Extrapolation factors

Extrapolation can reduce computational effort by a large factor, but computation is cheap. The value of the computational reduction will be trivial for most problems. Convergence acceleration can be useful for complex problems or for the inside loops in optimization studies. For such cases, you should also consider more sophisticated integration schemes such as Runge-Kutta. It too can be extrapolated, although the extrapolation rule is different. The extrapolated factor for Runge-Kutta integration is based on the series... 

Data on the toxicokinetics of a substance can be very useful in the interpretation of toxicological findings, and may replace the use of some default extrapolation factors used in route-to-route (Section 5.5) or interspecies extrapolations (Section 5.3). In addition, interindividual differences in sensitivity to toxicants may be identified on the basis of toxicokinetic data, thereby making it possible to make the risk assessment more comprehensive by including sensitive subpopulations (Section 5.4). In conjunction with information on the relationship between concentration-dose at the target site and the toxic effect, toxicokinetic information may be an important tool for extrapolation from high to low dose effects. 

The terminology within this area is not standardized. Other terms include safety factor, uncertainty factor, extrapolation factor, adjustment factor, and conversion factor. None... 

The approach proposed by Renwick (1991, 1993) is also based on the 100-fold factor. It attempts to give a scientihc basis to the default values of 10 for the interspecies and 10 for the intraspecies (interindividual human) differences. Renwick also proposed a division of each of these UEs into sub-factors to allow for separate evaluations of differences in toxicokinetics and toxicodynamics. The advantage of such a subdivision is that components of these UEs can be addressed where data are available for example, if available data show similar toxicokinetics of a given chemical in experimental animals and humans, then only an interspecies extrapolation factor would be needed to account for differences in toxicodynamics. Renwick examined the relative magnitude of toxicoki-netic and toxicodynamic variations between and within species in detail. He found that toxicokinetic differences were generally greater than toxicodynamic differences resulting in the proposal that the 10-fold factors (for inter- and intraspecies variation) should, by default, be subdivided into factors of 4 for toxicokinetics and 2.5 for toxicodynamics. It should be noted that the proposed default values were derived from limited data. 

In a report on a research project quantification of extrapolation factors (Kalberlah and Schneider 1998), it is noted that extrapolation factors are intended to replace lack of knowledge by a plausible assumption, and that instimtions with responsibihty for establishing the mles must decide which level of statistical certainty, e.g., applicable for 50% or for 90% of a representative selection of substances, is desired for the selection of a standard value. It is furthermore noted that extrapolation factors are required for (1) time extrapolation, e.g., from a subchronic to a chronic duration of exposure (2) extrapolation from the LOAEL to the NAEL (3) interspecies extrapolation, i.e., from experimental animals to humans and (4) intraspecies extrapolation, i.e., from groups of persons with average sensitivity to groups of persons characterized by special sensitivity. In addition to these extrapolations, route-to-route extrapolation, e.g., oral-to-inhalation or dermal-to-oral must also be discussed. 

If no substance-specific knowledge at aU is available for one of the extrapolation steps, the extrapolation factor in each case is used in unaltered form this factor is described as the standard value. 

A further problem lies in the combination of the individual extrapolation factors to form a total extrapolation factor. The type of combination results from the dependence or independence of the individual sub-factors. According to current knowledge, multiplicative combination of the individual factors is assumed. Substance-specific knowledge about the interdependencies among the sub-factors may lead to modification, i.e., a reduction of the total extrapolation factor. 

Kalberlah and Schneider (1998) have analyzed the information on the quantification of extrapolation factors. They noted that in interspecies extrapolation, two variables must be differentiated The systematic differences between different species, and the variability in the sensitivity of the species. Systematic differences can, e.g., be recorded by means of allometric approaches, scaling (Section 5.3.2). The reasons for the variability in sensitivity may be due to both toxicokinetic and toxicodynamic characteristics of a species. 

In their analyses, statistics on the relevant extrapolation factor from animals to humans, as reported in the literature, were considered synoptically, and distinctions were made between (1) publications which focused on allometrically justifiable differences (2) publications which examined the toxicodynamic or toxicokinetic variability and (3) pubhcations which considered the total (gross) interspecies factor. In addition, consideration of PBPK models was discussed as a possible alternative. 

If sufficient data are available, substance-specific PBPK models should always be given preference over the use of general scaling factors. However, PBPK models were considered not to replace all of the sub-factors in the interspecies comparison and should, by definition, only include toxicokinetic differences. A further extrapolation factor for toxicodynamic differences between the species needs to be discussed. 

The authors noted that, in comparison with the scaling factor, the traditional 10-fold factor contains an additional extrapolation factor for possible additional toxicokinetic or toxicodynamic variability apart from the basal metabolic rate scaling. This additional factor, which can be interpreted as the traditional 10-fold factor divided by the scaling factor, ranges from approximately 1.5 for the mouse (10/7= 1.4) to approximately 6 for the rhesus monkey (10/1.6 = 6.3). The authors considered that the additional factor thus comprises levels of safety, which are currently nonuniform, and this inhomogeneity is not supported toxicologically. 

Kalberlah and Schneider (1998) considered that the usually applied extrapolation factor of 10 is probably sufficient to protect a large part of healthy adults in the human population with regard to toxicokinetic differences, whereas groups like children, elderly people, and individuals with diseases are not fully considered in the 10-fold factor. In addition, the 10-fold factor was not considered to take account of the toxicodynamic differences. The authors proposed an interindivi-dual factor of 25 for the general population, consisting of a factor of 8 for toxicokinetic variation and... 

A Dutch smdy (Wilschut et al. 1998, as reviewed in Vermeire et al. 1999) has evaluated route-to-route extrapolation on the basis of absorption or acute toxicity data. Data were collected primarily on dermal and inhalation repeated dose toxicity. An extrapolation factor, defined as the factor that is applied in route-to-route extrapolation to account for differences in the expression of systemic toxicity between exposure routes, was determined for each substance by using data on absorption and acute toxicity data. As experimental data on absorption often were not available, default values for absorption were also used to determine an extrapolation factor. Despite a rather large overall database, relatively few data could be used for the evaluation and the selection criteria were modified in order to include data that initially were considered less suitable for data analysis interspecies extrapolation based on caloric demands was introduced, and a factor of 3 was applied in case a LOAEL instead of a NOAEL was available. The choice of NOAELs for different exposure routes known for a substance suitable for analysis was based primarily on the same effect, but this criterion could not be maintained. 

Source Modified fi om Kalberlah, F. and Schneider, K., Quantification of extrapolation factors. Final report of the research project No. 11606113 of the Federal Environmental Agency, Bremeihaven, 1998. 

The authors noted that there are fundamental difficulties in the prediction of a chronic effect when only subacute data are available and thus the overall uncertainty is very high and is possibly increased further by the assignment of an extrapolation factor therefore, such extrapolations should be avoided, at least in cases where the uncertainty is extended by other extrapolation steps such as, e.g., LOAEL-to-NAEL, interspecies, interindividual, and route-to-route. They also noted that, due to great uncertainties, the extrapolation from single short-term exposure in the high-dose range to lifetime exposure is rejected. However, they stated that, currently, no justified cutoff criterion has been identified to determine the minimum exposure for which an extrapolation to lifetime exposure may be permitted or should not be carried out. 

The authors also pointed out the connection between the duration of exposure extrapolation factor and the interindividual variance. If, e.g., young adult animals were exposed (normal case) and observed over 90 days, this might have to be assessed differently from a smdy on neonates or older animals. Therefore, it is necessary to examine which elements have already been included in the interindividual factor. If the time factor (children, elderly people) was considered as a separate subfactor in the interindividual factor, then the specific data on the exposure period must be considered in relation to the duration of exposure extrapolation factor in order to avoid double assessment. 

Vermeire et al. (1999) reviewed several studies comparing NOAELs from chronic and subacute/subchronic studies in order to evaluate the distribution of the extrapolation factor for duration of exposure. The ratios of observed NOAELs from oral studies using historical data for various compounds were calculated. The most likely distribution of the ratios was considered to be lognormal and the parameters of the distributions of the ratios were estimated, see Table 5.8. 

The authors noted that it may be expected that the NOAELs from subacute/subchronic smdies tend to be larger than NOAELs from chronic studies and it was considered that the GM ratios for the NOAELs assessed in the studies most likely overestimated the median of the distribution of the extrapolation factor for duration of exposure. The authors also noted that it is very likely that the databases used in these studies overlap each other significantly. It was also pointed out that the distributions presented in Table 5.8 were based on rather variable exposure periods for the subchronic NOAELs, included interspecies variation (no matching for species) for... 

ECETOC emphasized that the scientific basis for establishing meaningful extrapolation factors in this area is still weak. Nevertheless, a provisional default value of 2-3 was considered to be consistent with the available scientific data when extrapolating from subchronic to chronic exposure. Eor extrapolation from short-term repeated to subchronic exposure, a factor of 3 was recommended as a provisional default value. 

WHO/IPCS (1994, 1996, 1999) did not consider an extrapolation factor for duration of exposure specifically, but the uncertainty related to this element is included in a broader defined additional factor addressing the adequacy of the overall database (Section 5.9). 

WHO/IPCS (1994, 1996, 1999) did not consider an extrapolation factor for duration of exposure specifically, but the uncertainty related to this element is included in a broader defined additional factor addressing the adequacy of the overall database (Section 5.9). The US-EPA (1993) has adopted the 10-fold factor to account for the uncertainty involved in extrapolating from less than chronic NOAELs to chronic NOAELs. This default value has later on been reconfirmed (US-EPA 2002) when only a subchronic duration smdy is available to develop a chronic reference value no chronic reference value is derived if neither a subchronic nor a chronic smdy is available. For systemic effects, ECETOC (2001) recommended a default assessment factor of 6 for extrapolation from subacute (28 days) to chronic exposure, and a factor of 2 from subchronic (90 days) to chronic exposure. For local effects, no additional assessment factor is needed for duration of exposure extrapolation for substances with a local effect below the threshold of cytotoxicity. KEMl (2003) suggested that extrapolation from subchronic to chronic exposure should be based on the distribution of NOAEL ratios reported by Vermeire et al. (2001) with an assessment factor of 16 covering 95% of the substances compared and for extrapolation from subacute to chronic exposure, with an assessment factor of 39 covering 95% of the substances. 

If, in the case of poor data, dispensing with an extrapolation is not decided, a (poorly validated) benchmark extrapolation is to be preferred to a (likewise poorly validated) extrapolation using a standard extrapolation factor. 

Decision about whether to use the benchmark method or an extrapolation with an extrapolation factor must be taken in consideration of the available data. 

If a standard extrapolation factor is taken as the starting point, additional substance-specific information may result in a modification of the standard value, i.e., a reduction or an increase in relation to 10. 

The EU TGD (EC 2003) recognized that the NOAEL is not very accurate with respect to the degree to which it corresponds with the (unknown) true NAEL. In the case of a steep curve the derived NOAEL can be considered as more reliable (the greater the slope, the greater the reduction in response to reduced doses) in the case of a shallow curve, the uncertainty in the derived NOAEL may be higher and this has to be taken into account in the assessment. If a LOAEL has to be used in the assessment, then this value can only be considered reliable in the case of a very steep curve. According to KEMI (2003), extrapolation factors of between 3-5 are used for LOAEL-to-NOAEL extrapolation without any scientific basis in risk assessment reports of existing substances within the European Union. 

KEMI recommended that extrapolation using the historical LOAEL/NOAEL ratio should not be undertaken in order to arrive at the dose without adverse effects from the LOAEL. The BMD approach should be used if data are adequate. If it is not possible to use the BMD approach, or to set a NOAEL, an extrapolation factor of 3-10, depending on the shape of the curve, is suggested for extrapolation from LOAEL to NOAEL. A LOAEL should preferably only be used in the case of a steep dose-response curve, and there is no guarantee that extrapolation of a LOAEL with any factor will yield an estimate of the NOAEL. 

In both approaches, allowance is often made for these uncertainties by the application of numerical factors (assessment factors, extrapolation factors, uncertainty factors). 

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