1 Issues in Harmonizing Methods for Risk Assessment Kenny S. Crump Louisiana Tech University

NRC (2008) Recommendations for Harmonizing Risk Assessment Providing quantitative low-dose-extrapolated risk estimates not only for cancer, as is currently done, but for all types of health effects; Basing the quantitative approach not on the type of toxic effect (whether cancer or not), but on consideration of the perceived individual dose responses, the nature of human variability and how the toxic substance interacts with background processes that contribute to background toxicity; Proposing linear extrapolation not be restricted to carcinogenic responses but applied to some non-carcinogenic responses as well; and Providing not just a single estimate of risk, but a probabilistic description. 2

NRC (2008) Recommendations for Harmonizing Risk Assessment Proposed quantitatively estimating low-dose risk in all cases: Model 1 (threshold dose response on individual level, linear on population level); Model 2 (threshold response on individual level, nonlinear on population level); Model 3 (linear response on individual level, linear on population level). Determining which model is appropriate involves understanding whether the toxicological mechanisms are independent of background exposures and processes, or whether they augment background processes. 3

NRC (2008) Recommendations for Harmonizing Risk Assessment Proposed quantitatively estimating low-dose risk in all cases: Model 1 (threshold dose response on individual level, linear on population level); Model 2 (threshold response on individual level, nonlinear on population level); Model 3 (linear response on individual level, linear on population level). 4 However, there are conceptual and operational difficulties with the nonlinear approach (Model 2): Crump KS, Chiu WA, Subramaniam RP. (March 2010) Issues in using human variability distributions to estimate low-dose risk. Environmental Health Perspectives 118(3):

The Non-Linear Approach Utilizes Human Variability Distribution (HVD) Modeling 1.Individual sensitivities to a toxic response are determined by various pharmacokinetic and pharmacodynamic parameters. Log-normal distributions are estimated from data on these parameters. 2.These distributions are combined into an overall log-normal distribution for the product of the individual parameters by adding their variances, which assumes independence. 3.This log-normal distribution is transferred to the dose axis by centering it at a point of departure (POD) dose usually estimated from animal data. 4.The resulting log-normal distribution (median from animal data and log-variance from HVD modeling) is used to quantify low- dose risk. 5

Difficulties with HVD Modeling The theoretical basis for the log-normal assumption is not supportable. –No phenomenological support for assumption that factors affecting human variability act multiplicatively and independently. 6

A Simple Example The tolerance distribution for an adverse response is a log-normal function of serum concentration of a toxin. The half-life of the serum concentration has a log-normal distribution. Then (Crump et al., EHP, March 2010), These do not operate multiplicatively or independently. The risk from exposure to a constant dose rate, D, is which is not what is predicted by HVD modeling: 7

Difficulties with HVD Modeling The theoretical basis for the log-normal assumption is not supportable. –No phenomenological support for assumption that factors affecting human variability act multiplicatively and independently. –Other distributions fit the existing data as well as the log-normal but predict very different risks. 8

Distributions other than the log-normal can describe data equally well** Number of times the log-normal, gamma or shifted log-gamma (e X -1 where X has a gamma distribution) provided the best fit* to data on variability in pharmacokinetic parameters: Log-Normal 38 (19%) Gamma 77 (39%) Log-Gamma 83 (42%) *Based on Akaike AIC criterion **from Data Base Files 1-4 downloaded from These distributions have very different low-dose extrapolated risks. 9

10 Gamma and Log-Normal Distributions Can Fit Data Equally Well But Diverge at Low Doses

Difficulties with HVD Modeling The theoretical basis for the log-normal assumption is not supportable. –No phenomenological support for assumption that factors affecting human variability act multiplicatively and independently. –Other distributions fit the existing data as well as the log-normal but predict vastly different risks –Even if the Central Limit Theorem basis for asymptotic log-normality were valid, predictions of low risks (e.g., ≤ ) could still be seriously in error. 11

Comparison of exact risks expressed as the product of between 5 and 80 log-gamma or reciprocal log-gamma variables with the risks predicted by the Central Limit Theorem. 12 Product of 10 Reciprocal Log-Gammas with shape α = 2 Agree in observable range (risk >= 0.10) Diverge at low doses

Although these problems are illustrated using the example methodology in the Science and Decision report that utilize a log-normal distribution, similar problems will be present with any particular distribution. 13

Threshold determination must refer to an endpoint Exposure Biochemical Effect Cellular Effect Apical Effect 1. Exposure doesn’t result in any biochemical perturbation 2. Exposure causes some biochemical perturbation, but doesn’t cause a cellular response 3. Exposure that causes biochemical perturbation that results in a cellular response but does not increase apical risk THRESHOLD IN: Biochemical Cellular Apical Cellular Apical 14

As illustrated in the next few slides, it is not possible to have enough data to distinguish between a low-dose linear response and a threshold response. 15

16 Threshold versus Low-Dose Linear Red curve is linear at low-dose.

17 Threshold versus Low-Dose Linear Red Curve is still linear at low-dose.

18 Threshold versus Low-Dose Linear Red Curve is still linear at low-dose.

19 Threshold versus Low-Dose Linear Red Curve is still linear at low-dose.

20 Threshold versus Low-Dose Linear Red Curve is still linear at low-dose..

21 Threshold versus Low-Dose Linear Blue curve exhibits a threshold.

22 Threshold versus Low-Dose Linear Blue curve still exhibits a threshold.

23 Threshold versus Low-Dose Linear Blue curve still exhibits a threshold.

24 Threshold versus Low-Dose Linear Blue curve still exhibits a threshold.

25 Threshold versus Low-Dose Linear Blue curve still exhibits a threshold. (And the two curves predict very different low-dose risks.)

What about statistical methods for setting lower bounds for thresholds? As illustrated in the next few slides, such statistical methods are based on highly specific and often implausible assumptions. 26

Model Dependence of Threshold Estimates Example: 27

Model Dependence of Threshold Estimates 28

Model Dependence of Threshold Estimates 29

Model Dependence of Threshold Estimates 30

Model Dependence of Threshold Estimates 31

Even if a population threshold exists, it cannot be bounded away from zero (i.e., no threshold) without making unverifiable assumptions about the shape of the dose response. 32 Likewise, a non-linear, non-threshold low- dose response cannot provide lower bounds for low-dose risk different from those provided by a low-dose linear model without making unverifiable assumptions.

Consequently, Whenever low-dose risk is estimated, upper bounds on risk should generally allow for the possibility of low-dose linearity, e.g., Models 1 or 3 from the Science and Decisions report. 33 low-dose linearity is generally difficult to completely rule out (e.g., any amount of additivity to background will lead to low-dose linearity). Without strong and likely unverifiable distributional assumptions (e.g., log-normal), upper bounds from threshold and non-linear models will still reflect low-dose linearity. (There are threshold and low-dose non-linear models arbitrarily close to any low-dose linear model and vice-versa.)

Interest in the threshold concept is stimulated by the current approach to risk assessment that involves two incompatible paths: 1.If the response is thought to be linear at low dose, low dose risk is estimated by linear extrapolation below a point of departure (POD). 2.If the response is thought to be threshold or sub- linear, safety or uncertainty factors are applied to a POD (POD-safety factor approach) and low dose risk is not estimated. The threshold also is not estimated, but only used in a qualitative sense. 34

estimate risk and provide uncertainty bounds. No population thresholds. No estimates of apical risk. Estimate thresholds (exposures that will not result in biologically significant perturbations) and 2008 NRC Committees’ Recommendations Need To Be Harmonized NRC 2008 Science and Decisions NRC 2007 Toxicity Testing in 21 st Century 35 Apply POD-safety factor approach and use scientific judgment in setting of safety factors. Better reflects the true nature of our knowledge about low-dose risks, which is mainly qualitative. Does not need to assume a threshold, but safety factors should reflect toxicological judgment on dose response below POD. Safety factors should account for severity of disease. Harmonized Approach for In Vivo or In Vitro Data

Appendix 36

Science has been described as formulating falsifiable hypotheses and testing these hypotheses using observational data. None of the following statements are falsifiable: “The dose response for chemical X has a threshold.” “The dose response for chemical X does not have a threshold.” “The dose response for chemical X is low-dose linear.” “The dose response for chemical X is not low-dose linear.” “Dose Y of chemical X has an effect on response Z.” Although the statement, “Dose Y of chemical X has no effect on response Z.” is in principle falsifiable, in practice it often is not falsifiable at very low doses that may be of interest in risk assessment. 37

Example of linear dose response resulting from additivity to background – inactivation of acetylcholinesterase molecules by an organophosphorus pesticide (adapted from Figure 3.3 of Rhomberg, L. R. (2004). Mechanistic considerations in the harmonization of dose-response methodology: the role of redundancy at different levels of biological organization. In Risk Analysis and Society: An Interdisciplinary Characterization of the Field, McDaniels TL, Small MJ, eds. New York: Cambridge University Press.) 38

Inactivation of acetylcholinesterase molecules individual level 39

Inactivation of acetylcholinesterase molecules Population Level 40

Inactivation of acetylcholinesterase molecules Population Level distribution after exposure defined by law of mass action (# bound molecules ~ dose of organophosphorus pesticide, proportionality constant determined by binding affinities) 41

Inactivation of acetylcholinesterase molecules Population level response is linear at low-dose. δU = [change in # active molecules] ~ Dose (law of mass action – Rhomberg 2004) δP = [change in proportion with # active molecules below cutoff for normal function] ~ δU ~ Dose 42