K Walton

Mathematical modelling and quantitative methods

The present review reports on the mathematical methods and statistical techniques presently available for hazard characterisation. The state of the art of mathematical modelling and quantitative methods used currently for regulatory decision-making in Europe and additional potential methods for risk assessment of chemicals in food and diet are described. Existing practices of JECFA, FDA, EPA, etc., are examined for their similarities and differences. A framework is established for the development of new and improved quantitative methodologies. Areas for refinement, improvement and increase of efficiency of each method are identified in a gap analysis. Based on this critical evaluation, needs for future research are defined. It is concluded from our work that mathematical modelling of the dose-response relationship would improve the risk assessment process. An adequate characterisation of the dose-response relationship by mathematical modelling clearly requires the use of a sufficient number of dose groups to achieve a range of different response levels. This need not necessarily lead to an increase in the total number of animals in the study if an appropriate design is used. Chemical-specific data relating to the mode or mechanism of action and/or the toxicokinetics of the chemical should be used for dose-response characterisation whenever possible. It is concluded that a single method of hazard characterisation would not be suitable for all kinds of risk assessments, and that a range of different approaches is necessary so that the method used is the most appropriate for the data available and for the risk characterisation issue. Future refinements to dose-response characterisation should incorporate more clearly the extent of uncertainty and variability in the resulting output.

Uncertainty factors for chemical risk assessment. human variability in the pharmacokinetics of CYP1A2 probe substrates.

A 100-fold uncertainty factor is used to derive acceptable daily intakes for compounds causing thresholded toxicity. The 10-fold factor for human variability can be further subdivided into two factors of 10(0.5) (3.16) to allow for toxicokinetics and toxicodynamics. The validity of the human kinetic subfactor has been analysed in relation to CYP1A2 metabolism using published in vivo pharmacokinetic parameters selected to reflect chronic exposure (metabolic and total clearances and area under the plasma concentration-time curve: CLm, CL and AUC) and acute exposure (the peak plasma concentration, C(max)). The variability in CYP1A2 activity in healthy adults, based on data after oral and intravenous dosage (CLm, CL and AUC), ranged from 34 to 42%. The variability in C(max) was 21%. The default kinetic factor of 3.16 would cover at least 99% of the healthy adult population, assuming that the data were log-normally distributed, but would give lower protection for some subgroups (pregnant women at term, healthy elderly, patients with liver disease), and was inadequate for neonates. This analysis of in vivo kinetic data for CYP1A2 substrates illustrates the importance of quantifying human variability in specific metabolic pathways, and of identifying potentially susceptible subgroups of the human population, in order to determine the scientific validity of uncertainty factors.

Human variability in CYP3A4 metabolism and CYP3A4-related uncertainty factors for risk assessment

CYP3A4 constitutes the major liver cytochrome P450 isoenzyme and is responsible for the oxidation of more than 50% of all known drugs. Human variability in kinetics for this pathway has been quantified using a database of 15 compounds metabolised extensively (>60%) by this CYP isoform in order to develop CYP3A4-related uncertainty factors for the risk assessment of environmental contaminants handled via this route. Data were analysed from published pharmacokinetic studies (after oral and intravenous dosing) in healthy adults and other subgroups using parameters relating primarily to chronic exposure [metabolic and total clearances, area under the plasma concentration-time curve (AUC)] and acute exposure (Cmax). Interindividual variability in kinetics was greater for the oral route (46%, 12 compounds) than for the intravenous route (32%, 14 compounds). The physiological and molecular basis for the difference between these two routes of exposure is discussed. In relation to the uncertainty factors used for risk assessment, the default kinetic factor of 3.16 would be adequate for adults, whereas a CYP3A4-related factor of 12 would be required to cover up to 99% of neonates, which have lower CYP3A4 activity.

Human variability in polymorphic CYP2D6 metabolism: is the kinetic default uncertainty factor adequate?

Human variability in the kinetics of CYP2D6 substrates has been quantified using a database of compounds metabolised extensively (>60%) by this polymorphic enzyme. Published pharmacokinetic studies (after oral and intravenous dosing) in non-phenotyped healthy adults, and phenotyped extensive (EMs), intermediate or slow-extensive (SEMs) and poor metabolisers (PMs) have been analysed using data for parameters that relate primarily to chronic exposure (metabolic and total clearances, area under the plasma concentration time-curve) and primarily to acute exposure (peak concentration). Similar analyses were performed with the available data for subgroups of the population (age, ethnicity and disease). Interindividual differences in kinetics for markers of oral exposure were large for non-phenotyped individuals and for EMs (coefficients of variation were 67-71% for clearances and 54-63% for C(max)), whereas the intravenous data indicated a lower variability (34-38%). Comparisons between EMs, SEMs and PMs revealed an increase in oral internal dose for SEMs and PMs (ratio compared to EMs=3 and 9-12, respectively) associated with lower variability than that for non-phenotyped individuals (coefficients of variation were 32-38% and 30% for SEMs and PMs, respectively). In relation to the uncertainty factors used for risk assessment, most subgroups would not be covered by the kinetic default of 3.16. CYP2D6-related factors necessary to cover 95-99% of each subpopulation ranged from 2.7 to 4.1 in non-phenotyped healthy adults and EMs to 15-18 in PMs and 22-45 in children. An exponential relationship (R(2)=0.8) was found between the extent of CYP2D6 metabolism and the uncertainty factors. The extent of CYP2D6 involvement in the metabolism of a substrate is critical in the estimation of the CYP2D6-related factor. The 3.16 kinetic default factor would cover PMs for substrates for which CYP2D6 was responsible for up to 25% of the metabolism in EMs.

Human variability in glucuronidation in relation to uncertainty factors for risk assessment.

The appropriateness of the default uncertainty factor for human variability in kinetics has been investigated for glucuronidation using an extensive database of substrates metabolised primarily by this pathway. Inter-individual variability was quantified for 15 compounds from published pharmacokinetic studies (after oral and intravenous dosing) in healthy adults and other subgroups using parameters relating to chronic exposure (metabolic and total clearances, area under the plasma concentration time-curve (AUC)) and acute exposure (C(max)). Low inter-individual variability (about 30-35%) was found for all parameters (clearance corrected or not corrected for body weight, metabolic clearance, oral AUC and C(max)) after either iv or oral administration to healthy adults. The overall variability of 31% for glucuronidation in healthy adults supported the validity of the default kinetic uncertainty factor of 3.16 for this group, because it would cover more than 99% of individuals. Comparisons between potentially sensitive subgroups and healthy adults using differences in means and variability indicated that neonates showed the greatest impairment of glucuronidation, and that the 3.16 kinetic default factor applied to the mean data for adults would be inadequate for this subpopulation. The in vivo data have been used to derive pathway-related default factors for compounds eliminated largely via glucuronidation.

Polymorphic CYP2C19 and N-acetylation: human variability in kinetics and pathway-related uncertainty factors

CYP2C19-mediated oxidation and N-acetylation constitute major phase I and phase II polymorphic pathways of xenobiotic metabolism in humans. Analysis of human variability in kinetics for these pathways has been carried out for compounds metabolised extensively (>60%) by these routes. Data for minor substrates for CYP2C19 metabolism (10-60%) have also been analysed. Published pharmacokinetic studies (after oral and intravenous dosing) in CYP2C19 non-phenotyped healthy adults (NPs), and phenotyped extensive (EMs), slow-extensive (SEMs) and poor metabolisers (PMs) have been analysed using data for parameters that relate primarily to chronic exposure (metabolic and total clearances, area under the plasma concentration-time curve) and primarily to acute exposure (peak concentration). Similar analyses were performed for the N-acetylation pathway using data for fast acetylators (FA) and slow acetylators (SA). Interindividual variability in the kinetics of CYP2C19 substrates after oral dosage was greater in EMs than in NPs (60 vs 43% for clearances and 54 vs 45% for Cmax). Lower variability was found for N-acetylation for both phenotypes (32 and 22% for FA and SA, respectively). The internal dose of CYP2C19 substrates in PM subjects would be 31-fold higher than in EMs, while for N-acetylated substrates there was a three-fold difference between SA and FA subjects. Pathway-related uncertainty factors were above the default safety factor of 3.16 for most subgroups and values of 52 and 5.2 would be necessary to cover to the 99th centile of the poor metaboliser phenotype for CYP2C19 and N-acetylation, respectively. An exponential relationship (R(2)=0.86) was found between the extent of CYP2C19 metabolism and the difference in internal dose between EMs and PMs. The kinetic default factor (3.16) would cover PMs for substrates for which CYP2C19 was responsible for up to 20-30% of the metabolism in EMs.

Uncertainty factors for chemical risk assessment: interspecies differences in glucuronidation.

For the risk assessment of effects other than cancer, a safe daily intake in humans is generally derived from a surrogate threshold dose (e.g. NOAEL) in an animal species to which an uncertainty factor of 100 is usually applied. This 100-fold is to allow for possible interspecies (10-fold) and interindividual (10-fold) differences in response to a toxicant, and incorporates toxicodynamic and toxicokinetic aspects of variability. The current study determined the magnitude of the interspecies differences in the internal dose of compounds for which glucuronidation is the major pathway of metabolism in either humans or in the test species. The results showed that there are major interspecies differences in the nature of the biological processes which influence the internal dose, including the route of metabolism, the extent of presystemic metabolism and enterohepatic recirculation. The work presented does not support the refinement of the interspecies toxicokinetic default to species- and pathway-specific values, but demonstrates the necessity for risk assessments to be carried out using quantitative chemical-specific data which define the fundamental processes which will influence the internal dose of a chemical (toxicokinetics), or the interaction of toxicant with its target site (toxicodynamics).

The use of surrogate endpoints to assess potential toxicity in humans

Data on toxic effects in humans may come from epidemiology studies, accidental poisonings, surveillance schemes or following intentional exposures. In many cases, a surrogate endpoint related to the adverse effect is investigated. Effects produced following intentional exposures are usually restricted to readily reversible, mild surrogate endpoints of the adverse effect of concern. Not all initial interactions within the target organ are related to the toxic effect, and many measurements are biomarkers of exposure not response. Biomarkers of response represent surrogate endpoints of response only if they are critical to the mode of action. The use of biomarkers and the possible problems with using surrogate endpoints are illustrated with data on aniline, cadmium, carbon monoxide, erythrosine, paracetamol (acetaminophen) and styrene. In vivo surrogate endpoints are normally used in risk assessment directly, whereas in vitro surrogate endpoints can be incorporated by the development of a biologically based dose-response model, or used to replace a default uncertainty factor by a chemical-specific adjustment factor.

Default Factors for Interspecies Differences in the Major Routes of Xenobiotic Elimination

For the risk to human health posed by chemicals that show threshold toxicity there is an increasing need to move away from using the default approaches, which inherently incorporate uncertainty, towards more biologically defensible risk assessments. However, most chemical databases do not contain data of sufficient quantity or quality that can be used to replace either the interspecies or interindividual aspects of toxicokinetic and toxicodynamic uncertainty. The purpose of the current analysis was to evaluate the use of alternative, species-specific, pathway-related, “categorical” default values to replace the current interspecies toxicokinetic default uncertainty factor of 4.0. The extent of the difference in the internal dose of a compound, for each test species, could then be related to the specific route of metabolism in humans. This refinement would allow for different categories of defaults to be used, providing that the metabolic fate of a toxicant was known in humans. Interspecies differences in metabolism, excretion, and bioavailability have been compared for probe substrates for four different human xenobiotic-metabolizing enzymes: CYP1A2 (caffeine, paraxanthine, theobromine, and theophylline), CYP3A4 (lidocaine), UDP-glucuronyltransferase (AZT), and esterases (aspirin). The results of this analysis showed that there are significant differences between humans and the four test species in the metabolic fate of the probe compounds, the enzymes involved, the route of excretion and oral bioavailability — all of which are factors that can influence the extent of the difference between humans and a test species in the internal dose of a toxicant. The wide variability between both compounds and the individual species suggests that the categorical approach for species differences may be of limited use in refining the current default approach. However, future work to incorporate a wider database of compounds that are metabolized extensively by any pathway in humans to provide more information on the extent to which the different test species are not covered by the default of 4.0. Ultimately this work supports the necessity to remove the uncertainty from the risk assessment process by the generation and use of compound-specific data.

Pathway-Related Factors: The Potential for Human Data to Improve the Scientific Basis of Risk Assessment

The default uncertainty factors used for risk assessment are applied either to allow for different aspects of extrapolation of the dose-response curve or to allow for database deficiencies. Replacement of toxicokinetic or toxicodynamics defaults by chemical-specific data allows the calculation of a chemical-specific “data-derived factor”, which is the product of chemical-specific values and default uncertainty factors. Such chemical-specific composite values will improve the scientific basis of the risk assessment of that chemical, but the necessary chemical-specific data are rarely available. Categorical defaults related to pathways of elimination and mechanisms of toxicity could be used when the overall fate or mechanism is known, but there are no chemical-specific data sufficient to allow replacement of the default, and the development of an overall data-derived factor. The development of pathway-related categorical defaults is being undertaken using data on selected probe substrates for which adequate data are available. The concept and difficulties of this approach are illustrated using data for CYP1A2.