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; Portierand Kopp-Schneider, 1991; Portieret 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
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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., Moolgavkaretal., 1996; Portierand Kohn, 1996; Portieret 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 (Portieret al., 1996; Moolgavkaretal., 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 dose-
response 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 CUT) 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
CUT Hamner Institutes developed a model (the "CUT 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 CUT model and the
characterization of associated uncertainty in risk predictions (Subramaniam et al.,
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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 CUT 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
CUT 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 CUT 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 DMA protein cross-link levels.
Subramaniam et al. (2007) implements a quantitative analysis of select
uncertainties in the CUT 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
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dependence in variables. The original CUT 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 CUT 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:
• CUT 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 DMA
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:
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• 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
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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-of-
action 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 CUT formaldehyde model, even a basic sensitivity analyses can quickly
proliferate into a large number of scenarios that need to be examined.
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