Annals of Occupational Hygiene Advance Access originally published online on July 14, 2008
Annals of Occupational Hygiene 2008 52(6):481-495; doi:10.1093/annhyg/men038
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Sensitivity Analysis of Biologically Motivated Model for Formaldehyde-Induced Respiratory Cancer in Humans
1 ENVIRON International Corporation, 1900 North, 18th Street, Suite 804, Monroe, LA 71201, USA
2 National Center for Environmental Assessment, Office of Research and Development, US Environmental Protection Agency, Mail Code 8623D, 1200 Pennsylvania Avenue, NW, Washington, DC 20460, USA
* Author to whom correspondence should be addressed. Tel: +318-257-4051; fax: +318-257-3182; e-mail: kennycrump{at}email.com
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ABSTRACT |
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Conolly et al. (2003, 2004) developed biologically motivated models of formaldehyde carcinogenicity in F344 rats and humans based on a two-stage clonal expansion model of cancer. Based on the human model, Conolly et al. (2004) claimed that cancer risks associated with inhaled formaldehyde are deminimis at relevant human exposure levels. However, they did not conduct a sensitivity analysis to evaluate the robustness of this conclusion. Here, we present a limited sensitivity analysis of the formaldehyde human model. We show that 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 (UB) to human risk. No data went into the model on the effect of formaldehyde on the division rates and death rates of initiated cells. We show that slight numerical perturbations to the Conolly et al. assumptions regarding these rates can be made that are equally consistent with the underlying data used to construct the model, but produce estimates of human risk ranging anywhere from negative up to 10 000 times higher than those deemed by Conolly et al. to be ‘conservative’. Thus, we conclude that estimates of human risk by Conolly et al. (2004) are extremely sensitive to modeling assumptions. This calls into question the basis for the Conolly et al. claim of de minimis human risk and suggests caution in using the model to derive human exposure standards for formaldehyde.
Keywords: formaldehyde • nasal cancer • quantitative risk assessment • respiratory cancer • sensitivity analysis • two-stage clonal expansion model
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONSUPPLEMENTARY MATERIALFUNDINGACKNOWLEDGEMENTSREFERENCES |
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Inhaled formaldehyde induces squamous cell carcinomas (SCCs) in rat nasal tissue with a very steep dose response (Kerns et al., 1983; Monticello et al., 1996). The time-to-tumor data from these studies and results from a number of other investigations (Casanova et al., 1991; Monticello et al., 1991; Casanova et al., 1994; Subramaniam et al., 1998; Conolly et al., 2000; Kimbell et al., 2001a,b; Overton et al., 2001) were used to develop biologically motivated models for formaldehyde carcinogenicity in F344 rats (Conolly et al., 2003) and humans (Conolly et al., 2004). These models are based on a two-stage clonal expansion model of cancer (Moolgavkar and Venzon, 1979; Moolgavkar and Knudson, 1981; Moolgavkar et al., 1988).
The formaldehyde rat model accounts for two modes of action that may be relevant to formaldehyde carcinogenicity. First, the model incorporates an indirect mode of action in which the regenerative cell proliferation in response to formaldehyde cytotoxicity increases the probability of errors in DNA replication. This mode of action is modeled using labeling data on normal cells in nasal mucosa of rats exposed to formaldehyde. Second, there is a possible direct mutagenic mode of action, based on information indicating that formaldehyde is mutagenic (Grafstrom et al., 1985; Heck et al., 1990; Speit and Merk, 2002) and which is modeled using rat data on formaldehyde production of DNA–protein crosslinks (DPXs) (Casanova et al., 1994; Conolly et al., 2000). An important and novel feature of the two-stage modeling in Conolly et al. (2003) is that DPXs and cell replication and death rates are linked to regional formaldehyde flux simulated using computational fluid dynamics (CFDs) modeling (Subramaniam et al., 1998).
No data are available on initiated cells, and consequently two critical assumptions had to be made: (i) The effect of formaldehyde upon the division rates for these cells is modeled assuming a two-parameter function that relates these unknown rates to those of normal cells. (ii) Death rates of initiated cells are assumed to equal the division rates of normal cells for all values of formaldehyde flux. The rat model involves six statistical parameters that are estimated by fitting the model to the rat formaldehyde bioassay data, plus data from several thousand control rats from bioassays conducted by the National Toxicology Program (NTP). The resulting model predicts the probability of a nasal SCC in the F344 rat as a function of age and exposure to formaldehyde.
The human model for formaldehyde carcinogenicity (Conolly et al., 2004) is conceptually very similar to the rat model; however, the model does not incorporate any data on human responses to formaldehyde exposure. Rates of cell division and cell death are, with a minor modification, assumed to be the same in humans as in rats. The concentration of formaldehyde-induced DPX in humans is estimated by ‘scaling up’ from values obtained from experiments in the F344 rat and rhesus monkey. The statistical parameters for the human model are either estimated by fitting the model to the human background data, assumed to have the same value as obtained in the rat model, or (in one case) fixed at a value suggested by the epidemiological literature.
Based upon weighting rat cell labeling data in Monticello et al. (1991, 1996) by exposure time and averaging over six nasal sites, the response of cell replication to formaldehyde is assumed to either have a ‘J shape’, in which at low exposures the replication rates are below background, or a ‘hockey stick’ shape, in which there is a threshold of exposure below which formaldehyde has no effect. The formaldehyde-induced probability of mutation per cell generation (added to the spontaneous mutational probability) in the Conolly et al. models was assumed to be proportional to the DPX concentration in the tissue. In the development of the human model, Conolly et al. (2004) made what they considered to be conservative estimates of human risk by use of the hockey stick model, use of overall respiratory tract cancer incidence data in humans and evaluating the model at the statistical UB of the proportionality parameter relating DPX to the probability of mutation. Based on the estimates of additional human risk obtained in this fashion, Conolly et al. (2004) concluded that ‘this analysis of the human implications of the rat SCC data indicates that (1) cancer risks associated with inhaled formaldehyde are de minimis (10–6 or less) at relevant human exposure levels and (2) protection from the non-cancer effects of formaldehyde should be sufficient to protect from its potential carcinogenic effects’. However, Conolly et al. did not conduct a sensitivity analysis of their model to determine the extent to which changes to their assumptions might also be consistent with their data but which produce higher estimates of human risk.
The results in Conolly et al. (2004) have been used by regulatory agencies to support exposure standards for formaldehyde (Health Canada, 2001; Liteplo and Meek, 2003; BfR (Germany), 2006; the German MAK Commission, 2006; USEPA, 2006a,b). The attractive features of this model include its incorporation of biological knowledge regarding the mechanisms of formaldehyde carcinogenicity and incorporation of a substantial amount of biological data in the quantitative modeling of these mechanisms. However, to more fully characterize the model and determine the appropriate use of modeling results for regulatory purposes, it is informative to conduct a sensitivity analysis of the model to determine how robust the model predictions are and to see if other biologically plausible assumptions might also be consistent with the available data but predict different estimates of human risk.
This paper presents the results of a limited sensitivity analysis of the Conolly et al. (2004) human model. This analysis is limited to evaluating the effect upon the human model of (i) the use of the alternative sets of control data for the rat bioassay data that were considered in the sensitivity analysis of the rat model (Subramaniam et al., 2007) and (ii) minor perturbations in model assumptions regarding the effect of formaldehyde upon the division rates of initiated cells. There are no data to even crudely inform the kinetics of initiated cells for use in the models, even in rats, and the two-stage clonal expansion model is very sensitive to initiated cell kinetics (Crump, 1994a,b; Gaylor and Zheng, 1996). We examine this sensitivity in the formaldehyde model while constraining variations in model assumptions to only those that do not meaningfully degrade the fit of the model to the underlying data. Our results are compared to those of Conolly et al. (2004) with respect to concordance with available data and predicted levels of additional human risk associated with formaldehyde exposure.
Our sensitivity analysis of the Conolly et al. model involves, as one would expect, making certain modifications to this model and presenting consequences of these modifications. However, we wish to make it abundantly clear that we are not proposing these modifications as alternatives to the Conolly et al. model for assessing human risk from exposure to formaldehyde. We present results from these modifications only to provide insights on the sensitivity of the Conolly et al. model to certain assumptions in the model.
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Description of the Conolly et al. (2003, 2004) formaldehyde models
The Conolly et al. (2004) human model for formaldehyde carcinogenicity is patterned closely after the rat model (Conolly et al., 2003) and uses much of the same data. We briefly describe these models below and refer the reader to earlier papers (Conolly et al., 2003, 2004; Subramaniam et al., 2007) and to supplementary material (available at Annals of Occupational Hygiene online) for further modeling and statistical details.
The two-stage clonal expansion model, upon which both the Conolly et al. (2003, 2004) formaldehyde models are based, is a stochastic Markov birth and death process that is defined in terms of the following parameters: N, number of normal cells that are eligible for progression to malignancy; 
N, division rate of normal cells (h–1); µN, rate at which an initiated cell is formed by mutation of a normal cell (per cell division of a normal cell); I, division rate of an initiated cell (h–1); βI, death rate of an initiated cell (h–1); µI, rate at which a malignant cell is formed by mutation of an initiated cell (per cell division of an initiated cell) and D, delay from occurrence of the first malignant cell to the resulting death of the host.
Some of these parameters in Conolly et al. (2003) incorporate data from auxiliary studies of cell replication (N, I and βI) or DPX formation (µN and µI). However, all of them except N, the number of normal cells, also involve statistical parameters that are estimated by fitting to the data on nasal SCCs from two large rat inhalation bioassays of formaldehyde (Kerns et al., 1983; Monticello et al., 1996). The parameters N, I, βI, µN and µI are characterized as a function of the local regional flux of formaldehyde into the rat nasal tissue using a CFD model (Kimbell et al., 2001a). Estimates of the division rate of normal cells (N) are obtained by applying a formula of Moolgavkar and Luebeck (1992) to the Monticello et al. (1991, 1996) cell labeling data in formaldehyde-exposed rats. Division rates for exposure concentrations not applied in the rat experiments are calculated by linear interpolation or extrapolation.
In the rat modeling, Conolly et al. (2003) consider two models for N, the division rate of normal cells (Fig. 1), based on data from cell labeling experiments Monticello et al. (1991, 1996). In the J-shape model, the division rate decreases below the basal value at low values of flux. The hockey stick model contains a threshold value of flux, below which formaldehyde has no effect upon cell division rates. The J shape represents the time-weighted average over nasal sites of division rate constants calculated from the cell labeling data. The fit of the hockey stick model to the cell replication data was not statistically significantly different from that of the J shape (Gaylor et al., 2004).
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No data are available on the division or death rates of initiated cells (i.e. on
I or βI). The flux-specific rate of division of initiated cells, I, is estimated from the rate for normal cells by the empirical formula,
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N for all values of formaldehyde flux. The dose responses for normal and initiated cell replication rates considered in Conolly et al. (2003) are shown in Fig. 1.
The mutation rates of normal cells, µN, and of initiated cells, µI, are assumed to be equal and linearly related to DPX, i.e.
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In the rat model (Conolly et al., 2003), both the basal mutation rate, µbasal, and the linear slope, KMU, are estimated from fitting to the rat data. The concentrations of DPX are estimated from applying a pharmacokinetic (PBPK) model to experimental rat data (Conolly et al., 2000).
The delay, D, from the occurrence of the first malignant cell until the resulting death of the animal is also an estimated parameter. In summary, the rat model involves six statistical parameters estimated from fitting to the rat bioassay data: max, multb, multfc, µbasal, DPX and D.
Our implementation of the Conolly et al. (2003) rat model (Subramaniam et al., 2007) corrected some errors in the Conolly et al. implementation and made some other fairly minor changes that we believed led to an improvement in the model. However, even with these corrections and changes, we were still able to reproduce the results of the Conolly et al. implementation in all major respects.
The Conolly et al. (2004) human model is conceptually very similar to the rat model, although rather than considering only nasal tumors, it is used to predict the risk of all human respiratory tumors. Local formaldehyde flux to respiratory tissue is estimated by a CFD model for humans (Kimbell et al., 2001a; Overton et al., 2001). The rat cell-labeling data are used in the same manner as in the rat model to estimate cell division rates in the human, except that a human estimate is used for the fraction of cells capable of dividing in the Moolgavkar and Luebeck (1992) formula. DPX in humans is estimated by scaling up from experiments in rats and monkeys.
The delay, D, is fixed at 3.5 years, based on a fit to the incidence of lung cancer in a cohort of British doctors (Doll and Peto, 1978). The two other parameters that affect the background rate of cancer (multb and µbasal) are estimated by fitting to US cancer incidence or mortality data. Since max, multfc and KMU do not affect the background cancer rate, they cannot be estimated from the human data. Therefore, in Conolly et al. (2003, 2004), max and multfc are assumed to have the same values in humans as in rats, and the human value for KMU is obtained by assuming that the ratio KPX 
KMU/µbasal is invariant across species. Thus,
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RESULTS |
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Our earlier evaluation of the rat model (Subramaniam et al., 2007) found that the ratio KMU of the DPX coefficient to the basal mutation rate was very sensitive to the choice of control data included in the model. Since this ratio is assumed to be the same in rats and humans (
equation (3)), we hypothesized that the choice of control data could also have a large impact upon estimates of human risk. In this section, we evaluate quantitatively the impact of different control groups upon estimates of additional human risk. No data are available on the rates of division and death of initiated cells. Conolly et al. (2003, 2004) assumed a mathematical expression (equation (1)) for the division rates of initiated cells that is based upon their estimate of the division rates of normal cells and showed that this expression, after estimating the two parameters (multb and multfc in equation (1)) by optimizing the fit to the rat tumor data, provided a reasonable fit to these data. However, they did not conduct a sensitivity analysis to determine whether other expressions would also fit the rat data but lead to different estimates of human risk. In this section, we modify their assumptions and consider the effect both upon the fit to the rat data and the predictions of additional human risk.
Fit of model to human data
Conolly et al. (2004) developed estimates of additional human risk of respiratory cancer from formaldehyde exposure in US males, using Surveillance Epidemiology and End Results (SEER) data, and separately in smokers and non-smokers. In the limited sensitivity analysis that is the focus of the present work, to illustrate the points we wish to make, we only consider risks to the general US population from constant lifetime exposure to various levels of formaldehyde under the Conolly et al. (2004) environmental scenario (8 h day–1 sleeping, 8 h day–1 sitting and 8 h day–1 engaged in light activity). Figure 2 shows our fit of the formaldehyde human model to the SEER data for incidence of respiratory cancer in males and females combined for 2000–2002 (SEER, 2005; see supplementary Table A1, available at Annals of Occupational Hygiene online). The model does not predict the downturn in human respiratory cancer past age 80, and, as we believe Conolly et al. (2004) also did, we only fit the model to the incidence data between the ages of 20 and 80. Fits based on the hockey stick and J-shape models were identical, and of the three estimated parameters (µbasal, multb and D), only the estimate of µbasal differed between the two models (Table 1).
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Whereas Conolly et al. (2004) used a fixed value for the delay, D, in our implementation of the human model, we estimated D by fitting the model to the SEER data (see supplementary material, available at Annals of Occupational Hygiene online) in the same way that D was estimated in the rat model by fitting to the rat tumor data. Our estimate of D = 21.8 years is considerably larger than the value of 3.5 years assumed by Conolly et al. (2004), which was based on a finding that, among a cohort of British doctors who began smoking at an average age of 19 years, the incidence of lung cancer was proportional to (age – 22.5) years raised to a power (Doll and Peto, 1978). In reviewing this approach, it seemed to us that there was no strong basis for assuming that the difference of 22.5 – 19 = 3.5 years represents the delay from the occurrence of the initial malignant cell to death. The Doll and Peto (1978) model is a statistical description of the lung cancer data, and the authors do not suggest such a biological interpretation for a 3.5 years delay. Our estimate of D in humans is much nearer to the same fraction of a human life span (22 years/75 years = 0.3) as the estimate of D in rats is to the fraction of a rat life span (300 days/730 days = 0.4) than is the 3.5 years delay assumed by Conolly et al. (2004) (3.5 years/75 years = 0.05). Estimating D made a small, but not dramatic, improvement in the fit to the SEER data. Likewise, estimating D made no meaningful difference upon estimates of human risk, and, as to be discussed later, our implementation was able to reproduce the Conolly et al. risk estimates very closely.
Effect of alternative background rates of nasal tumors in rats
In their implementation of the rat model, Conolly et al. (2003) augmented the rat formaldehyde bioassay data by incorporating data on background rates of nasal SSC in 7684 historical control rats from NTP bioassays. As discussed in our evaluation of the rat model (Subramaniam et al., 2007), these controls came from different rat colonies and from experiments conducted in different laboratories over a wide span of years, so it is clearly problematic to assume that background rates in these historical control animals are the same as those in the concurrent control group. There are considerable differences among the background tumor rates of SCC in all NTP controls (13/7684 = 0.0017), NTP inhalation controls (1/4551 = 0.0002) and concurrent controls (0/341 = 0.0) (Subramaniam et al., 2007). The rate in all NTP controls is significantly higher than that in NTP inhalation controls (P = 0.01, Fisher’s exact test). Subramaniam et al. (2007) showed these differences to significantly impact the calibration of the rat model. The biggest influence is on the estimated basal mutation rate in rats, µNbasal(rat), which, in turn, influences the estimated mutation effect in humans through equation (3).
To understand the effect of the decision by Conolly et al. (2004) to include data on NTP historical animals in their model, we conducted analyses that included (i) the same controls as used by Conolly et al. (2004) (i.e. concurrent controls plus all NTP controls), (ii) concurrent controls plus controls from NTP inhalation studies and (iii) only concurrent controls. Table 1 contains parameter estimates for both the animal and human models obtained from these analyses [The estimates in this table differ from those in Table 3 of Subramaniam et al. (2007) because the latter table was obtained using a different model for DPX formation than was used by Conolly et al. (2003, 2004).]. Each set of control data was applied with both the J-shape and hockey stick models for cell replication for a total of six analyses. The top portion of Table 1 contains the parameter estimates obtained from fitting the rat model, and the bottom portion contains the parameters that affect background tumor rates and which consequently were obtained from fitting the human model to the background human data. Parameters max, multfc and KMU were estimated in exactly the same manner as in Conolly et al. (2004) (see supplementary material, available at Annals of Occupational Hygiene online). Table 1 also contains 90% statistical confidence intervals for KPX. For comparison, parameter values from Conolly et al. (2003, 2004) (which were obtained using all NTP controls) are also listed. Except for minor differences, our results in Table 1 using all NTP controls are similar to those obtained by Conolly et al. (2003, 2004). The reasons for these minor differences have been addressed in our rat paper Subramaniam et al. (2007).
To determine how estimates of human risk obtained from our implementation of the human model compared to those in Conolly et al. (2004), we compared estimates of human risk from constant lifetime formaldehyde exposure derived using our implementation with all NTP controls (columns 1 and 5 of Table 1) to corresponding estimates in Conolly et al. (2004). This paper only presents estimates of additional human risk derived using UB estimates of KMU. In order to compare with these estimates, we replaced the MLE of KPX = KMU/µbasal by its 95% UB in computing our estimates. Throughout the range of formaldehyde exposures considered by Conolly et al. (from 0.001 to 1 p.p.m.), our estimates of additional risk differ from their estimates only by factors of 1.3 (J-shape model) and 1.7 (hockey stick model). These factors are quite small compared to the overall uncertainty in low-dose risk estimates in general and demonstrate that the differences in our implementation of the Conolly et al. (2004) model, as described earlier (see also supplementary material, available at Annals of Occupational Hygiene online), did not have important effects upon estimates of low-dose risk.
Unlike the analyses that include all NTP controls, Table 1 shows that MLE estimates of the ratio KPX = KMU/µbasal are statistically significantly greater than zero (and consequently so are estimates of the mutational coefficient, KMU) when either inhalation NTP controls or only concurrent controls are used. The 95% UBs for KPX = KMU/µbasal obtained using inhalation NTP controls are 20–30 times higher than the comparable bounds obtained using all NTP controls. Moreover, when only concurrent controls are used, this parameter cannot be bounded. (The UB is undefined, or infinite, due to the fact that the estimate of µbasal cannot be bounded away from zero.) Since the estimate of KMU in the human (the parameter that determines the mutational effect) is computed by multiplying the animal ratio, KPX = KMU/µbasal by the human µbasal, a large value for KPX produces a large mutational effect in the human model.
We now consider differences in additional human risk resulting from the use of different control groups for modeling the rat bioassay data. Figure 3 contains predictions resulting from the analyses shown in Table 1 of additional risk in humans from constant lifetime exposure to various levels of formaldehyde. The lowest dotted curve in this figure represents the highest estimates of human risk developed by Conolly et al. (2004), which resulted from use of the hockey stick model for cell division rates in conjunction with the statistical UB for KMU. As indicated in Fig. 3, corresponding estimates based on the J-shape model were all negative for exposures <1 p.p.m. Figure 3 also shows the MLE risks predicted by the six analyses shown in Table 1, along with (analogous to the risk estimates obtained by Conolly et al., 2004) the estimates of human risk obtained in each case by replacing the MLE of KPX = KMU/µbasal by the corresponding 95% UB. Note that the close correspondence of the two dotted curves confirms, at least for the hockey stick model for cell replication, our previous observation that our implementation essentially reproduced the risk estimates obtained by Conolly et al. (2004).
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Figure 3 also shows that the choice of controls to include in the rat model can make an enormous difference in estimates of additional human risk. For the J-shape model, both MLE estimates and those based upon the 95% UB on KPX = KMU/µbasal are negative for formaldehyde exposures <1 p.p.m., when either all NTP controls or only NTP inhalation controls are included. However, when only concurrent controls are used in the model, the MLE from the J-shape model is positive and is more than three orders of magnitude higher than the highest estimates obtained by Conolly et al. (2004), and estimates based upon the 95% UB on KPX are unboundedly large, as indicated by the block arrows at the top of Fig. 3.
Choice of control animals makes a similarly large difference in the estimates of additional risk obtained using the hockey stick model. Using all NTP controls, the estimates based on the MLE are zero for exposures less than 
0.5 p.p.m., but, as noted above, the estimates based on the 95% UB on KPX closely approximate the Conolly et al. (2004) UB estimates. However, if only inhalation controls are added, the MLE are about seven times larger than the Conolly et al. (2004) UB estimates, and the estimates based on the 95% UB on KPX are 50 times larger than the Conolly et al. (2004) estimates. If only concurrent controls are used, both the MLE estimates and those based on the 95% UB on KPX are unboundedly large.
Effect of alternative assumptions regarding the rate of replication of initiated cells
Conolly et al. (2004) estimated the replication rate of initiated cells, I, based on the rate in normal cells, N, using equation (1). The dose response of initiated cells with formaldehyde flux predicted by this formula is very similar to either the J shape or hockey stick shape assumed for normal cells (Fig. 1). In both cases, for high values of flux, I < N. Consequently, since βI = N at these flux levels, we also have I < βI.
Since no data or information are available on division rates of initiated cells to inform a likely relationship between normal and initiated cell division rates for cells in the respiratory epithelium, parameters in equation (1) were estimated based solely on fitting the tumor probability predicted by the rat model to the rat tumor data. It is therefore important to explore alternative assumptions about these rates. In addition to determining how estimates of additional risk are affected, each alternative should be evaluated with respect to biological plausibility and concordance of the modified tumor model with the underlying rat and human tumor data.
We considered two alternatives for each of the J-shape and hockey stick models. Figure 4 shows the hockey stick model for initiated cells in rats. In the first modification to the hockey stick model (Hockey Mod 1), rather than having a threshold at a flux of 1240 µm m–2 h–1, the division rate increases linearly with increasing flux until the graph intersects the original curve at 4500 µm m–2 h–1 where it then assumes the same value as in the original curve for larger values of flux. The second modification (Hockey Mod 2) is similar, except the modified curve intersects the original curve at a flux of 3000 µm m–2 h–1.
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Figure 5 shows the rat J-shape model for initiated cells. In the first modification to this dose response (J-shape Mod 1), rather than having a J shape, the division rate of initiated cells remains constant at the basal value until the original curve rises above the basal value and has the same value as the original curve for larger values of flux. In the second modification (J-shape Mod 2), the J shape is retained, but somewhat mitigated. In this modification, the division rate initially decreases in a linear manner similar to that of the original model, but with a less negative slope, until it intersects the original curve at a flux of 1240 µm m–2 h–1 where it then follows the original curve for higher values of flux. These modifications to the cell replication rates assumed by Conolly et al. (2004) for initiated cells are small compared to the variation in the measured values of cell replication rates in normal cells (Fig. 6).
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Each of the modified models in Figs 4 and 5 was applied in the version of the tumor models that employed all NTP controls. We continued to use all NTP historical controls since the purpose of this work is only a sensitivity analysis (as opposed to developing alternate credible risk estimates). Since none of these modifications affect the basal rate of cell division, they likewise have no effect upon the fit to the human background data. Table 2 shows the changes in the log-likelihoods for the rat tumor data resulting from these modifications. The largest change occurs with the Hockey Mod 2, and the reduction in the log-likelihood in this case is only 0.64, which indicates a very modest effect of the modification upon the fit of the model to the rat tumor data. This conclusion is borne out graphically in Fig. 7. This figure shows curves of the cumulative probability of a rat dying from a nasal SCC by a given age for bioassay exposure groups of 6, 10 and 15 p.p.m. These estimates are based upon the form of the formaldehyde model that uses all NTP controls and the hockey stick model. For comparison purposes, the corresponding Kaplan–Meier (non-parametric) estimates of the probability of death from a nasal tumor are also shown. What is not readily apparent from the graph is that two sets of probabilities are graphed: the original unmodified ones and the ones obtained using Hockey Mod 1. The changes in the tumor probability resulting from this modification are so slight that the two models cannot be readily distinguished in this graph. In fact, the largest change in the tumor probability resulting from this modification, for any dose group and any age up through 900 days is <0.002, a change so small that it would be impossible to detect, even in the largest bioassays ever conducted. The changes in tumor probability resulting from the remaining three modifications are even smaller (Table 2). These comparisons were made without reoptimizing the likelihood, which would have made the fit of modified models even better. Thus, these modifications to the models for the division rates of initiated cells caused an inconsequential change in the fit of the model-predicted tumor incidence to the animal tumor data.
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Figure 8 contains graphs of the additional human risks estimated by applying these modified models for
I using all NTP controls, compared to those obtained using the original Conolly et al. (2004) model. It should be noted that since KPX = KMU/µbasal is estimated as zero using either the J shape or hockey stick model (Table 1), no mutational component is included in these graphs. The additional risks predicted by the hockey stick model in Conolly et al. (2004) drop off rapidly with decreasing parts per million of formaldehyde down to a threshold of 0.5 p.p.m. and remain zero below this threshold. The additional risks predicted by the original J-shape model (not pictured) also drop off rapidly with decreasing parts per million and assume negative values below 1.5 p.p.m. However, each of the four modified models presents a very different picture. At low exposures, these risks are three to four orders of magnitude larger than the largest estimates obtained by Conolly et al. (2004). At 0.1 p.p.m., the exposure at which Conolly et al. (2004) claimed the risk was de minimis, the additional risks predicted by these models modified to evaluate model sensitivity are all >0.01. Since the additional risk from the two-stage model is a continuous function of the division rate of initiated cells, it is clear that by making suitable small perturbations to the these rates, one can obtain any additional risk ranging from negative values up to at least four orders of magnitude higher than the conservative estimates of Conolly et al. (2004), while fitting the underlying data equally as well as the original model.
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DISCUSSION |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONSUPPLEMENTARY MATERIALFUNDINGACKNOWLEDGEMENTSREFERENCES |
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This paper presents a limited sensitivity analysis of only two aspects of the formaldehyde model: (i) assumptions regarding the dose response for the division rate of initiated cells and (ii) assumptions regarding the incorporation of historical control data into the rodent model. This analysis shows that the estimates of additional human risk obtained from the formaldehyde model are highly sensitive to these assumptions. Other reasonable assumptions are also consistent with the available data, but lead to estimates of human risk that are far higher than those in Conolly et al. (2004). Consequently, the estimates of human risk obtained by Conolly et al. (2004) cannot be considered conservative.
Model estimates of low-dose risks invariably require assumptions about the shape of dose–response curves at low doses. Whereas purely statistical models make assumptions about the shape of the frank tumor response, models like the formaldehyde model incorporate assumptions regarding the dose response for upstream steps in the carcinogenic process. We performed sensitivity analyses to examine the range of risks predicted by models with assumptions different from those of Conolly et al. about these upstream steps, but which are also consistent with the data. To this end, we made minor modifications to the assumed division rates of initiated cells in Conolly et al. (2004) while keeping all other aspects of the model and input data unchanged (Figs 4 and 5) and considered the resulting change to estimates of additional human risk (Fig. 8). This work demonstrates that perturbing the dose response for I slightly without changing βI can result in a very large increase (by three to four orders of magnitude) in estimated additional human risk, while making essentially no difference in the fit to the available data (Table 2 and Fig. 7). In the case of the J-shape model for I, our sensitivity analyses indicate that it is not necessary to remove the J shape to produce these large increases in estimated additional human risk; keeping the J shape but simply mitigating it slightly is sufficient to produce positive estimates of additional risk that are >1000-fold higher than the Conolly et al. (2004) estimates (Fig. 5, J-shape Mod 2).
A crucial result in the Conolly et al. (2004) modeling was that the optimal value for KMU in equation (2) was zero, which implies no mutational effect of formaldehyde. As a consequence, the optimal value of additional risk at low exposures was negative for the J-shape model and zero for the hockey stick model. To obtain a conservative estimate of risk in the hockey stick model, Conolly et al. (2004) increased the value for KMU by an amount such that the fit to the tumor data was not changed significantly, thereby introducing a small linear formaldehyde-induced contribution to the mutational probability. The resulting additional human risk, although then positive, was concluded to be de minimis at environmental levels of human exposure (Conolly et al., 2004). However, this conclusion does not consider the potential effect of changes in other parameters or plausible variations in model specification, as were partially explored in the present sensitivity analyses. It is important to note that the large increases in risk described in the previous paragraph are from models in which it was assumed that formaldehyde has no mutational effect. Thus, even without invoking formaldehyde’s mutagenic action, a much higher low-dose risk than obtained by Conolly et al. (2004), and which is also consistent with the tumor data, cannot be ruled out.
In general, the rate of growth of clones of intermediate cells depends primarily upon I – βI, the difference in the birth rate and death rate of intermediate cells (Schulte-Hermann et al., 1999). This difference is an important determinant of risk as predicted by the two-stage model. There is some evidence that I and βI rise or fall concomitantly (Grasl-Kraupp et al., 1997; Schulte-Hermann et al., 1999; Grasl-Kraupp et al., 2000). Apart from this broad determination, even assuming that it is relevant for formaldehyde-exposed respiratory epithelial cells, there is no indication as to how tightly one might expect these rates to track each other. Furthermore, it appears that I – βI will likely have a strong temporal dependence, as suggested by the work of Grasl-Kraupp et al. (2000). The site and temporal variability in the measured labeling index in the formaldehyde rodent bioassays, and thus in the derived normal cell replication rates, was recognized to be large by Conolly et al. (2003). However, this variability was not characterized for input to their two-stage modeling and is therefore not expressed in (nor does it influence) the model-derived values of I. Thus, in summary, we have seen nothing in the literature, either generally or specifically for formaldehyde, to rule out the small increases in I – βI resulting from our modifications.
The increase in I – βI stemming from our modifications at low flux values are much smaller than the increase assumed in the Conolly et al. (2004) model at higher flux values. In the Conolly et al. (2004) hockey stick model, I – βI reaches a maximum of 5.0 x 10–4 h–1 at a flux of 17190 pmole mm–2-h in the human respiratory tract, and then decreases with increasing flux eventually becoming negative. By comparison, the largest difference in I – βI in the flux region where we modified the model is 2.9 x 10–4 h–1 for Hockey Mod 1 and 7.7 x 10–5 h–1 for Hockey Mod 2. Likewise, in the Conolly et al. (2004) J-shape model, I – βI reaches a maximum of 5.2 x 10–4 h–1, whereas, in the range where we modified I, the maximum of I – βI is only 1.2 x 10–4 h–1 for J-shape Mod 1 and 6.1 x 10–5 h–1 for J-shape Mod 2. Thus, while we do not see any compelling argument for assuming the values of I – βI resulting from our modifications that are implausibly large, if there were such an argument, it should apply with even greater force to the assumptions about I – βI in the original Conolly et al. (2004) model.
There are other biological considerations that motivate our exercise. The averaged cell replication rate constants as tabulated in Table 1 of Conolly et al. (2003) (for various exposure concentrations and corresponding average formaldehyde flux values in the F344 rat nose) demonstrate an increase over baseline values only at exposure concentrations of 6 p.p.m. and higher. Increased cell proliferation at these concentrations of formaldehyde, whether transient or sustained, have been associated in the literature with epithelial response to the cytotoxic properties of formaldehyde (Monticello et al., 1991, 1996; Monticello and Morgan, 1997; Conolly et al., 2002), and the labeling data are considered to show a lack of cytotoxicity and regenerative cell proliferation in the F344 rat at exposures of 2 p.p.m. and below (Conolly et al., 2002). In the Conolly et al. modeling, it is further assumed that the formaldehyde flux levels at which cell replication exceeds baseline rates remains essentially unchanged for initiated cells not only for the rodent but also when extrapolated to the human. These assumptions need to be viewed in the context of the uncertainty and variability in the data discussed further in Subramaniam et al. (2008). In addition, it may be noted that there are some limited data indicating that exposure to formaldehyde can result in increased cell replication at doses far below those that are considered to be cytotoxic. Tyihak et al. (2001) treated different human cell lines in culture to various doses (0.1–10 mM) of formaldehyde and found that the mitotic index increased at the lowest dose of 0.1 mM. These findings considered along with human population variability and susceptibility (for example, polymorphisms in alcohol dehydrogenase-3, Hedberg et al., 2001) indicate that it is necessary to consider the possibility of small increases in the human I over baseline levels at exposures well below those at which cytotoxicity-driven proliferative response is thought to occur. This intent is represented by the increments in Hockey Mod1 and Mod2. Although we replaced the threshold model for initiated cells in Conolly et al. with a model that had a small positive slope at the origin, we could also have shifted the resulting curves ‘Mod1’ and ‘Mod2’ slightly to the right along the flux axis, so as to introduce a threshold for I and without materially affecting the risk estimates resulting from these modified curves. Thus, the assumption of a linear no-threshold response is not an essential feature of our modifications to the hockey stick model, as clearly threshold models exist that would produce essentially the same effect.
Heck and Casanova (1999) have provided arguments to explain that the formation of DPX by formaldehyde leads to inhibition of cell replication. As per this effect, the formation of DPX is thought to activate a checkpoint in the cell cycle so as to enable DNA repair; i.e. if this effect alone is considered, normal cell replication rate of the exposed cells would be less than the baseline rate. However, this hypothesis was posed for normal cells. If an initiated cell is created by a specific mutation that impairs this cell cycle control, the effect would be to mitigate the DPX-induced inhibition in cell replication, either partially or fully, depending on the extent to which the cell cycle control has been disrupted. In the absence of data on initiated cells, the above argument provides biological motivation to the modification we applied to the J-shape model for cell division.
Although there are no data on division rates of initiated cells upon which to evaluate the modifications we made to these rates, we can gain some perspective by comparing them to the variability in the division rates obtained from the data on normal cells used to construct the formaldehyde model. As shown in Fig. 6 and discussed further in Subramaniam et al. (2008, Fig. 3), these data show roughly an order of magnitude variation in the cell replication rate at a given flux. As part of a statistical evaluation of these data, we calculated a standard deviation for the log-transforms of individual measurements of division rates of normal cells of 0.32. By comparison, the maximum change in the log-transform division rate of initiated cells resulting from hockey stick Mod 2 was only 0.20, and the average change would be considerably smaller. Thus, although there are no data for initiated cells, we can say that the modifications we introduce for initiated cells are extremely small in comparison to the dispersion in the data for normal cells.
Thus, the previous paragraphs suggest that the changes made in our analysis to the assumption by Conolly et al. regarding the dose response for the division rate of initiated cells are not implausible. Nevertheless, given that these changes are very small, and that there are no data on initiated cells, we believe that before the Conolly et al. model is accepted as conservative, the onus should be on showing that these small differences cannot occur.
Another major assumption in the formaldehyde modeling (and which was retained in our modifications) is that initiated cell death rates (βI) are equal to the replication rates of normal cells (N) for all values of flux. To evaluate the effect of this assumption, we also made small changes to the death rates of initiated cells and obtained similarly large values for estimates of additional human risk at low exposures (results not shown). Obtaining reliable data on cell death rates in the nasal epithelium appears to be an unusually difficult proposition (Monticello and Morgan, 1997; Hester et al., 2003).
We want to make it abundantly clear that we are not claiming that the particular modifications we made to the Conolly et al. (2004) model resulted in more reliable or plausible models. Rather, we simply used these modifications to demonstrate that predictions of additional human risk from the Conolly et al. (2004) model are highly sensitive to small changes in model formulation that cannot be ruled out on either biological grounds or on the basis of concordance with the available data. Our analysis indicates that there is a continuum of alternative values of I that fit the available data and predict a corresponding continuum of low-dose additional human risks that range from negative values up through several orders of magnitude greater than any of the values estimated by Conolly et al. (2004). In other words, by making appropriate small changes in the assumptions by Conolly et al. regarding I (which are both consistent with biological knowledge and with the underlying data), one can get any additional risk one wants at low exposures, ranging from negative up to several orders of magnitude higher than the ‘conservative estimates’ obtained by Conolly et al. We have not examined whether the upper end of the range of additional risk is consistent with existing human epidemiology because that is not germane to the point we are making. Even if an inconsistency were found, that should only increase concern about the reliability of the CIIT model for assessing human risk. This extreme sensitivity of model results to small changes in I suggests that experimental data on initiated cells sufficiently accurate to restrict the human cancer risk projections from the two-stage formaldehyde model in a useful way are unlikely to be obtainable.
Our sensitivity analysis also evaluated the effect that use of different control groups for the formaldehyde animal bioassay data has on estimates of additional human risk. Since the incidence of nasal SCC in NTP inhalation controls is significantly different (P = 0.01) from that in the controls from all routes of exposure, we see no basis for preferring controls from studies that used all routes of exposure over controls from only inhalation studies. Replacing all NTP controls with NTP inhalation controls caused the additional human risk resulting from the UB estimate of the mutational effect to increase by 50-fold (Fig. 3) over the UB obtained by Conolly et al. (2004).
Genetic and other time-related variation can lead to differences in tumor and survival rates across studies (Rao et al., 1987; Haseman, 1992; Peddada et al. 2007). Studies also differ with regard to animal husbandry and pathology procedures. Given these differences, the inclusion of any type of historical controls is problematic and is thought to have limited value if these factors are not controlled for (Haseman, 1992).
However, if only concurrent controls are used, the formaldehyde human model does not place any UB on the risk. This is because the µbasal value in rats cannot be bounded away from zero, which allows the mutational component in humans to be unboundedly large. Although it can be argued that the rate of SCC among the controls in the rat bioassay is probably not zero, it is also problematic to assume that this rate can be adequately represented by the background rate in NTP historical controls or even in NTP inhalation historical controls. If only inhalation controls from the NTP database are included, this leads to the rather bizarre situation in which, despite all of the biological data that went into the formaldehyde model, the only piece of data that is keeping the human risk estimates bounded is a single tumor found among several thousand rats from NTP bioassays. This tumor came from the very first NTP inhalation study, dated in 1976, and the animals in this study were from Hazelton Laboratories, whereas the concurrent animals were all from Charles River Laboratories. Thus, it is problematic to assume that this tumor is representative of the risk of SCC in the formaldehyde bioassays.
The sensitivity analysis of the Conolly et al. (2003, 2004) formaldehyde model presented herein is limited, both in terms of the issues addressed and in terms of the range of alternatives investigated for those issues. A number of additional issues have been raised in this work that could be discussed, particularly concerning the validity of the data on the division rates of normal cells and how these data were incorporated into the model (Subramaniam et al., 2008).
The human model for formaldehyde (Conolly et al., 2004) has already been used by regulatory agencies to various degrees in supporting human health risk assessments or exposure standards for formaldehyde (Health Canada, 2001; Liteplo and Meek, 2003; BfR (Germany), 2006; the German MAK Commission, 2006; USEPA, 2006a,b). However, the analysis presented herein shows that the Conolly et al. model is highly sensitive to uncertain model assumptions, and other reasonable assumptions are equally compatible with the data but lead to much higher risks. These risks can be considerably higher than what would be obtained using standard statistical modeling approaches (USEPA, 2005). Thus, the formaldehyde human model cannot reasonably be used to narrow the range of low-dose human risk over that predicted by the standard regulatory approach.
The uncertainty in the Conolly et al. (2003, 2004) models is particularly acute because there are no data on initiated cells. However, it appears to us that any attempt to quantify low-dose human risk using animal data on intermediate steps in the carcinogenic process would be similarly uncertain. Nonetheless, the formaldehyde model is a very useful demonstration of a conceptual framework for integrating hybrid models for predicting regional toxicokinetics with toxicodynamic data. Such models can be valuable tools for hypotheses generation and testing and therefore can be important components in a risk assessment process that places importance on a chemical’s mode of action. Our analysis shows that uncertainty and sensitivity analyses are essential tools in evaluating such models.
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Supplementary materials and Table A1 can be found at http://annhyg.oxfordjournals.org/
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US Environmental Protection Agency (IAG No. DW89939822-01-0) to K.S.C. and C.V.L. through its Office of Research and Development, under assistance agreement to the Department of Energy and via a contract with the Oak Ridge Associated Universities/Oak Ridge Institute for Science and Education by subcontract to ENVIRON Corporation.
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We wish to express to the Hamner Institutes for Health Sciences (formerly CIIT) and to Dr Rory Conolly, our profound gratitude for providing the data needed for this work. We are indebted to Paul White, Danielle DeVoney, Chad Thompson and Paul Schlosser for useful discussions and Peter Preuss, John Vandenberg and David Bussard for their encouragement of this work. We thank Tammie Covington for her valuable assistance.
Disclaimer—The views expressed in this article are solely those of the authors and do not necessarily reflect the views or policies of the US Environmental Protection Agency or the views of those we acknowledge.
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3 Present address: Department of Mathematics and Statistics, Louisiana Tech University, Railroad Avenue, George T. Madison Hall, Room 330, PO Box 10348, Ruston, LA 71272-0046, USA.
The original version was incorrect. A few errors had not been corrected.
Received April 2, 2008; in final form May 30, 2008
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