EPA/600/R-08/103. 

Analysis of the Sensitivity and Uncertainty in 2-stage Clonal Growth 

Models for Formaldehyde with Relevance 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 growth 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 containing the third 

publication. 

Introduction

As knowledge of the biology of cancer has evolved, researchers have 

sought to apply biologically motivated models to estimate risks from exposures to 

carcinogens. The understanding of carcinogenesis as a process with multiple 

steps, and the observed increasing patterns of cumulative cancer incidence with 

age, provided motivation for the multistage model of Armitage and Doll (1954). 

The terms in this model can be interpreted to represent a series of mutagenic 

changes or more general distinct stages related to carcinogenesis. In turn, this 

model led to the development of the linearized 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 carcinogenesis as a process that involves 

initial and subsequent mutations, with growth and focal expansion of cells 

subsequent to mutations (Moolgavkar 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 mutation or stimulation of cellular growth. 

As such, clonal growth models also represent 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 the biology and the implications for human 

health risk. Inferences from these models 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-response model for diesel exhaust using 

rodent bioassay data. The modeling 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 particulate effects, while the mutagenic and 

1
genotoxic effects from particle-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) based 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-induced liver tumorigenicity in mice. 

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

estimate of low-dose risk but, 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 dioxin, addressing several important questions 

(e.g., Moolgavkar et al., 1996; Portier 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 efforts suggest that dioxin-induced 

secondary mechanisms associated with mutations could be important factors in 

the carcinogenicity of this chemical (Portier et al.,1996; Moolgavkar et al., 1996). 

Additionally, Portier and co-workers conclude 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 curve for the number of altered foci 

per unit volume. The different approaches 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, however, the clonal growth models in the 

literature (and sophisticated BBDR models more broadly) have generally not

been used in formal risk assessment to predict risk at human exposures from 

toxicological data. A prominent exception in this regard is the formaldehyde 

modeling effort by scientists at the Hamner Institutes for Health Sciences 

(formerly CIIT) in which a clonal growth model and associated dosimetry 

calculations were developed specifically for 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 inhaled formaldehyde, within a conceptual 

framework, that incorporates substantial mechanistic information and advanced 

computational methods at both the toxicokinetic and toxicodynamic levels. 

The remainder of our report summarizes published NCEA investigation of 

the mathematical and biological assumptions of the CIIT model and the 

characterization of associated uncertainty in risk predictions (Subramaniam et al., 

2
2008; Subramaniam et al., 2007; Crump et al., 2008). The presence of 

considerable biological data at various levels and advances in computational 

resources have made it possible to examine 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 increase application of biological data in risk 

assessment: 

(1) To what extent does the formulation of the model allow sound 

characterization (and hopefully reduction) of uncertainties present 

in cancer risk assessment? 

(2) To what extent does the modeling 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 important examination 

of these questions. In addition to strengthening the characterization of 

formaldehyde risks, NCEA’s work can provide 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 evaluation if such two-stage clonal expansion 

models are to be used for extrapolation of cancer risk from animal bioassays to 

human exposure. Broadly, these pertain to the following issues: 

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

historical control animals 

• The use and interpretation of experimental labeling index and tumor data, 

and the uncertainty and variability in these data 

• The evaluation and biological interpretation 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 inferences 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 quantitative analysis of select 

uncertainties in the CIIT model for rats. This paper implements solutions to the 

2-stage cancer model that are mathematically valid for non-homogeneous 

models (i.e., models with time-dependent parameters), thus, accounting for time 

3
dependence 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 sensitivity of model predictions to pooling historical and 

concurrent control data and to lumping sacrificed animals, in which tumors were 

discovered incidentally with those in which death was caused by the tumors. An 

inference of the CIIT modeling approach is that formaldehyde-induced 

tumorigenicity could be optimally explained 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 significantly altered with the non-homogeneous 

solutions. 

• Dose-response predictions below the range of exposures where tumors 

occurred in the bioassays are highly sensitive to the choice of control data. 

• In the range of exposures where tumors were observed, the model 

attributes up to 74% of the added tumor probability to formaldehyde’s 

mutagenic action when the reanalysis restricted 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) concentration, a surrogate for the dose-metric 

linked to formaldehyde-induced mutations, prompting these authors to 

utilize weekly averages for this quantity. 

Various other biological and mathematical uncertainties in the model identified 

(qualitatively) in Subramaniam et al. (2008) have been retained unmodified in this 

analysis. These include the model specification 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 model is that the risks associated with 

inhaled formaldehyde are de-minimis at relevant human exposure levels. Crump 

et al. (2008) presents a limited 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 which controls are used in the animal 

model 

• The impact of the lack of data on the 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” calculated by Conolly et al. (2003). 

These modifications are just as consistent with the underlying data used to 

construct the model and fit the bioassay 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 three papers discussed above provide a 

significant reference point for other potential applications of BBDR modeling in 

quantitative health risk assessment. Biologically motivated models that explicitly 

incorporate mechanistic information have the potential to provide improved 

technical tools for human health risk assessment and to support a more 

scientifically based evaluation 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. Nonetheless, the usefulness 

of BBDR models over standard statistical 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 modeling, 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 assessment (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 represents 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 

5
changes 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 replication rates to rule out the model variations considered 

in this exercise. The hypersensitivity of clonal growth modeling to these 

uncertainties suggests that other attempts to quantify low-dose human risk using 

animal data on intermediate upstream steps in the carcinogenic process may 

encounter related uncertainties, even when substantial biological data are 

available. 

Modeling assumptions and uncertainties pertaining to upstream 

intermediate steps in biologically motivated models are generally significant and 

can be strongly amplified when propagated downstream to risk end points. In 

essence, the BBDR process involves replacing general relationships, having 

some empirical support in a baseline (or “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 for consistent regulatory utility (OMB, 2006). In the 

case of statistical model fits to data on frank 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 biologically based models. In biologically 

based models, the statistical uncertainty in the dose response for tumor (or other 

effect) incidence is replaced by the statistical uncertainty propagated from fitting 

models to some intermediate upstream step. It is an open question whether (and 

under what circumstances) overall statistical 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 conclusion in Conolly et al. (2003), that 

formaldehyde’s direct mutagenic action is not relevant to its tumorigenicity, is 

highly sensitive to the specific data that was utilized. It was shown that the clonal 

growth modeling could also substantiate the opposite point of view—that 

formaldehyde induced mutations played a key role in carcinogenesis. Thus, the 

analyses presented here emphasize that uncertainty and sensitivity analyses are 

essential tools when evaluating inferences about fundamental biological 

processes (e.g., modes of action) that 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 models. In the case of complex models, such as 

the CIIT formaldehyde model, even a basic sensitivity analyses can quickly 

proliferate into a large number of scenarios that need to be examined. 

6
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