and a Stern model of the electric double layer are discussed. The model is physically plausible, and mathematically consistent with adsorption and surface potential data. 

Fisher polynomials can be used only within the T range for which they were created. Extrapolation beyond the T limits of validity normally implies substantial error progression in high-F entropy and enthalpy calculations. For instance, figure 3.4 compares Maier-Kelley, Haas-Fisher, and Berman-Brown polynomials for low albite. As can be seen, the first two interpolants, if extended to high T, definitely exceed the Dulong and Petit limit. The Berman-Brown interpolant also passes this limit, but the bias is less dramatic. 

Bias in subject selection may not be avoided simply by randomisation. Randomisation will avoid weighted allocation to one treatment regimen rather than another, but it will not avoid selection of the wrong kind of subject in the first place, which will subsequently affect the degree to which the data can be extrapolated. Thus, an investigator may have a preconceived idea about the safety of a drug or about its effectiveness in a particular subset of subjects who nonetheless meet the entry criteria. This prejudice may be avoided by stratification of subjects... 

The existence of mathematical features of the models used in mixture extrapolation does not mean that it is appropriate to apply unchecked models to all assessment problems. Most data for which the models were tested pertain to the higher exposure (e.g., EC50) level. There may be mathematical features of the models that introduce bias when applied to lower exposure levels. The models should be applied with a clear understanding of the potential biases that may occur. A model might be discarded for a certain use because of its bias. For example, using concentration addition for all mixtures, even when there is clearly a case of different modes of action, would typically overestimate mixture risks when assessing risks at a contaminated site, which would be an undesired feature for this type of assessment. 

Assessors should base their selection of methods on clearly defined decision criteria, and they need to communicate the results using clear and transparent language. This includes statements on the extrapolation issues that were considered but not addressed, and the magnitude and direction of the bias that may have been introduced by the extrapolation or lack thereof. In lower tiers and prospective risk assessment, this should lead to setting more appropriate UFs and ensure that lower tier approaches are more conservative than higher tier approaches. All this helps assessors to make informed decisions, on one hand, but it also allows the identification of future research needs, on the other hand, especially when methods are not available. 

Using n-Ti02 electrodes, either naked or platinized, we have studied reaction [2] in a photoelectrochemical cell (PEC) under conditions of controlled electrolyte pH, illumination intensity and external applied bias (Tafalla and Salvador, 1987). These results can be extrapolated to the case of Ti02 suspensions help to go further into the mechanisms of 02 photo-uptake. ... 

The depletion layer profile contains information about the density of states distribution and the built-in potential. The depletion layer width reduces to zero at a forward bias equal to and increases in reverse bias. The voltage dependence of the jimction capacitance is a common method of measuring W V). Eq. (9.9) applies to a semiconductor with a discrete donor level, and 1 is obtained from the intercept of a plot of 1/C versus voltage. The 1/C plot is not linear for a-Si H because of the continuous distribution of gap states-an example is shown in Fig. 4.16. The alternative expression, Eq. (9.10), is also not an accurate fit, but nevertheless the data can be extrapolated reasonably well to give the built-in potential. The main limitation of the capacitance measurement is that the bulk of the sample must be conducting, so that the measurement is difficult for undoped a-Si H. 

An example of the size of the impurity effects that may arise is shown in Fig. 1, which gives the electrode kinetics for the ferro-ferricyanide reaction on three different zinc oxide single crystals of varying conductivity. Each of the crystals was in excess of 99.999% pure. As can be seen, each crystal gives a linear Tafel plot under cathodic bias. However, the exchange currents, i.e, the extrapolations back to the reversible potential (+. 19 volts), differ by a factor of about 1000 and... 

Estimation of the nugget effect can provide valuable information about the process. For example, if it is substantially larger than an estimate of the material variation obtained independently, then we know that extraneous variation and/or bias is being introduced through incorrect sample collection, handling, or imacceptably large analytical variation. Extrapolation of the variogram to... 

---