Biologically Motivated Computational Modeling of ...

TOXICOLOGICAL SCIENCES 75, 432– 447 (2003) DOI: 10.1093/toxsci/kfg182

Biologically Motivated Computational Modeling of Formaldehyde Carcinogenicity in the F344 Rat Rory B. Conolly, 1 Julia S. Kimbell, Derek Janszen, 2 Paul M. Schlosser, Darin Kalisak, Julian Preston, 3 and Frederick J. Miller CIIT Centers for Health Research, 6 Davis Drive, Research Triangle Park, North Carolina 27709 Received March 7, 2003; accepted June 23, 2003

Key Words: formaldehyde; F344 rat; squamous cell carcinoma; dose-response; clonal growth; DNA-protein cross-links; regenerative cellular proliferation; computational modeling; risk assessment.

1 To whom correspondence should be addressed. Fax: (919) 558-1300. E-mail: [email protected]. 2 Present address: Wyeth-Ayerst Research, Collegeville, PA 19426. 3 Present address: Environmental Carcinogenesis Division, U.S. EPA, NHEERL, Research Triangle Park, NC 27711.

Toxicological Sciences 75(2), © Society of Toxicology 2003; all rights reserved. 432

F344 rats that inhaled formaldehyde chronically (6, 10, and 15 ppm, 6 h/day, 5 days/week) developed nasal squamous cell carcinoma (Kerns et al., 1983; Monticello et al., 1996). This result raised concern for the potential human carcinogenicity of formaldehyde, since lower-level human exposure to formaldehyde is widespread. Environmental exposures are typically in the range of a few parts-per-billion (Health Canada, 2001). The current occupational Permissible Exposure Limit (PEL) for formaldehyde is 0.75 ppm (OSHA, 2003). Occupational exposures above the PEL have been reported, though such excursions are not typical (Stewart et al., 1987). Extensive mechanistic studies were conducted with the broad goal of characterizing the underlying mechanisms of the carcinogenic response (see reviews by Heck et al., 1990; Morgan, 1997). These studies focused on the contributions of DNA-protein cross-links (DPX; Casanova et al., 1994) and of cytolethality-regenerative cellular proliferation (CRCP; Monticello et al., 1996) to tumor development. DPX have been used as a measure of target tissue dose in formaldehyde risk assessments (Hernandez et al., 1994; Starr, 1990). CRCP data have not previously been used for risk assessment per se though some mechanistic implications of these data were considered by Monticello et al. (1996). In parallel with the mechanistic studies, an anatomically realistic three-dimensional computational fluid dynamics (CFD) model of airflow in the F344 rat nasal airways was developed (Kimbell et al., 1997a). This CFD model provides the capability for high resolution predictions of regional flux of formaldehyde from the inhaled air into the adjacent tissue (Kimbell et al., 2001b). This article describes a quantitative, biologically motivated dose-response model for the carcinogenicity of inhaled formaldehyde in the rat and is part of a larger effort to assess the human cancer risks of inhaled formaldehyde. CFD-generated

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Formaldehyde inhalation at 6 ppm and above causes nasal squamous cell carcinoma (SCC) in F344 rats. The human health implications of this effect are of significant interest since human exposure to environmental formaldehyde is widespread, though at lower concentrations than those that cause cancer in rats. In this article, which is part of a larger effort to predict the human cancer risks of inhaled formaldehyde, we describe biologically motivated quantitative modeling of the exposure-tumor response continuum in the rat. An anatomically realistic, three-dimensional fluid dynamics model of the F344 rat nasal airways was used to predict site-specific flux of formaldehyde from inhaled air into tissue, since both SCC and preneoplastic lesions develop in a characteristic site-specific pattern. Flux into tissue was used as a dose metric for two modes of action, direct mutagenicity and cytolethality-regenerative cellular proliferation (CRCP), which in turn were linked to key parameters of a two-stage clonal growth model. The direct mutagenicity mode of action was represented by a low dose linear dose-response model of DNA-protein cross-link (DPX) formation. An empirical J-shaped dose-response model and a threshold model fit to the empirical data were used for CRCP. In the clonal growth model, the probability of mutation per cell generation was a function of the tissue concentration of DPX while the rate of cell division was calculated from the CRCP data. Maximum likelihood methods were used to estimate parameter values. Survivor (a nontumor outcome) and tumor data for controls from the National Toxicology Program database and from two formaldehyde inhalation bioassays were used for likelihood calculations. The Jshaped dose-response for CRCP provided a better description of the SCC data than did the threshold model. Sensitivity analyses indicated that the rodent tumor response is due to the CRCP mode of action, with the directly mutagenic pathway having little, if any, influence. When evaluated in light of modeling and database uncertainties, particularly the specification of the clonal growth model and the dose-response data for CRCP, this work provides suggestive though not definitive evidence for a J-shaped doseresponse for formaldehyde-mediated nasal SCC in the F344 rat.

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predictions of regional flux are linked to two modes of action, each of which contributes to tumor development. Low-dose linear, direct mutagenicity is mediated by DPX. Both J-shaped and threshold dose-responses for CRCP are evaluated. These modes of action jointly affect parameters of a two-stage clonal growth model, which describes cancer as a succession of genetic changes and altered growth behaviors that lead to progressive conversion of normal cells into cancer cells. While the clonal growth model may not be an accurate representation of the actual cellular mechanism of formaldehyde carcinogenesis, it provides insight into the relative roles of direct mutagenicity and CRCP in tumor development. The data-intensive, computational modeling approach to exposure-response assessment for formaldehyde described here is intended to (1) provide as clear a description as possible, given the database, of the biological basis of formaldehyde carcinogenicity in rodents, (2) minimize the uncertainty of the model linking exposure with tumor response, and (3) serve as a starting point for assessment of the dose-response for formaldehyde carcinogenicity in humans. MODEL DEVELOPMENT The overall exposure-response model (Fig. 1) links exposure to formaldehyde with the probability of tumor in the F344 rat. The model is flexible with respect to the ages at which exposure begins and ends, the h/day and days/week of exposure, and the inhaled concentration. In the following sections, development of the exposure-response model is described using the organizational scheme depicted in Figure 1. Several aspects of the overall modeling effort, including the CFD modeling and flux binning procedure that partitions the nasal surface area into regions of similar flux, the DPX modeling, and the treatment of the raw CRCP data have previously been described in detail (Conolly et al., 2000, 2002; Kimbell et al.,

2001a). In these cases the current article provides only an overview of the development effort. Regional Dosimetry in the F344 Rat Nose CFD-generated predictions of the flux of formaldehyde from inhaled air into adjacent tissue in the nose of the F344 rat indicate that the flux varies in a site-specific manner (Kimbell et al., 1993, 2001b). The intensity of tissue effects such as CRCP and DPX does vary throughout the nasal airways for a constant inhaled concentration of formaldehyde (Casanova and Heck, 1987; Morgan et al., 1986). The site specificity in CRCP and DPX is even greater than would be predicted solely by the regional variation in flux, since the relationships of flux with CRCP and DPX are nonlinear (Conolly et al., 2000, 2002; Monticello et al., 1996). Capturing regional dosimetry information was thus a key step in development of the formaldehyde exposure-tumor response model. An anatomically realistic, three-dimensional CFD model of the rat nose was used for this purpose. This CFD model has been described in detail elsewhere (Kimbell et al., 1997a, 2001b). The need to link site-specific predictions of flux to DPX and CRCP required a strategy for partitioning the nasal surface into areas of similar flux (Kimbell et al., 2001a). The rat nose was partitioned into 20 such areas, hereafter called flux bins, which were obtained by dividing the CFD-predicted flux range into 20 evenly spaced segments. The CFD model was used to determine the specific regions of nasal airway surface assigned to each bin. The computational model, described below, that linked flux into each bin with CRCP, DPX and tumor development was implemented in parallel for each flux bin. This flux binning strategy allowed the model to capture the influence of site-specific variation in rat nasal flux on the tumor response. The question of how many flux bins are sufficient to adequately characterize the influence of regional variation in dosimetry on tumor response was addressed through a sensitivity analysis. Binning strategies from 1 to 25 bins were evaluated by optimizing the fit of the model to the rat tumor data as described below. With 10 or more flux bins the optimal values of the adjustable parameters were stable (data not shown), indicating that 10 bins were sufficient to capture the effects of rat nasal anatomy on regional dosimetry. The use of 20 flux bins as described in this report was thus intended to be a conservative choice providing confidence that the minimum number of bins needed to describe regional variation in dosimetry was less than the number used.


FIG. 1. Interrelationships of the major components of the dose-response model for formaldehyde-induced nasal squamous cell carcinoma (SCC) in the F344 rat.

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Modes of Action Linking Regional Dosimetry with Tumor Response

Average division rate constant for cells in the six sites (1/h)

Formaldehyde (ppm)

Average flux (pmol/mm 2/h) a

Based on raw labeling index data

Based on hockey stick model for labeling index

0 0.7 2.0 6.01 9.93 14.96 14.96

0.00 ⫻ 100 4.36 ⫻ 10 2 1.24 ⫻ 10 3 3.74 ⫻ 10 3 6.23 ⫻ 10 3 9.34 ⫻ 10 3 3.93 ⫻ 10 4b

3.39 ⫻ 10 –4 2.59 ⫻ 10 –4 2.41 ⫻ 10 –4 4.86 ⫻ 10 –4 1.62 ⫻ 10 –3 3.06 ⫻ 10 –3 4.35 ⫻ 10 –2c

2.79 ⫻ 10 –4 2.79 ⫻ 10 –4 2.79 ⫻ 10 –4 4.86 ⫻ 10 –4 1.62 ⫻ 10 –3 3.06 ⫻ 10 –3 4.35 ⫻ 10 –2c

a Average flux was sampled across six sites in rat nose (Monticello et al., 1991, 1996). b Highest flux for any site predicted by CFD model. c ␣ max, the division rate corresponding to highest flux.

Labeling index data are used for calculation of the division rate constants that describe the growth kinetics of cellular populations as described below. Calculation of a division rate constant from labeling index data requires an estimate of the length of the interval over which tissue is exposed to the labeling agent. Since this estimation is problematical for injection studies, the injection data were transformed to equivalent minipump data using a factor of 6.83, which was the ratio of minipump labeling index to injection labeling index for all of the control data. This ratio was interpreted as approximating the ratio of the durations of exposure to label for the minipump and injection studies. Monticello et al. (1991) measured ULLI at five sites (anterior lateral meatus [ALM], posterior lateral meatus [PLM], anterior mid-septum [AMS], posterior mid-septum [PMS], and medial maxilloturbinate [MMT]) while Monticello et al. (1996) measured ULLI at seven sites (ALM, PLM, AMS, PMS, MMT, anterior dorsal septum [ADS], and maxillary sinus [MS]). CFD predictions of site-specific flux were available for all sites except for the MS. It was therefore possible to develop a quantitative relationship between formaldehyde flux into the tissue and ULLI for six sites: the ALM, PLM, AMD, PMS, MMT, and ADS. Since the final goal of this work was to assess human cancer risk, the quantitative relationship between flux into tissue and ULLI was developed in a manner that would facilitate its use not only for the rat clonal growth model but also a human version of the model that will be described elsewhere. First, for a given exposure level, the relationship between duration of exposure and ULLI varied with time (Conolly et al., 2002). The largest values of the ULLI occurred during the first six weeks of exposure. Since it was not clear how the data on temporal variation in ULLI in the rat should be extrapolated to the human model, a time-weighted average ULLI was calculated for the entire 78 weeks of exposure for each site at which ULLI was measured. The calculation removed the explicit time-dependence of the data and provided a single ULLI value for each measured site and exposure concentration. Second, site-to-site differences in ULLI did not vary with predicted flux in a consistent manner (Conolly et al., 2002), possibly due to variability in the ULLI data. Sources of this variability include the squamous metaplasia that occurs in response to higher levels of formaldehyde exposure and which could change the tissue uptake of formaldehyde (Kimbell et al., 1997b) and factors that contribute to variability in the measurement of the ULLI. The CFD model was not capable of dynamic reconfiguration to describe development of squamous metaplasia. Misspecification of the CFD model in other respects is unlikely to have been the major reason for the lack of correlation between site-specific predictions of


DNA-protein cross-links. Formaldehyde is genotoxic and mutagenic (Heck et al., 1990) and formaldehyde inhalation leads to the formation of DPX in the nasal mucosa of rats. DPX data have been used as a measure of tissue dose in cancer risk assessments for formaldehyde (Hernandez et al., 1994; Starr, 1990). In the current model, however, DPX are interpreted as a promutagenic lesion, such that the probability of mutations that lead to tumor development is proportional to the DPX burden. A recent publication (Merk and Speit, 1998) found that DPX were not correlated with gene mutations in V79 cells at subcytotoxic doses. We nevertheless interpreted the DPX burden as a predictor of the probability of procarcinogenic mutation per cell division. Given the uncertainty about the role of DPX in mutation formation, the description of a mutagenic role for DPX in the current model can be interpreted as a surrogate for the actual but unknown pathway. Dose-response and time-course data on DPX concentrations in the nasal mucosa of F344 rats were collected by Casanova et al. (1994). These data were used for development of a computational model of DPX formation (Conolly et al., 2000). This model uses CFD model-generated predictions of flux into the tissue compartment as input, describes saturable metabolic clearance of formaldehyde in the tissue compartment, a first-order clearance pathway to account for the innate reactivity of formaldehyde, and a pseudo-first-order reaction of the tissue concentration of formaldehyde with DNA to produce DPX. Formaldehyde is metabolized primarily by formaldehyde dehydrogenase (FDH; Keller et al., 1990), which is a member of the aldehyde dehydrogenase (ADH) family (Duester et al., 1999). Since ADHs other than FDH may also metabolize formaldehyde (Duester et al., 1999), though to a lesser extent than FDH, the saturable pathway described in the DPX model should be thought of as representing the sum of the ADH activities for formaldehyde. First-order clearance of DPX is also described, since Casanova et al. (1994) showed that DPX do not accumulate with repeated daily exposures and Quievryn and Zhitkovich (2000) found that DPX are removed from human cell lines by a combination of enzymatic repair and spontaneous hydrolysis. The DPX model is low dose linear for DPX formation (since DNA reactivity is first-order and all clearance pathways in the model are effectively linear at low doses). At higher doses, such as those used in the rodent bioassays, DPX are predicted to increase in a greater-than-linear manner due to saturation of metabolic clearance. This nonlinear dose-response behavior is in accord with the DPX data of Casanova et al. (1994) and also with the tumor data (Kerns et al., 1983; Monticello et al., 1996; Appendix). The DPX model could have been used to calculate DPX estimates simultaneously with the calculation of tumor incidence. However, we calculated DPX values separately and provided tables of these precomputed values as inputs to the clonal growth model. This approach avoided the need for numerical integration to compute DPX values and provided a substantial increase in computational throughput. Cytotoxicity-regenerative cellular proliferation. The reactivity of formaldehyde leads, at sufficiently high doses, to frank cytolethality followed by regenerative cellular proliferation. The present model focuses on regenerative proliferation using the assumption that measured regenerative proliferation is a quantitatively accurate surrogate for the cytolethality of formaldehyde. The relationship between fluxes into tissue and cell division rate constants is defined by a data table (Table 1) without any attempt to describe the intervening mechanistic events. The rate of cell division is an important determinant of the behavior of clonal growth models (Gaylor and Zheng, 1996) and measurement of labeling index (LI) in rat nasal epithelium at multiple sites, time points and exposure levels is an outstanding feature of the formaldehyde bioassay described by Monticello et al. (1991, 1996). LI data, expressed as unit length labeling indices (ULLI), were collected at 1 day, 4 days, 9 days, and 6 weeks (Monticello et al., 1991) and 13, 26, 52, and 78 weeks (Monticello et al., 1996) in rats exposed to 0, 0.7, 2.0, 6.0, 10.0, or 15 ppm formaldehyde. ULLIs for exposure durations from 1 day through 6 weeks (Monticello et al., 1991) were measured by injecting BrdU while subsequent time points (Monticello et al., 1996) used osmotic minipumps implanted for 3 days.

TABLE 1 Formaldehyde Flux and Cell Division Rate Constants for Rats

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RAT TUMOR DOSE-RESPONSE OF FORMALDEHYDE flux and ULLI. The airflow predictions of a human nasal CFD model agreed with measurements in a human nasal mold (Subramaniam et al., 1998) and site-specific predictions of formaldehyde flux from air into tissue were shown in simulation studies to be consistent with site-specific respiratory mucosal DPX levels after subchronic formaldehyde inhalation in F344 rats and acute exposures of rhesus monkeys (Conolly et al., 2000). Consistent variation of ULLI-derived division rate constants (see below) with predicted flux was obtained, however, by averaging the ULLI and predicted flux across the six sites (Table 1).

␣⫽

1 䡠 ln 2t

冢冣 1

1⫺

LI f

for LI ⬍ f

(1)

where t is the interval over which the cells are exposed to label, LI is the fraction of cells labeled, and f is the fraction of cells having replicative potential (i.e., this calculation excludes terminally differentiated cells). The value of f for the respiratory and transitional epithelia lining the rat nose was estimated to be 0.819 using epithelial surface area data (Kimbell et al., 2001a) and cell distribution and number data reported by Mercer et al. (1994) for the trachea, assuming a comparable distribution in the mucous-lined epithelium in the nose. The impact on model behavior of using f ⫽ 0.819 rather than f ⫽ 1.0 was evaluated by comparing optimal fits to the tumor data (see below) using these alternative values. Shapes of LI exposure-response curves. When division rate constants derived from the ULLI data were plotted against formaldehyde concentration, a J-shaped exposure-response relationship was obtained (Table 1). The 95% confidence intervals on the means of the ULLI data at 0, 0.7, and 2 ppm included the overall mean for the combined data from these three groups. The J-shape in the data was thus interpreted as not being significantly different from a threshold model with the threshold set above 2 ppm. Since the tumor risk predicted by clonal growth models is sensitive to cell kinetics (Gaylor and Zheng, 1996; Lutz and Kopp-Schneider, 1999), we decided to develop alternative versions of the exposure-tumor response model. One of these used the raw, J-shaped data while the other used a hockey stick-shaped (threshold) transformation of the data, as described by Conolly et al. (2002). The two empirical functions thereby obtained, relating flux into tissue with division rate constants (Table 1), were used without further adjustment for simulations of rat tumor incidence. Linear interpolation was used to identify values of the division rate constant consistent with intermediate flux values, i.e., flux values not specifically listed in Table 1. Special case of division rate associated with largest CFD model-predicted flux. The range of fluxes predicted for the six sites in the rat nose where CRCP was measured (503– 824 pmol/mm 2-h-ppm) was smaller than the range predicted for the entire nasal epithelium for the rat (0 –2620 pmol/mm 2-hppm). Implementation of the clonal growth model thus required estimation of the division rate constant (␣ max) associated with a flux of 2260 pmol/mm 2-hppm. Plausible values of ␣ max from 1.0 ⫻ 10 –2 to 5.5 ⫻ 10 –2 h –1 were evaluated by maximizing the likelihood of the tumor data (see section on parameter estimation below). For both the J-and hockey stick-shaped index dose-re-

Formaldehyde concentration (ppm)

Monticello et al. (1996) Number SCC Number examined Additional animals Number SCC Number examined Total number of SCC Total number of animals examined

0.0

0.7

2.0

6.01

9.93

14.94

0 90

0 90

0 90

1 90

20 90

69 147

0 14 0 104

0 17 0 107

0 24 0 114

0 18 1 108

2 13 22 103

10 14 79 161

Note. Ninety-four rats that were part of the pathogenesis bioassay described by Monticello et al. (1996) were not examined for tumors at the time of that report. This table includes the previously unpublished tumor results for these 94 rats.

sponses the maximum likelihoods of the data were associated with an ␣ max value of 4.35 ⫻ 10 –2 (Table 1). The inverse of a division rate constant (h –1) provides an estimate of the cell cycle time (h). The inverse of the ␣ max estimate of 4.35 ⫻ 10 –2 h –1, which is 22.9 h, is similar to estimates of the cell cycle time that can be calculated from the literature. Evans and Shami (1989) reported that total times for transition through DNA synthesis, G2 and mitosis for respiratory tract basal cells and nonciliated columnar cells were 15.4 h (range 14.3–16.6 h) and 12.0 h (range 10.1–14.0 h), respectively. Hotchkiss et al. (1997) estimated that time for transition of these cell types though G0 is 12–20 h, with the lower end of this range appearing to be more realistic. These experimental data provide a range of complete cell cycle times for basal, nonciliated columnar and type II cells (i.e., progenitor cells) from 22 through about 36 h, with a preference for the lower end of this range. The range derived experimentally and the value obtained computationally are thus consistent with each other. Rat Nasal Squamous Cell Carcinoma Data The nasal squamous cell carcinoma (SCC) dose-response data reported by Kerns et al. (1983) and Monticello et al. (1996) for chronic formaldehyde inhalation were similar. We therefore combined the SCC data from the two studies for subsequent analyses. Monticello et al. (1996) described results from 597 rats exposed to formaldehyde. Tissues from an additional 94 rats from this study were available that had not been previously examined. These tissues were from the 12, 18, and 24-month time points and were distributed approximately evenly across the six exposure concentrations. The SCC data from these 94 rats (Table 2) were combined with the Kerns et al. and Monticello et al. SCC data (Appendix). A Kaplan-Meier adjustment was used to correct the calculation of the cumulative probability of tumor for intercurrent mortality (JMP, v.4, SAS, Cary, NC). No nasal SCC were seen in controls in either the Kerns et al. (1983) or Monticello (1990) bioassays. The NTP historical control database on squamous cell carcinoma in F344 rats listed 11 SCC in 3866 males and 4 in 3818 females (as of 1999 when our work was conducted). The archived slides for these 15 rats were examined (Dr. Kevin Morgan, personal communication) to determine the extent to which the 15 tumors might be secondary to dental or other problems and, therefore, not actually of nasal epithelial cell origin. Two of 11 male tumors were reclassified as being secondary to dental problems. The nasal epithelial origin of the 4 female tumors was confirmed. Because the data are from control animals, intercurrent mortality would not be expected to have occurred to any substantial extent. In addition, because of the large database,


Calculation of division rates from labeling index data. ULLI were translated into cell division rate constants for use in the clonal growth model. This first required that the ULLI data be transformed into more typically reported labeling indices (LI). Fortunately, Monticello et al. (1990) provide ample information for translation. Briefly, both the total number of cells and the number of labeled cells in a given length of basement membrane were reported by Monticello et al. (1990). It was thus possible to calculate ULLI and LI from the same data set. From a total of eight such comparisons, the average ratio of LI/ULLI was 0.60 (range 0.45– 0.71). This ratio was used to convert the much larger number of ULLI data points to LI values. The data transformed into LI were used to calculate division rate constants (␣) according to a modified form of the equation given by Moolgavkar and Luebeck (1992):

TABLE 2 Formaldehyde-Induced Nasal Squamous Cell Carcinoma in F344 Rats: Bioassay Described by Monticello et al. (1996)

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the loss of a small number of animals during their natural lifetime would not unduly affect the estimate. Consequently, the lifetime cumulative probability of spontaneous nasal SCC in F344 rats was estimated as 13/7684 ⫽ 1.69 ⫻ 10 –3 for combined females and males.

generation in flux bin i (␮ N,i, ␮ I,i, respectively) have a basal value independent of formaldehyde exposure (␮ basal) and a formaldehyde-dependent component:

␮ ⫽ ␮ basal ⫹ KMU 䡠 DPX i

(3)

Clonal Growth Model Model structure. The two-stage clonal growth model used for this analysis (Fig. 2) is identical in its biological structure to other two-stage models (also called MVK models) that have been described in recent years (Cohen and Ellwein, 1990; Moolgavkar and Knudsen, 1981; Moolgavkar and Venzon, 1979; Moolgavkar et al., 1988; Portier and Kopp-Schneider, 1991). The model describes populations of normal cells and of intermediate cells with one mutation. Mutations are specified as arising during the process of cell division, so that the mutation parameter (␮) is a probability, in particular, the probability of mutation per cell division. A tumor cell arises when an intermediate cell acquires a second mutation. Clinically observable tumors are assumed to arise by clonal expansion of this single progenitor. The time needed for this clonal expansion is incorporated into the model through use of a delay function where a clinically observable tumor (detected either microscopically or grossly) was described as appearing at the end of a fixed interval from the production of its progenitor cell. The parameters of the model and the sources of parameter values are provided in Table 3. Equations. The model was written in the simulation language ACSL (The AEgis Technologies Group, Huntsville, AL). A discrete time implementation was used, with the analytical expression for growth of cell populations used across time steps (⌬t) of 1 h. The Nelder-Mead algorithm as implemented in ACSL Math was used for parameter estimation. A copy of the computer code is available from R.B.C. ([email protected]). The total number of normal cells (N) as a function of age (t) (i.e., the number of N cells in all the flux bins combined) was assumed to be proportional to body weight:

N共t兲 ⫽ N adult

冉

BW共t兲 BW adult

冊

(2)

N adult is the total number of normal cells at risk in the adult, BW(t) is body weight at age t and BW adult is adult body weight. Gompertz curves fitted to time dependent body weight data for rats (Fig. 3) were used to define BW(t). The probabilities of mutation of normal and intermediate cells per cell

where ␮ denotes either ␮ N,i or ␮ I,i, KMU (mm 3/pmol) is a proportionality constant, and DPX i (pmol/mm 3) is the DNA-protein crosslink concentration in bin i. ␮ basal and KMU are fitted parameters as described below. The number of mutations (M) of normal cells in flux bin i occurring during a time step ⌬t is given by: M N,共t⫺⌬t,t兲,i ⫽ ␮ N,i 共t兲䡠 N共t兲 i 共e ␣ N,i共t兲䡠⌬t ⫺ 1兲

(4)

where ␮ N,i(t) is the probability of mutation per cell generation in bin i at age t, ␣ N,i(t) is the division rate constant (1/h) for normal cells in bin i at age t, and ⌬t is the time step. The change in the number of initiated (I) cells in bin i during a time step ⌬t is given by: I 共t⫺⌬t,t兲,i ⫽ I i 共t兲e ⌬t共multf i䡠 ␣ I,i共t兲⫺ ␤ I,i共t兲兲 ⫹ M N,共t⫺⌬t,t兲,i ⫺ C i

(5)

where ␣ I(t) and ␤ I(t) are the division and death rate constants (1/h) of initiated cells, multf i is a bin-specific factor that allows for a growth advantage or disadvantage of initiated cells relative to normal cells (see below), and C i is a stochastic correction that allows the model to describe the exact tumor incidence (Hoogenveen et al., 1999; Moolgavkar et al., 1988):

冢

C i ⫽ ⌬t 䡠 multf i 䡠 ␣ I,i 共t兲䡠 ␮ I,i 共t兲䡠 I i 共t兲 1 ⫹

⌬t 䡠 I i 共t兲䡠 multf i 䡠 ␣ I,i 共t兲

冘 T

i⫽0

M N,共t⫺⌬t,t兲,i

冣

(6)

where T is the sum of the intervals ⌬t. The flux bin-specific growth advantage parameter multf i consists of a basal component (multb) that is independent of formaldehyde exposure and a formaldehyde-dependent component (multfc):


FIG. 2. Two-stage clonal growth model. The biological structure depicted is the same as that for the “MVK” model.

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TABLE 3 Parameters of the Clonal Growth Model Parameter N I ␣N ␣I ␣ max

␤I multb multfc

␮N ␮I ␮ Nbasal

KMU D

Source

Number of normal cells at risk Number of intermediate cells (cells with one mutation) Division rate constant for N cells (1/h) Division rate constant for I cells (1/h) Division rate constant at site of maximum flux in the rat nose predicted by CFD model Death/differentiation rate constant for initiated cells (1/h) Defines a growth advantage for I cells in the absence of formaldehyde exposure Defines the effect of formaldehyde exposure on the growth advantage for I cells. Total probability of mutation per cell generation for N cells. Total probability of mutation per cell generation for I cells. Probability of mutation per cell generation for N cells in the absence of formaldehyde exposure Probability of mutation per cell generation for I cells in the absence of formaldehyde exposure Proportionality constant relating tissue concentration of DPX to ␮ N and ␮ I. Time delay required for a single cell with two mutations created by mutation of a precursor initiated cell to expand clonally into a clinically detectable tumor.

Stone et al. (1992); Mercer et al. (1994); Monticello et al. (1996); Equation 2 Equation 5 Calculated from ULLI data (Monticello et al., 1996) Set equal to ␣ N Estimated by maximum likelihood Set equal to ␣ I Estimated by maximum likelihood. Equation 7. Estimated by maximum likelihood. Equation 7. Sum of basal probability and probability due to formaldehyde. Equation 3. Sum of basal probability and probability due to formaldehyde. Equation 3. Estimated by maximum likelihood. Equation 3. Set equal to ␮ Nbasal. Equation 3. Estimated maximum likelihood. Equation 3. Estimated by maximum likelihood. Equation 9.

Note. See Figure 2.

multf i ⫽ multb ⫺ multfc 䡠 max共共 ␣ I,flux i ⫺ ␣ I,basal 兲, 0兲

(7)

The term max((␣ I,fluxi – ␣ I,basal),0) specifies the maximum of 0 and the difference between the division rate constant associated with the flux in bin i and its corresponding basal value. A negative value is otherwise possible since, for some of the cell replication data used with this expression, the values of the division rate constant in the presence of formaldehyde exposure are less than the control value (Table 2). The behavior of this expression is to progressively

decrease the growth advantage for intermediate cells from the basal value (multb) as the bin-specific flux increases. This decrease was necessary for fitting the model to the tumor data (see below). The need to decrease the growth advantage arises because multb is used as part of a product that also involves ␣ I (Equation 5). As division rates increase with increasing inhaled concentrations of formaldehyde (Table 1) the effect of multb on the I cell growth rate is multiplicative. With this mathematical implementation the concentration-dependent negative value found to be necessary for multfc indicates that the growth advantage for I cells does not increase multiplicatively with the I cell division rate. Both multb and multfc are fitted parameters as described below. The bin-specific mutation of initiated cells across a time step (M I, (t-⌬t, t)), is given by:

M I,共t⫺⌬t,t兲,i ⫽ mutator 䡠 ␮ I,i 共t兲䡠 I i 共t兲共e multf i䡠 ␣ I,i共t兲䡠⌬t ⫺ 1兲

(8)

where mutator is used to evaluate mutator phenotype behaviors (Jackson and Loeb, 1998) with the second mutation rate greater than the first. Unless specifically stated to be otherwise, the first and second mutation rates were set equal to each other (mutator ⫽ 1). When the possibility of a mutator phenotype was evaluated, mutator was set to 10. The cumulative probability of tumor at age T is calculated by summing the mutation of intermediate cells across all the flux bins:

binnum

P共T兲 ⫽ 1 ⫺ e 共⫺¥ i⫽1 FIG. 3. Lifetime body weight for the male F344 rat. Data points are from the Monticello et al. (1990) bioassay. The solid line depicts a Gompertz curve fit to the data using ACSL. The data above 0.3 kg were not used in fitting the Gompertz curve as this is thought to represent primarily an increase in body fat.

T ¥ t⫽0 M I,共t⫺D⫺⌬t,t⫺D兲,i 兲

(9)

where binnum is the total number of flux bins and D is a delay representing the time required for a single cell created by mutation of a precursor initiated cell to expand clonally into a clinically detectable tumor.


␮ Ibasal

Description and units

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Parameter Estimation Using Maximum Likelihood Likelihood methods were used to estimate the adjustable parameters of the rat clonal growth model (␣ max, ␮ basal, KMU, multb, multfc, and D). For a rat that did not develop a tumor (a survivor), the likelihood was inversely related to the number of I cell mutations (e –M), where M is the number of mutations. Two alternative expressions were evaluated for the rats that did develop tumors, depending on whether the tumors were considered fatal or incidental. For fatal tumors, the likelihood was defined by the ratio of the hazard (the rate at which I cells were mutating) to M. For incidental tumors, the likelihood was one minus the likelihood for a survivor. Log likelihoods (logli) rather than likelihoods were calculated for computational reasons (Equation 10). The logli for all rats were added to obtain the overall log likelihood (LLF). Larger values of the LLF indicate better fits to the data (in the current model this means smaller negative numbers, though no particular significance should be attributed to the sign of the number). Parameter estimation involved maximization of the LLF using the Nelder-Mead

冢

共survivor兲

M I,共T⫺D⫺⌬t,T⫺D兲,i

i⫽1

t⫽0

binnum

log

i⫽1

M I,共T⫺D⫺⌬t,T⫺D兲,i ⌬t

冊

binnum T

⫺

i⫽1

共fatal tumor兲

t⫽0

binnum

log共e ⫺¥ i⫽1


T ¥ t⫽0 M I,共T⫺D⫺⌬t,T⫺D兲,i

冘冘

⫺ 1兲

binnum T

⫺

i⫽1


共incidental tumor兲

t⫽0

冣

(10)

algorithm that is part of the optimization capability of ACSL. All the rats used in the Kerns et al. (1983) and Monticello et al. (1996) bioassays and in the NTP control F344 rat database (Appendix) were included in these calculations. When the number of parameters in alternative models differs, the likelihood ratio test (␹ 2 ⫽ –2LLF 0/LLF 1), where LLF 0 is the restricted model, i.e., the model with fewer parameters and LLF 1 is the unrestricted model, can be used to test the assumption that the models provide equally good descriptions of the data. Significance is achieved when the value of ␹ 2 is larger than a Chi-Square percentile with k degrees of freedom, where k is the difference in the number of parameters between the two models. This test was used to compare the LLF of models where KMU, the proportionality constant between DPX and the probability of mutation per cell generation, had zero and nonzero values. A 1-tailed test with 1 degree of freedom (i.e., ⫾ KMU), at the 0.05 level of significance was used. The likelihood ratio test was not applicable when alternative models had the same numbers of parameters. In these cases the parameterization providing the larger likelihood was preferred and no formal attempt was made to distinguish between models. Descriptions of the tumor data when LLFs differed by 5 or more units (e.g., –2131 vs. –2136) tended to be visually distinguishable.

RESULTS

Simulation of the F344 Rat SCC Data The SCC data from controls through the 15 ppm exposed group span fourorders of magnitude in age-dependent, KaplanMeier adjusted cumulative probability of tumor. Maximum likelihood estimation of the values of the six adjustable parameters (Table 4) provided visually acceptable fits to these prob-

Parameter

J-shaped ULLI

Hockey stick ULLI

LLF multb multfc ␮N KMU D ␣ max

–2131.5 1.072 2.583 1.352 ⫻ 10 –6 0a 6982 h 0.0435 h –1

–2133.1 1.070 2.515 1.472 ⫻ 10 –6 0a 7137 h 0.0435 h –1

Note. See Table 3 for parameter descriptions. a Values as great as 8.192 ⫻ 10 –7 did not make a significant difference in the LLF as evaluated using a likelihood ratio test.

abilities plotted in time-to-tumor form when the tumors were assumed to be fatal (Fig. 4). Fits that were visually somewhat better were obtained when the model was fit to data from a single bioassay (results not shown) rather than to the combined data as is shown in Figure 4. This result is presumably due to variability between the experiments, which were conducted about 10 years apart. The fits of the time-to-tumor data obtained with the J- and hockey stick-shaped CRCP models were not visually distinguishable from each other, though the Jshaped data provided the larger likelihood (i.e., a better fit to the data; Table 4). Likelihood calculations based on the assumption that the tumors were incidental did not provide good descriptions of the data. Simulations of the end-of-study dose response were also developed (Fig. 5). The main interest with these simulations was to examine model predictions of dose-response behavior for exposures below the concentrations tested in the bioassays (i.e., 0.7, 2, 6, 10, and 15 ppm). The alternative J- and hockey stick-shaped dose-response descriptions for CRCP generated qualitatively different low dose dose-responses. The J-shaped dose-response for CRCP produced a J-shaped dose-response for cumulative probability of tumor, with the predicted tumor risk at low levels of exposure below control (Fig. 5a). This result is interesting given that the low-dose-linear directly genotoxic mode of action was concurrently operative over this dose-range. Lutz and Kopp-Schneider (1999) showed exactly this behavior in a theoretical study of the properties of the two-stage clonal growth model, where a J-shaped dose-response for the cell division rate interacted with a low-doselinear dose-response for direct mutagenicity. The model-predicted dose-response using the hockey stickshaped dose-response for CRCP was monotonically increasing (Fig. 5b). For this latter case, no downward pressure on the probability of tumor is exerted by the low-dose dose-response for CRCP, allowing the low-dose-linear dose-response for mutagenicity to define the shape of the curve.


log l i ⫽

冘冘冉冘冘冘

binnum T

⫺

TABLE 4 Log Likelihood Function and Optimal Parameter Values for the Rat Clonal Growth Model


439

Parameter Estimation A grid search approach was used for parameter estimation, since this provides sensitivity analysis information and reduces the number of parameters that are varied simultaneously by the optimization algorithm. The values of KMU and ␣ max were used to specify points on a two-dimensional grid while ␮ N, multb and multfc and D were varied by the Nelder-Mead algorithm at each point (Fig. 6). Smooth surfaces and clear overall optima were obtained (Fig. 6; Table 4). The maximum likelihood increased with decreasing values of KMU and was maximal when KMU ⫽ 0. The likelihood was maximal with values of ␣ max at or near 4.35 ⫻ 10 –2. Mutator Phenotype The LLF was maximized with mutator ⫽ 10 in an attempt to approximate the model behavior expected if the first mutation created a promutagenic environment for subsequent mutations. The maximum LLF obtained with J-shaped CRCP and muta-

FIG. 5. Dose-response simulations. (A) Using J-shaped dose-response for CRCP. Note low dose behavior, from 0 to about 2 ppm, where the formaldehyde-exposed probability of tumor is predicted to be below the control level. Shift in control probability at 15 ppm is due to a later end-of-study than for the other concentrations. (B) Using hockey stick-shaped dose-response for CRCP. Low dose behavior is monotonically increasing. Other details as in (A).


FIG. 4. Optimal simulations of rodent tumor data based on the J-shaped dose-response for CRCP. Data are in time-to-tumor form as Kaplan-Meier-adjusted cumulative probability of tumor (Y axis). The maximum likelihood procedure used to estimate parameter values uses information on both the rats that developed nasal SCC, as shown in this plot, and the “survivor” rats that did not develop tumors. Plots for model with hockey stick-shaped dose-response for CRCP were similar.

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tor ⫽ 10 was –2133.1, which was smaller than the best LLF obtained with the first and second mutation rates set equal to each other (–2131.5). This result should not be overinterpreted. At most we can say that the result is consistent with the hypothesis that a mutator genotype is not part of the mechanism of formaldehyde carcinogenicity in F344 rats. This interpretation is, of course, dependent on the extent to which the two-stage clonal growth model is an accurate reflection of the actual mechanism of formaldehyde-induced rat nasal squamous cell carcinoma.

to overall model behavior and uncertainty analyses that identify an appropriate level of confidence in the model structure and parameterization. Uncertainty analyses may be either quantitative or qualitative. The hazard and dose-response characterizations used in the U.S. EPA’s draft Guidelines for Carcinogen Assessment (U.S. EPA, 1999) are good examples of qualitative uncertainty analyses. Sensitivity and qualitative uncertainty analyses are presented in the following.

Cells at Risk

The grid search-maximum likelihood method used for parameter identification provides information not only on the optimal values of parameters but also on the sensitivity of model behavior to changes in parameter values. Sensitivity information was obtained for KMU, the proportionality constant relating DPX concentration to the probability of mutation per cell generation, and the division rate constant associated with maximum flux into the rat nose (␣ max) (Fig. 6). For both the J- and hockey stick-shaped CRCP data, the maximum value of the LLF was obtained with KMU at or near 0. This result means that the optimal descriptions of the data obtained with the current model did not depend on a directly mutagenic effect of formaldehyde. Furthermore, the optimal configuration of the current model explains the tumor data in terms of (1) the basal probability of mutation per cell generation, (2) the effect of formaldehyde on the cell division rate, (3) a basal growth advantage for initiated cells, (4) a concentration-dependent inhibition by formaldehyde of the growth advantage and, (5) a time delay for appearance of clinically detectable tumors.

The sensitivity of risk predictions to the specification of the fraction of cells at risk was evaluated by maximizing the log likelihood of the data for versions of the rat clonal growth model having 81.9 or 100% of the cells at risk. The difference in cells at risk did not affect the maximum value of the log likelihood (–2131.4 vs. –2131.5 for 100 and 81.9%, respectively). The key point here is that the values of the adjustable parameters of the model are constrained by the values of the parameters that are fixed. The more accurately the fixed parameters, such as fraction of cells at risk, are specified the more accurate will be the estimation of the adjustable parameters. DISCUSSION

In this work we sought to maximize the use of mechanistic information to describe the nasal SCC response to chronically inhaled formaldehyde in the F344 rat. The model we describe can be evaluated in a number of ways, including sensitivity analyses that characterize the contributions of key parameters

Sensitivity Analyses


FIG. 6. Contour plot of the maximum log likelihood using the J-shaped dose-response for CRCP (Table 4). The X axis, ␣ max, represents the cell division rate constant associated with the maximum CFD model-predicted flux in the rat nose. The Y axis, KMU, represents the proportionality between DPX and the probability of mutation. At each ␣ max, KMU pair the LLF was maximized by varying multb, multfc, ␮ Nbasal, and D. The log likelihood increases as KMU decreases and is maximal for values of ␣ max between 0.04 and 0.05. Although the likelihoods were smaller with the hockey stick-shaped dose-response for CRCP, the contour plot was similar.


to address this issue. Other aspects of uncertainty in rat nasal CFD dosimetry modeling are discussed by Kimbell et al. (2001a,b). DNA-protein cross-links. The rat DPX model is based on a relatively rich dose- and time-response data set. The DPX model provides good fits to these data (Conolly et al., 2000). Separate data sets for model validation are not available and model uncertainty could be reduced by the availability of such data. More information on repair rates of DPX would be helpful. The rate constant for loss of DPX is currently set based on the observation that DPX in the rat do not accumulate on a day-to-day basis with daily exposure. However, overall, the predictions of DPX concentrations by the rat model can be viewed with a good deal of confidence. More information is needed on the role of DPX in mutagenicity. Conolly et al. (2000) provide a more extensive discussion of uncertainties associated with the DPX modeling. Cytotoxicity-regenerative cellular replication. Experimental work that clarifies whether or not the J-shape for CRCP is real would reduce uncertainty of this assessment. We would also like to know about hourly variation in rates of regenerative cellular proliferation in rats as a function of formaldehyde exposure level and exposure scenario. For example, does the cell division rate vary between a 6 h/day, 5 day/week exposure and continuous exposure to the same level of formaldehyde? Data that answers this question would reduce the uncertainty of the current clonal growth model since we assume a constant rate of cell division for a given level of formaldehyde exposure (Fig. 7). Clonal growth model. Compelling evidence from histopathological, epidemiological, and molecular biological studies indicates that malignant transformation is the end result of an accumulation of alterations in the cellular genome and

Uncertainty Analyses Uncertainties in the clonal growth model can best be evaluated by considering separately issues related to dosimetry and to tissue response. Dosimetry. High-resolution regional dosimetry information is supplied by the CFD model, which represents the state-of-the-art for describing the regional flux of formaldehyde in the rat respiratory tract. Modeling of steady state inspiratory flow with the CFD models, rather than of the breathing cycle, is a source of uncertainty. Future work on breathing cycle simulations using the CFD models is expected

FIG. 7. Predicted variation in DPX and cell replication during two weeks of simulated exposure to formaldehyde for 8 h/day, five days/week. DPX varies on an hour-by-hour basis while the rate of cell replication switches from it basal value to the value associated with formaldehyde exposure and is constant at its new value until exposure ends.


The optimal values of D, 6982 h (41.5 weeks) and 7137 h (42.5 weeks), for J- and hockey stick-shaped CRCP, respectively, are large fractions of the typical 2–2.5 year lifetime of a rat. In the absence of data on tumor growth rates, there was no basis for using anything other than the optimal values. The possibility that the actual number of stages in the development of nasal SCC in the F344 rat is greater than 2 is a potential explanation for this large value of D. The curvature (concavity) of the relationship between duration of exposure and cumulative probability of tumor increases with the number of stages. A large value for D in a two-stage model could be an indication that the actual number of stages in SCC development is greater than 2. The delay associated with a model of three or more stages would be correspondingly smaller, because increasing the number of stages in the model increases number of mutations required for tumor development and thereby tends, other things being equal, to increase the time required for tumor development. The optimal value of ␣ max was 0.0435 for both the J- and hockey stick-shaped CRCP. The theoretical maximum cell division rate constant, based on an estimate of the cell cycle time of 23 h, is 0.0435. Thus the clonal growth model predicts that the cell division rate at the site of highest CFD-predicted flux is at or close to its maximum value. This is a reasonable prediction, given the dramatic cytotoxicity seen at 10 and 15 ppm formaldehyde. The J-shaped ULLI data set provided a better fit to the tumor data than did the hockey stick-shaped ULLI. It is tempting to interpret this result as indicating the biological reality of the J-shape. Heck and Casanova (1999) presented a theoretical argument that DPX act as roadblocks to replication complexes during replicative synthesis of DNA, leading to an overall reduction in the rate of replicative synthesis and of cell replication. Whether or not this effect could be sufficient to account for the measured J-shape is not clear, however. We did conduct an “in silico” experiment where the CRCP dose-response was described initially as hockey stick-shaped and then allowed to vary as part of a maximum likelihood optimization. The maximum likelihood was associated with a J-shaped curve for CRCP with division rate constants similar to the values measured experimentally.

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clonal growth model. Curvature is also strongly affected by parameters such as multb and multfc, that define the growth advantage of intermediate (I) cells, and by the time delay D. End-of-study probability of tumor, on the other hand, is a single data point that can be reached by many different timeto-tumor behaviors. Finally, it is worth noting that the more rigorous exercise of modeling time-to-tumor data was only possible because such data were available from the bioassays described by Kerns et al. (1983) and Monticello et al. (1996). Experimental designs that evaluate both dose-response and time-course behaviors provide much stronger support for development of biologically motivated quantitative models than do simpler designs. A data-intensive description of the relationship between formaldehyde exposure and development of nasal SCC in the F344 rat was developed. Regional dosimetry was described by an anatomically realistic, three-dimensional CFD model of the rat nasal airways. Two modes of action, mutagenicity mediated through DPX, and cytolethality-regenerative cellular proliferation, linked CFD model predictions with the parameters of a two-stage clonal growth model. Alternative descriptions of the dose-response for CRCP led to qualitatively different predictions of the low dose dose-response for probability of tumor. J-shaped CRCP, based on the raw data, provided a J-shaped tumor dose-response while a hockey stick-shaped transformation of the raw CRCP data provided a monotonically increasing tumor dose-response. When these results are evaluated in light of the modeling and database uncertainties discussed above, particularly the specification of the clonal growth model and the dose-response data for CRCP, this work provides suggestive but not definitive evidence for (1) a J-shaped dose-response for formaldehyde-mediated nasal SCC in the F344 rat and (2) little or no contribution of a directly mutagenic effect of formaldehyde to this response.


that the process of accumulating these alterations is profoundly affected by changes in cell proliferation kinetics (Gaylor and Zheng, 1996; Lutz and Kopp-Schneider, 1999). The two-stage clonal expansion model is the simplest mathematical model of carcinogenesis to incorporate explicitly both genomic alterations and cell proliferation kinetics. However, Moolgavkar et al. (1999) have emphasized that the model should not be interpreted to mean that carcinogenesis results from two ratelimiting mutations. Indeed, for most cancers, the number of rate-limiting mutations is not known. Rather, the model can be interpreted within the framework of the initiation-promotionprogression paradigm of chemical carcinogenesis. Initiation, which typically confers a growth advantage, is a rare event that may involve one or more mutations. Promotion consists of the clonal expansion of these initiated cells. Finally, one of the initiated cells may be converted into a malignant cell. This step may also involve more than a single mutation. The two-stage clonal expansion model is thus best thought of as a biologically motivated model, as opposed to a mechanistic model of cancer. Use of this model does not avoid uncertainty about the actual mechanism, and we should realize that the structure and parameters of the model might not have a one-to-one correspondence with specific cellular or biochemical entities. Both time-to-tumor and dose-response simulations of the F344 rat nasal SCC data were developed. Accurate simulation of the time-to-tumor data was much the greater challenge of the two. Optimal simulation of the time-to-tumor data provided only a rough approximation of the control tumor data (Fig. 4), for example, while a visually accurate dose-response simulation was easy to achieve (Fig. 5). The time-to-tumor data is more difficult to fit because it is more sensitive to the model structure and parameter values than is the end-of-study probability of tumor. As noted above, the curvature of the time-totumor relationship is a function of the number of stages in the

443


APPENDIX TABLE 1 Tumor Data Weeks from start of exposure

Number of rats with tumor

Cumulative probability

N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A

1 1 1 1 1 1 1 1 1 1 1 1 1

0.0001 0.0003 0.0004 0.0005 0.0007 0.0008 0.0009 0.0010 0.0012 0.0013 0.0014 0.0016 0.0017

89.4 104.3

1 2

0.0056 0.0188

79.3 79.7 81.1 88.7 89.1 89.4 91.7 93.6 96.6 98.1 101.3 104.3

1 3 1 1 1 1 2 1 1 1 1 8

0.0192 0.0769 0.1000 0.1273 0.1546 0.1818 0.2383 0.2665 0.2958 0.3251 0.3573 0.6144

49.1 49.7 51.3 52.1 53.1 55.3 57.1 60.1 63.0 66.6 67.4 68.4 68.6 69.0 69.9 70.4 71.1 71.4 72.1 72.4 72.7 73.3 73.4 73.6 74.1 74.4 74.7 75.1 76.3 76.0 76.6 77.1

1 1 1 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 1 1 2 2 1 1 1 2 2 1 1 1

0.0031 0.0063 0.0094 0.0189 0.0296 0.0332 0.0367 0.0403 0.0439 0.0511 0.0547 0.0584 0.0620 0.0657 0.0694 0.0731 0.0768 0.0842 0.0916 0.0954 0.0991 0.1067 0.1142 0.1180 0.1217 0.1255 0.1330 0.1369 0.1483 0.1445 0.1521 0.1560

Weeks from start of exposure

Number of rats with tumor

Cumulative probability

1 1 15 2 2 1 1 1 1 3 1 1 2 2 2 1 1 5 2 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 2 1 1 1 1 1 3 27 1 1 1 2

0.1599 0.2185 0.2280 0.2375 0.2423 0.2471 0.2569 0.2618 0.2872 0.3233 0.2519 0.2719 0.2770 0.2973 0.3024 0.3181 0.3495 0.3600 0.3653 0.3705 0.3758 0.3810 0.3863 0.3917 0.3972 0.3972 0.4026 0.4081 0.4136 0.4192 0.4248 0.4303 0.4471 0.4527 0.4583 0.4639 0.4694 0.4750 0.4807 0.4864 0.4922 0.4982 0.5042 0.5162 0.5283 0.5101 0.5343 0.5404 0.5464 0.5585 0.5647 0.5710 0.5773 0.5837 0.5901 0.6096 0.7853 0.8121 0.8390 0.8658 0.9195

15 ppm (continued)

0 ppm

6 ppm

15 ppm


10 ppm

77.7 79.3 79.7 80.1 81.1 81.4 82.1 83.7 85.1 87.7 81.9 84.1 84.4 85.3 86.3 86.7 88.0 88.1 88.7 88.9 89.3 89.7 90.1 90.3 90.7 91.4 91.9 92.0 92.1 93.3 93.6 94.0 94.4 94.6 94.9 95.1 96.1 96.3 97.1 97.7 98.1 98.6 99.1 99.4 99.6 99.3 99.7 100.0 100.4 100.9 101.9 102.1 102.6 103.0 103.1 104.0 104.3 107.3 107.7 109.7 117.3

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APPENDIX TABLE 2 Survivor Data Group


Number of rats

0.1 0.6 1.6 5.6 11.7 17.4 26.0 35.3 38.4 52.1 59.4 67.4 73.0 75.7 77.1 79.7 81.1 81.9 82.4 84.6 86.9 87.3 88.6 88.7 89.0 89.1 89.7 89.9 90.4 92.3 92.6 94.1 96.7 97.0 97.6 98.1 100.0 100.3 100.4 102.1 102.3 102.7 103.0 104.0 104.3 104.4 110.0 113.4 114.9 117.0 117.3 118.0 120.1 125.4 127.9 128.4 130.1

6 6 6 6 6 1 26 1 1 33 1 1 1 1 1 50 2 1 1 1 2 1 2 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 2 1 1 1 122 7671 1 1 1 1 19 1 1 2 1 1 10

0.1 0.6 1.6 5.6

6 6 6 6

Controls (0 ppm)

Group


Number of rats

9.3 11.7 26.0 52.1 64.1 72.9 75.1 75.7 78.1 79.7 80.6 81.3 85.4 89.4 89.7 90.4 91.7 94.4 95.7 101.1 101.3 101.9 102.4 103.1 104.3

1 6 6 12 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1 1 1 1 1 2 27

0.1 0.6 1.6 5.6 11.7 26.0 52.1 62.1 67.4 68.4 68.9 74.4 77.3 79.7 81.0 82.0 83.1 84.3 85.0 85.3 86.7 86.9 89.4 89.7 90.0 90.9 91.3 91.7 92.0 92.1 93.7 95.0 96.4 98.0 98.1 98.7

12 6 6 6 6 26 32 1 1 1 1 1 1 51 1 1 1 2 2 1 1 1 1 1 1 1 1 1 1 2 1 1 2 1 1 1

0.7 ppm (continued)


0.7 ppm

2 ppm

445


APPENDIX TABLE 2—Continued Group


Number of rats

99.3 99.7 100.7 101.3 101.4 101.9 102.6 104.0 104.3 106.3 107.9 109.4 109.6 111.3 113.9 115.6 116.3 116.7 117.3 121.0 124.1 124.7 126.9 129.9 130.1

1 2 1 1 2 1 1 1 126 1 1 1 1 1 1 1 1 1 20 1 1 1 1 2 5

0.1 0.6 1.6 5.6 11.7 16.6 19.7 26.0 47.1 48.9 51.7 52.1 52.3 52.4 60.0 60.1 60.3 65.7 74.1 75.3 77.4 78.1 78.6 79.7 80.9 82.3 84.6 85.7 87.3 88.3 89.3 91.9 93.1 93.7 94.1 94.3 94.9 95.3

6 6 6 6 6 1 1 26 1 1 1 32 1 1 1 1 1 1 1 1 1 1 1 53 1 1 2 1 1 1 1 2 1 1 1 1 1 1

2 ppm (continued)

Group


Number of rats

6 ppm (continued) 2 1 1 1 1 1 2 1 1 1 1 1 1 3 110 1 1 2 2 19 2 1 1 1 1 8

0.1 0.6 1.6 5.6 11.7 26.0 43.6 52.1 56.4 66.1 66.6 71.7 79.7 80.6 82.4 83.4 84.3 86.3 87.1 88.1 89.7 95.9 98.1 99.6 104.3

6 6 6 6 6 6 1 10 1 1 1 1 7 1 1 1 1 1 1 1 1 1 1 1 12

0.1 0.6 0.9 1.6 5.6 11.7 26.0 31.4 35.9 36.1 39.3

6 6 1 6 6 6 29 1 1 1 1

10 ppm

15 ppm


6 ppm

96.3 97.3 97.7 98.3 99.4 99.7 100.1 100.7 101.3 101.7 103.0 103.1 103.3 103.9 104.3 106.9 110.6 110.9 117.0 117.3 119.9 120.6 121.0 127.1 128.6 130.1

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APPENDIX TABLE 2—Continued Group


Number of rats

39.6 39.7 43.1 45.7 50.6 51.7 52.1 55.9 61.9 66.6 67.9 68.3 68.4 68.6 70.3 70.9 71.3 72.1 72.9 73.1 73.3 75.1 75.9 76.0 76.9 78.0 79.4 79.7 81.7

1 1 1 1 1 1 34 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 36 1

15 ppm (continued)

Group


Number of rats

15 ppm (continued)

Thanks to Drs. Suresh Moolgavkar and Georg Luebeck for their help with maximum likelihood calculations, Dr. Kevin Morgan for his reading of the NTP archival material, Dr. Jeff Everitt for reading the additional material from the pathogenesis bioassay, and Ms. Betsy Gross for her competent and cheerful assistance with data retrieval. Dr. Mel Andersen and Ms. Annie Jarabek provided thought-provoking reviews of the manuscript.

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