EPA/600/R-08/103. Analysis of the Sensitivity and Uncertainty in 2-stage Clonal Growth Models for Formaldehyde with Relevan ce to Other Biologically Based Dose Response (BBDR) Models.

The National Center for Environmental Assessment (NCEA) has published a series of papers addressing 2-stage clonal gr owth models for cancer as applied to formaldehyde. Herein, we summarize these papers, discuss the significance of this work for other BBDR applications, and provide journal reprints of two of these publications and a Web link to the scientific journal c ontaining the third publication.

Introduction

As knowledge of the biology of canc er has evolved, researchers have sought to apply biologically motivated model s to estimate risks from exposures to carcinogens. The understanding of carci nogenesis as a process with multiple steps, and the observed increasing patterns of cumulative cancer incidence with age, provided motivation for the multist age model of Armitage and Doll (1954). The terms in this model can be interpre ted to represent a series of mutagenic changes or more general distinct stages re lated to carcinogenesis. In turn, this model led to the development of the linea rized multistage model that the U.S. EPA has employed in many assessments to extrapolate risks for environmental exposure to carcinogens (Crump et al., 1976; U.S. EPA, 1986). Clonal growth models, on the other hand, represent carc inogenesis as a process that involves initial and subsequent muta tions, with growth and focal expansion of cells subsequent to mutations (Moolgavka r and Venzon, 1979; Moolgavkar and Knudson, 1981; Portier and Kopp-Schneider, 1991; Portier et al., 1996). Clonal growth models are valuable due to their ability to represent the different effects that carcinogens may exert on rates of muta tion or stimulation of cellular growth. As such, clonal growth models also repres ent important examples of biologically motivated models, which foster descriptions of multiple events in complex disease processes.

Clonal growth modeling efforts have been fruitful in generating hypotheses, leading to a better understanding of t he biology and the implications for human

health risk. Inferences from these m odels have also highlighted relevant data gaps. Examples of such chemical carcinogens include diesel exhaust emissions, dioxin, and trichloroethylene. Chen and Oberdorster (1996) successfully linked pharmacokinetic and pharmacodynamic information in an integrated lung dosimetry and clonal growth dose-respons e model for diesel exhaust using rodent bioassay data. The m odeling allowed them to study the relative roles of the particulate and adsorbed volatile organic components (e.g., polycyclic aromatic hydrocarbons) of diesel in the cancer process at various exposures. Their modeling results suggest that lung tumors observed in the rat bioassays may arise mainly due to the particula te effects, while the mutagenic and

1genotoxic effects from parti cle-associated organics may play a primary role in tumorigenesis at low doses relevant to most human exposures. Chen (2000) used clonal growth modeling in a similar vein for modeling liver cancer risk upon exposure to trichloroethylene (TCE) bas ed upon the extensive bioassay data for this compound and its two metabolites, dichloroacetic acid (DCA) and trichloroacetic acid (TCA). Their modeling results indicate that the effects of DCA, alone, could potentially account for TCE-in duced liver tumorigenicity in mice.

The authors did not characterize their effort as enabling a more accurate

estimate of low-dose risk bu t, rather, as elucidating the effect of plausible biological assumptions on risk.

Several laboratories have contributed to the clonal growth modeling of the

cancer and non-cancer effects of diox in, addressing several important questions (e.g., Moolgavkar et al., 1996; Portie r and Kohn, 1996; Portier et al., 1996; Conolly and Andersen, 1997; Portier, 2000; Luebeck et al., 2000; Luebeck et al., 1995). For example, while dioxin is generally not considered a mutagen as per in

vitro studies, clonal growth modeling e fforts suggest that dioxin-induced secondary mechanisms associated with muta tions could be impor tant factors in the carcinogenicity of this chemical (Porti er et al.,1996; Moolga vkar et al., 1996). Additionally, Portier and co-workers conc lude that the data do not fully support a threshold in the cancer dose-response for dioxin (Portier, 2000) . In a different contribution to the debate, the clonal growth modeling of Conolly and Andersen (1997) proposes a U-shaped dose-response cu rve for the number of altered foci per unit volume. The different appr oaches taken indicate how modeling investigations can underscore significant biological uncertainties affecting doseresponse assessments.

These clonal growth and other BBDR modeling efforts typically require considerable effort—both in gathering the relevant empirical data and in computational resources. Notably, how ever, the clonal growth models in the literature (and sophistic ated BBDR models more broadly) have generally not been used in formal risk assessment to pr edict risk at human exposures from toxicological data. A prom inent exception in this regard is the formaldehyde modeling effort by scientists at the Ha mner Institutes for Health Sciences (formerly CIIT) in which a clonal gr owth model and associated dosimetry calculations were developed specifically fo r use in extrapolation of cancer risk.

In a series of papers and a health risk assessment report, scientists at the CIIT Hamner Institutes developed a model (the “CIIT model”) for estimating respiratory cancer risk due to inhal ed formaldehyde, within a conceptual framework, that incorporates substant ial mechanistic information and advanced computational methods at both the toxicokinetic and toxicodynamic levels.

The remainder of our r eport summarizes published NCEA investigation of

the mathematical and bi ological assumptions of the CIIT model and the characterization of associated uncertainty in risk predictions (Subramaniam et al.,

22008; Subramaniam et al., 2007; Crum p et al., 2008). The presence of considerable biological data at various levels and advances in computational resources have made it possible to ex amine uncertainties somewhat more extensively than in the past.

We used two general questions to frame our approach regarding the application of models that seek to incr ease application of biological data in risk

assessment: (1) To what extent does the formu lation of the model allow sound characterization (and hopefully reduc tion) of uncertainties present

in cancer risk assessment? (2) To what extent does the modelin g approach allow characterization of the relative weights of key events in the mode-of-action of a carcinogen? NCEA’s research regarding the CIIT model showcases an impor tant examination of these questions. In addition to strengthening the characterization of formaldehyde risks, NCEA’s work can provi de insights for investigators looking towards future applications of BBDR models in risk assessment.

Synopsis of NCEA publications

Subramaniam et al. (2008) reviews key biological and statistical

uncertainties that need careful evaluatio n if such two-stage clonal expansion models are to be used for extrapolation of cancer risk from animal bioassays to human exposure. Broadly, these per tain to the following issues:

• The sensitivity of the dose response to constraints on the heterogeneity of

historical control animals

• The use and interpretation of experi mental labeling index and tumor data, and the uncertainty and variability in these data

• The evaluation and biological interp retation of the estimated parameters

• The uncertainties in model specification— in particular that of initiated cells. Given the paucity of data on the kinetics of initiated cells, Subramaniam et al. (2008) explores various biological in ferences that were indicated by the CIIT formaldehyde modeling and examines their plausibility in the face of known biology.

Subramaniam et al. (2008) also identifies key uncertainties in the scale-up of the CIIT model to humans, focusing on assumptions that underlie the model parameters for cell replication rates and formaldehyde-induced mutation. The authors discuss uncertainties in identifying parameter values in the model used to estimate and extrapolate DNA protein cross-link levels.

Subramaniam et al. (2007) implements a quantitativ e analysis of select

uncertainties in the CIIT model for rats . This paper implements solutions to the 2-stage cancer model that are mat hematically valid for non-homogeneous models (i.e., models with time-dependent para meters), thus, accounting for time

3dependence in variables. The original CIIT model used a solution method that was not valid for time-dependent parameters. In this re-implementation, the

authors examine the sensitiv ity of model predictions to pooling historical and concurrent control data and to lumping sa crificed animals, in which tumors were discovered incidentally with those in which death was caused by the tumors. An inference of the CIIT modeling appr oach is that formaldehyde-induced tumorigenicity could be optimally expl ained without the role of formaldehyde’s mutagenic action. Subramaniam et al. ( 2007) examines the strength of this result. The primary conclusions are as follows:

• CIIT model results are not signific antly altered with the non-homogeneous

solutions.

• Dose-response predictions below t he range of exposures where tumors occurred in the bioassays are highly sensitiv e to the choice of control data.

• In the range of exposures where tumors were observed, the model attributes up to 74% of the added tu mor probability to formaldehyde’s mutagenic action when the reanalysis re stricted the use of the National Toxicology Program (NTP) historical control data to only those obtained from inhalation exposures.

• Model results are insensitive to hourly or daily temporal variations in DNA protein cross-link (DPX) concentrati on, a surrogate for the dose-metric linked to formaldehyde-induced mutati ons, prompting these authors to utilize weekly averages for this quantity.

Various other biological and mathematical uncertainties in the model identified (qualitatively) in Subramani am et al. (2008) have been re tained unmodified in this analysis. These include the model spec ification of initiated cell division and death rates, and the uncertainty and variability in the dose-response for cell replication rates.

Crump et al. (2008) , the third paper in this series, evaluates the modeling in Conolly et al. (2004). In this model, risk estimated using the rat model in Conolly et al. (2003) was extrapolated to human exposures in Conolly et al. (2004). The primary result of the human mo del is that the risks associated with inhaled formaldehyde are de-minimis at relevant human exposure levels. Crump et al. (2008) presents a lim ited sensitivity analysis of the formaldehyde human model by examining the impact of two key factors only while keeping all other major uncertainties unchanged:

• The effect upon the human model of wh ich controls are used in the animal

model

• The impact of the lack of data on t he division rates and death rates of

initiated cells

On both these accounts, analysis in Crump et al. (2008) shows the estimates of human risk in Conolly et al. (2004) to be hyper-sensitive to their modeling assumptions:

4• When the control animals from the National Toxicology Program (NTP) studies are replaced with control animals only from NTP inhalation studies, estimates of human risk are increased by 50-fold. When only concurrent control rats are used, the model does not provide any upper bound to

human risk.

• In Crump et al. (2008), a decrease in initiated cell replication rates at low doses, as seen in the J-shaped curve used in Conolly et al. (2003), is retained, but varied to a small degree. The exercise shows that with very small numerical perturbations one could obtain quantitative risks in the human model ranging from negative up to 4 orders of magnitude higher

than the “conservative estimates” calc ulated by Conolly et al. (2003). These modifications are just as cons istent with the underlying data used to

construct the model and fit the bioassa y data as well as the original model that was based upon the Conolly et al. (2003) assumptions.

Summary and implications

The results developed in the thre e papers discussed above provide a significant reference point for other pot ential applications of BBDR modeling in quantitative health risk assessment. Biologic ally motivated models that explicitly incorporate mechanistic information hav e the potential to provide improved technical tools for human health risk assessment and to support a more scientifically based evaluatio n of uncertainty in health risk predictions. The realization of this potential depends on adequate characterization of the impacts of model assumptions on bottom-line risk predictions. BBDR modeling can make the resulting uncertainties explicit and identifiable. N onetheless, the usefulness

of BBDR models over standard statis tical modeling approaches for risk estimation at human exposures is not evident a priori

.

The wide range of plausible dose-response estimates that were obtained in NCEA’s work show that clonal growth m odeling, in this case, does not serve to usefully narrow uncertainty in the range of low-dose human risk for this compound. While some model realizations would predict very low risks at the low dose (or even reduction in baseline risks) , other realizations can predict risks as high as (or substantially higher than) those predicted by U.S. EPA’s baseline

methods of low-dose linear risk asse ssment (U.S. EPA, 2005). Thus, the analyses published in these papers do not support the claim in Conolly et al. (2004) that their risk estimate represent s a conservative estimate on human risk

in the face of model uncertainties.

The uncertainty in the Conolly et al . (2003, 2004) models is particularly

acute because there are no data on the formation or the growth rates of initiated cells due to formaldehyde exposure. These authors made assumptions about

division rates of initiated cells based upon analogy with data on normal cells, and evaluated these assumptions by comparing model predictions on tumor rates with animal tumor data. However, as concluded in Crump et al. (2008), the

5changes made to the assumptions regarding initiated cells are numerically so small that it would appear to be virtually impossible to obtain sufficiently precise measurements of cell replicat ion rates to rule out the model variations considered in this exercise. The hypersensitivity of clonal growth modeling to these uncertainties suggests that other attemp ts to quantify low-dose human risk using animal data on intermediate upstream steps in the carcinogenic process may encounter related uncertainties, even w hen substantial biol ogical data are

available.

Modeling assumptions and uncertainties pertaining to upstream intermediate steps in biologically moti vated models are generally significant and can be strongly amplified when propagated do wnstream to risk end points. In essence, the BBDR process involves replacing general relationships , having some empirical support in a baseline (o r “default”) approach to risk assessment,

with much more specific relationships and assumptions . These specific assumptions, while presumably appearing scientifically plausible, may have limited empirical support. In addition, the complexity of underlying parameters and their relationship to the empirical measurements can often lead to loss of transparency, a key feature fo r consistent regulatory util ity (OMB, 2006) . In the

case of statistical model fits to data on fr ank toxicological effects, different model forms typically produce widely different risk estimates outside the observed data (NRC, 1983). NCEA’s experience with formaldehyde modeling indicates that similar uncertainties can occur with biolog ically based models. In biologically based models, the statistical uncertainty in the dose response for tumor (or other effect) incidence is replaced by the stat istical uncertainty propagated from fitting models to some intermediate upstream st ep. It is an open question whether (and under what circumstances) overall statis tical uncertainty in extrapolating tumor risk can be reduced by this transfer of uncertainty.

A second question pertains to the extent to which modeling approaches can be used to deliberate upon the relative weights of key events in the mode-ofaction of a putative carcinogen. The work presented in the papers in this summary shows that the model-based conc lusion in Conolly et al. (2003), that formaldehyde’s direct mutagenic action is no t relevant to its tumorigenicity, is highly sensitive to the spec ific data that was utilized. It was shown that the clonal growth modeling could also substant iate the opposite point of view—that formaldehyde induced mutations played a ke y role in carcinogenesis. Thus, the analyses presented here emphasize that unc ertainty and sensitivity analyses are essential tools when evaluating infer ences about fundamental biological processes (e.g., modes of action) t hat may be drawn from a BBDR model.

NCEA’s work in examining properties of formaldehyde clonal growth modeling also illustrates the complexities and substantial resource requirements involved in evaluating BBDR m odels. In the case of complex models, such as the CIIT formaldehyde model, even a bas ic sensitivity analyses can quickly proliferate into a large number of scenarios that need to be examined.

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