A Comparison of Ratio Distributions Based on the NOAEL and the Benchmark Approach for Subchronic-to-Chronic Extrapolation
http://www.100md.com
《毒物学科学杂志》
Institute for Risk Assessment Sciences (IRAS), P.O. Box 80176, 3508 TD Utrecht, The Netherlands
National Institute of Public Health and the Environment (RIVM), P.O. Box 1, 3720 BA Bilthoven, The Netherlands
ABSTRACT
One approach to derive a data-based assessment factor (AF) for subchronic-to-chronic extrapolation is to determine ratios between the NOAELsubchronic and NOAELchronic for the same compounds. Instead of using ratios of NOAELs, the distribution can also be estimated by ratios of subchronic and chronic Benchmark Doses (or Critical Effect Doses, CEDs, for continuous data). In this study 314 dose-response datasets on body weights and liver weights of mice and rats were selected providing dose-response information after both subchronic and chronic exposure. NOAEL ratios could be derived in only 68 of these datasets, while CED ratios could be derived in 189 datasets. When only the (53) datasets suitable for both approaches were evaluated the variation of the CED ratio distribution (GSD [geometric standard deviation]: 2.9) was smaller than the one of the NOAEL ratio distribution (GSD: 3.3). After correcting for the estimation error of the individual CED ratios the GSD of the CED distribution decreased to 2.3. The geometric means (GMs) of the NOAEL and CED distributions were similar (1.2 and 1.6, respectively). Comparing the NOAEL distribution based on all 68 datasets suitable for deriving NOAEL ratios with the CED distribution based on the 189 ratios suitable for deriving CED ratios resulted in similar GMs (1.5 and 1.7, respectively), but the GSDs differed considerably (5.3 and 2.3 respectively). It is concluded that usage of the CED approach results in less wide distributions. Furthermore, a larger fraction of available datasets is useful to inform the ratio distribution. This results in more accurate, and less conservative distributions of AFs in general compared to the distributions based on NOAEL ratios that have been proposed so far.
Key Words: benchmark dose; NOAEL; critical effect dose; subchronic-to-chronic extrapolation; assessment factor; extrapolation factor.
INTRODUCTION
Regulatory agencies establish health-based acceptable exposure limits, like the Reference Dose and Acceptable Daily Intake, to protect the human population from adverse health effects in a situation of life-long exposure to non-genotoxic agents. Therefore, these limits are preferably based on chronic toxicity studies. If available, a No-Observed-Adverse-Effect-Level (NOAELchronic) is derived from these studies. The NOAELchronic is divided by assessment factors (AFs, also called uncertainty factors) accounting for interspecies and intraspecies variation to derive an exposure limit. If toxicity data after chronic exposure are not available subchronic toxicity data must be used to estimate a NOAELchronic.
A possible approach of deriving a NOAELchronic from a NOAELsubchronic is to apply another AF to the subchronic NOAEL. By default, a factor for subchronic to chronic extrapolation (AFsubchronic) of 10 is typically applied (Vermeire et al., 1999). Attempts have been made to find a data-based value for the AFsubchronic by taking a certain percentile (mostly the 95th percentile, P95) from the distribution of NOAELsubchronic/NOAELchronic ratios established for a number of compounds (McNamara, 1976; Pieters et al., 1998; Rulis and Hattan, 1985).
In the standard procedure for deriving limit values, various AFs are multiplied to obtain an overall AF. However, multiplication of point values of AFs implies a piling-up of worst-case assumptions. Therefore, the more extrapolation steps are taken into account, the higher the level of conservatism. The piling-up of worst-case assumptions can be avoided by using a probabilistic approach. Slob and Pieters (1998) introduced the term extrapolation factor (EF), which refers to the ratio of the "true" but unknown No-Adverse-Effect-Levels (NAELs) in a (in this case) subchronic and chronic study. The EF varies between different chemicals, resulting in an EF distribution where the AF is a certain chosen point (e.g., P95) of this distribution.
In this method each EF is considered uncertain and characterized as a random variable with a distribution. Multiplying all EF distributions yields a distribution for the overall EF (Baird et al., 1996; Slob and Pieters, 1998).
To obtain an EF distribution NOAELs could be used as a measure for the "true" NAEL. However, as various authors have already stated, there are some problems associated with the approach of deriving NOAELs (Brand et al., 1999; Crump, 1984; Edler et al., 2002; Kalberlah and Schneider, 1998; Kramer et al., 1996; Slob, 2002; Slob and Pieters, 1998; Vermeire et al., 1999). An important argument against the approach is the fact that a NOAEL is only an estimate of the "true" NAEL in the animal, and depends heavily on the particular experimental conditions (including sample size, dose spacing, scatter in the data). Thus, a NOAEL ratio can easily deviate from unity, even if the dose-response relationships related to both situations (associated with numerator and denominator) were in reality identical. The NOAELs are subject to substantial errors, and the error in the NOAEL ratios is even larger. When the error in the NOAEL is ignored, uncertainty distributions that are estimated from ratios of NOAELs will tend to be unnecessarily wide, i.e., the percentile (P95) of the distribution of NOAEL ratios overestimates the percentile of the "true" NAEL ratios (Slob, 2002).
In this article the benchmark approach is used to estimate Critical Effect Doses (CEDs) (Slob, 2002). The CED is defined as the dose associated with a certain "critical" effect size (CES) in continuous endpoints, e.g., 5% change in organ weight or 20% reduction of AChE activity. A CED is an alternative to a NOAEL and CED ratios are an alternative for informing the EFsubchronic distribution.
One possible approach of establishing a CED or NOAEL ratio distribution is to assess an overall CED or overall NOAEL for each of the two exposure durations, and determine their ratios for each compound. To be able to do that, data on the full set of endpoints (body weights, organ weights, hematology, clinical chemistry, urinalysis, necropsy findings, and histopathology) as described in the appropriate guidelines for chemical testing (EC, 1988, 2001; OECD, 1981, 1998) is needed for both the subchronic and the chronic study. Unfortunately, most studies evaluated in the present article report only a subset of these endpoints, in particular for chronic exposure. Because of the incompleteness of the data set no attempt was made to assess an overall CED and an overall NOAEL. Furthermore, since there is no consensus about the setting of a CES for each endpoint (Dekkers et al., 2001) deriving a subchronic/chronic ratio based on CEDs derived for two different endpoints may cause discussion. When one of the CESs of both endpoints would be changed, the ratio of CEDs would also change.
To avoid these problems, two endpoints were chosen which were reported in the majority of the studies, viz. body weight at necropsy and liver weight (absolute and relative). In this case the choice of CES does not have implications for the subchronic/chronic ratio, as is shown in the statistical analysis section. Per endpoint both the CED ratios and the NOAEL ratios were assessed. The distributions of all CED ratios and NOAEL ratios were compared. Theoretically, the NOAEL distribution contains more error than the CED distribution. Further, in contrast to the NOAEL approach, the error in the CED can be quantified. When the EF distribution is based on NOAEL ratios it may result in an unnecessarily conservative (wide) distribution. Using the CED approach may result in a more appropriate and precise EF distribution. These theoretical notions are further explored in the present analysis. The purpose of this analysis is to discuss the methodology of how to derive an EF distribution in general rather than to establish or propose a specific subchronic-to-chronic EF distribution.
DATA SELECTION
The toxicological dose-response data were retrieved from the technical reports (TRs) produced by the U.S. National Toxicology Program (NTP, http://ntp.niehs.nih.gov/index.cfmobjectid=084 801F0-F43F-7B74-0BE549908B5E5C1C). The NTP provides a sufficiently large number of studies allowing the comparison of subchronic to chronic exposure. An additional positive feature of the NTP studies is that they are performed at the same location with the same rat (F344/N) and/or mouse (B6C3F1) strains.
Only data from animals that were orally exposed by gavage, via food or drinking water were used. By default, for a given compound the same exposure route was used in the subchronic and chronic study. Many TRs contain a 13-week study, which is generally regarded as a subchronic study (EC, 2001; OECD, 1998) in rats and mice. Since no sufficient data on body weights and organ weights were available at the end of the two-year study (in most cases only the number of lesions was reported) the 15-month interim evaluation of the two-year study was used as the chronic study. According to testing guidelines the duration of a chronic test in mice and rats should be at least 12 months (EC, 1988; OECD, 1981).
Of each TR the following data were collected: doses (in mg/kg body weight/day), species (mouse or rat), duration of exposure, and sex. Furthermore, means, standard errors of means (SEM), and the sample sizes for total body weight (at necropsy) and liver weight (absolute and relative) were included. Datasets were only used when at least three doses of the compound and a control were available per exposure duration and per sex for a certain species.
Doses given in ppm (feed) and mg/ml (drinking water) were converted to mg/kg body weight/day, while correcting for animal growth. When feed consumption in the 13-week study was given in grams feed per kg body weight as an average of 13 weekly measurements, the dose was calculated as follows:
When feed consumption was given in grams feed per animal in week 1 and week 13, the dose was calculated as the mean of the doses from week 1 and 13. The same approach was used when the animals were exposed via drinking water:
where i refers to week number 1 or 13. In the two-year studies, the doses (in mg/kg bw/day) of every few weeks were listed in the TRs. The mean of these doses in the first 15 months (approximately 66 weeks) were taken as the chronic dose in mg/kg bw/day.
Some TRs deviated slightly from the terms set above. Occasionally, subchronic exposure durations were longer than 13 weeks (14 weeks in TR 493 and 445, 17 weeks in TR 384). Or chronic exposure duration was shorter than 15 months (12 months in TR 493).
The final database consisted of data from 31 TRs (Table 1), several of which contain both rat and mouse data (Table 2). After chronic (15 months) exposure, liver neoplasms were reported in mice in TRs 384 and 443. These studies are included in the present analysis. Using the 53 pairs of studies, a total of (53 x 2 sexes x 3 endpoints – 4 due to insufficient data =) 314 datasets were created that were theoretically suitable for deriving a ratio of NOAELs and CEDs. A dataset in this article consists of dose-response data for a particular compound/species/sex/endpoint with both subchronic and chronic exposure. An example of a particular dataset is given in Figure 1.
STATISTICAL ANALYSIS
Lowest-Observed-Adverse-Effect-Levels (LOAELs) were determined by taking the lowest dose showing a statistically significantly different ( = 0.05) effect, according to an ANOVA followed by pairwise t-tests. The NOAEL was set at the applied dose below the LOAEL, if possible. When a LOAEL could not be established (and consequently no NOAEL could be derived) the subchronic or chronic study was labelled as "no LOAEL."
The subchronic/chronic NOAEL ratios were assumed to be drawn from a lognormal distribution. Lognormal probability plots were constructed to check this assumption (see Results).
The CEDs were determined by dose-response analysis using the software PROAST (PROAST v8.9 or PROAST.gui.00) written in the S-language. A model was simultaneously fitted to the data associated with the four groups (malesubchronic, malechronic, femalesubchronic, and femalechronic) within a species. The following models were used:
Model 1: y = a with a > 0
Model 2: y = a exp(x/b) with a > 0
Model 3: y = a exp(±(x/b)d) with a > 0, b > 0, d 1
Model 4: y = a [c – (c – 1)exp(–x/b)] with a > 0, b > 0, c > 0
Model 5: y = a [c – (c – 1)exp(–x/b)d] with a > 0, b > 0, c > 0, d 1
These models are designed such that their fits can be compared using the likelihood ratio test (Slob, 2002). Variable y is any continuous endpoint, and x denotes the dose. In all models the parameter a represents the level of the endpoint at dose zero, b can be considered as the parameter reflecting the efficacy of the chemical, c can be interpreted as the maximum (or minimum) relative change, and d as an extra shape parameter. By being larger or equal to 1 parameter d prevents the slope of the function to be infinitive at dose zero.
The parameters a and b, as well as the residual variance were allowed to be dependent on sex and/or exposure duration if such resulted in a significant ( = 0.05) improvement of the fit. Otherwise these parameters were assumed equal between sexes and/or exposure durations. As an exception, parameter b was never assumed equal for both exposure durations: when the bs are equal, the CEDs are as well, while we are interested in the best estimate of the ratio of CEDs between exposure durations. As an example, Figure 1 shows the absolute liver weight for female mice after subchronic and chronic exposure observed in one of the NTP studies. Model 2 was fitted to both data sets simultaneously, allowing for parameters a, b, and the residual variance to be different between exposure durations. The data for both durations appear to be adequately described by this model. In this example, the CEDs associated with a 5% increase of the absolute liver weight in the subchronic and chronic study were 350 and 217 mg/kg body weight/day respectively, which gives a ratio of 1.6. When the CES is set at 10% the same ratio is found (685/423 = 1.6), illustrating that the ratio of CEDs does not depend on the value of CES in this model approach. The ratio can also be calculated by the ratio of the parameters b for both exposure durations (71.8/44.4 = 1.6). Thus, the difference in "sensitivity" between these two durations can be expressed by a single factor, that holds for any effect size in these models.
To determine the uncertainty of a CED the 90%-confidence interval was calculated with the likelihood-ratio method (Moerbeek et al., 2004). When the likelihood profile had a shape that strongly deviated from a parabolic shape the bootstrap method (500 runs) was applied to assess the confidence interval (Moerbeek et al., 2004; Slob and Pieters, 1998).
The CED ratios were assumed to be drawn from a lognormal distribution. Lognormal probability plots were constructed to check this assumption (see Results). The lognormal distributions for the CED and NOAEL ratios were characterized by the median and the geometric standard deviation (GSD). The median of the lognormal distribution is estimated by the geometric mean (GM). The GSD is a measure of the variation of the distribution and is defined as the backtransformed SD of the data on log-scale.
The estimation error of an individual CED ratio (on log-scale) was estimated by
where L05 is the lower and L95 the upper confidence bound of the CED, and 1.645 is the 95th percentile of the standard normal distribution. The corrected variance of the distribution of CED ratios (on log-scale) may then be roughly estimated by
where is the observed variance of all log-ratios. The corrected GSD of the CED ratio distribution then follows from
The log-transformed subchronic NOAELs or CEDs were plotted against their corresponding log-transformed chronic NOAELs or CEDs. In fitting a straight line, both variables were treated as random variables, with different errors, i.e., the intercept (a) and slope (b) were estimated by minimizing the sum of products,
where xi and yi are the subchronic and chronic NOAELs (or CEDs) of ratio i, respectively. Note that the fitted line
is equivalent with
where =10a. When b = 1, then the estimate of is equivalent to the GM of the chronic-to-subchronic ratios.
RESULTS
From the 314 datasets, 246 were not suitable for deriving a NOAEL ratio because no NOAEL could be assessed in the subchronic and/or chronic dataset (Table 3). NOAELs could not be derived when the lowest dose tested was a LOAEL or when no LOAEL could be assessed at all. The distribution of the remaining 68 NOAEL ratios (Table 4, first row) showed a GM of 1.5 and a GSD of 5.3. Figure 2 (left panel) shows the lognormal probability plot of the ratios. The linear relation indicates that the NOAEL ratios are approximately lognormally distributed.
When the log-transformed chronic NOAELs were plotted against the log-transformed subchronic NOAELs, the fitted line through these 68 data points had an intercept of –0.35, and a slope of 1.09. The correlation coefficient was 0.59 (Figure 3, left panel).
Although the quantification of a LOAEL-to-NOAEL extrapolation factor is without justification, it gives information about dose spacing rather than being a precisely quantified factor (Pieters et al., 1998; Vermeire et al., 1999), a factor of 10 is commonly used. By applying this factor of 10 to the studies resulting in a LOAEL for the lowest dose, the number of NOAEL ratios could be increased to 189. By including these ratios the variation (GSD) of the distribution increased to 9.6 (Table 4, second row).
To determine the CEDs, a dose-response model was selected from the family of models mentioned above by the log-likelihood criterion. In all cases model 1, 2, or 4 was selected. For several datasets the accuracy of the dose response data was doubtful (Table 5), the data points (i.e., average responses) were highly scattered. Furthermore, in 30 of the 314 datasets the subchronic study did not give any information about the response in the chronic study. For example, in 16 datasets there was no response after subchronic exposure, while after chronic exposure a response was found. In other datasets no CEDs, and thus no ratios, could be derived because there was no significant response (model 1 could not be significantly improved). For a total of 125 datasets no CED ratio was assessed for one of these reasons.
The resulting distribution of the remaining 189 CED ratios is reported in Table 4 (third row). Taking all studies and endpoints together, the GM of the subchronic/chronic CED ratios was 1.7 with a GSD of 2.9. By taking the estimation errors of the individual ratios into account, the GSD decreased to 2.3. Figure 2 (right panel) presents the lognormal probability plot of the CED ratios. The linear relation indicates that the CED ratios are approximately lognormally distributed. Log-transformed chronic CEDs were plotted against the log-transformed subchronic CEDs (Figure 3, right panel). The regression line through these data points has an intercept of –0.34 and a slope of 1.05. The correlation coefficient was 0.82.
Since the criteria for selecting ratios to be included in the NOAEL or CED distributions are different, both distributions are based on different datasets. For 53 datasets both approaches could be properly applied. The NOAEL distribution based on only these 53 datasets showed a GM of 1.2 and a GSD of 3.3. The CED distribution based on the same 53 datasets hardly changed, the GM was 1.6 and the corrected GSD was 2.3 (Table 4).
CED (Table 6) and NOAEL (data not shown) ratio distributions showed similar GMs and GSDs when comparing individual endpoints, species, and sexes. The distributions of the ratios based on drinking water studies appear to deviate from distributions of gavage and feed studies. However, the large confidence interval of the GM of the CED ratios for the drinking water studies indicates that the small number of ratios might have led to an unfortunate point estimate of the GM.
DISCUSSION
Since NOAELs may be expected to contain considerable error, it was hypothesized that a distribution of the CED ratios will have a smaller variation than one based on NOAEL ratios. In this study, distributions of NOAEL and CED ratios were assessed using the same dose-response data to evaluate this hypothesis. To that end, NOAELs and CEDs were derived from dose-response data relating to body weights and (absolute and relative) liver weights in (male and female) rats and mice, orally exposed by gavage, feed, or drinking water. The separate distributions of the subchronic-to-chronic ratios for these individual endpoints, sexes, species, and routes of exposure did not reveal clearly deviating subgroups (Table 6). Therefore, ratios of all datasets were taken together in a single NOAEL or CED distribution.
A straight line was fitted to the log-transformed chronic CEDs and NOAELs plotted against the log-transformed subchronic CEDs and NOAELs respectively (Fig. 3). Fortunately, the slope turned out to be close to unity, otherwise the use of a single AF, independent from the level of the NOAEL (or CED), would have been a doubtful practice.
The NOAEL distribution was based on 68 ratios while theoretically a number of 314 ratios could have been derived from the available datasets. In many cases no NOAEL or no LOAEL could be derived, resulting in a quite drastic drop of number of useable datasets. To increase the number of datasets LOAELs were converted into NOAELs by dividing them by 10. It is stressed that this factor, although widely used, is not quantified properly. When the LOAELs were nonetheless divided by 10 and included in the data set, the variation in the data set became even larger (GSD = 9.6). In this situation the number of ratios (189) is the same as the number of CED ratios, but this is coincidental (the underlying set of datasets was not identical).
The GMs of the CED (1.7) and NOAEL (1.5) ratios were virtually the same. But, the variation (GSD = 2.9) of the CED ratio distribution was considerably smaller than the GSD (5.3) of the NOAEL ratio distribution. The variation of the CED distribution can even be reduced (to 2.3) by correcting it for the estimation errors in the individual ratios. The reduction is only possible in case of the CED approach, since it is not possible to determine standard errors of NOAELs.
With the NOAEL approach only a small fraction of available datasets can be used to assess an EF distribution. This is a considerable disadvantage especially when only a few datasets are available. With the NOAEL approach about 80% of the available datasets was not useful in informing the ratio distribution. With the CED approach this percentage (about 40%) was much smaller. Out of this 40% datasets, 10% (30 datasets) contained subchronic studies that did not give any information about the response in the chronic study. This indicates that in several occasions the effect of chronic exposure to the compound could not be predicted by the subchronic study.
When exactly the same (53) datasets were evaluated the NOAEL and CED distributions were more similar (Table 4). The uncorrected GSD of the CED ratios (2.9) was still smaller than the GSD of the NOAEL ratios (3.3). This confirms the hypothesis that a distribution of CED ratios contains less error than a NOAEL ratio distribution, although the difference was not large. However, when corrected for the estimation error of the individual CED ratios the GSDcorrected became considerably smaller (2.3) than the GSD of the NOAEL ratios. The GSD (and GM) of the CED distribution stayed the same when the ratio sample size decreased from 189 to 53, indicating the CED ratio distribution to be independent of the sample of datasets. The NOAEL ratio distribution did change considerable, however, indicating that poor datasets (i.e., with scattered data) caused the larger GSD in the NOAEL distribution based on the 68 ratios.
In an evaluation where only the NOAEL approach would have been used, the NOAEL distribution derived from the 68 ratios would have been assessed. In that situation the GSD of the NOAEL distribution would have been estimated at a much higher value than when estimated from the 189 CED ratios. As a consequence of the larger GSD of the NOAEL distribution the P95 of this distribution is 3.3 times higher than the one derived from the CED distribution. In other words, when an AF (as a point estimate) is based on the 95th percentile of a NOAEL ratio distribution its value may be unnecessarily large. Using probabilistic risk assessment methods the resulting probabilistic RfD also would be unnecessarily conservative.
These results indicate that it is worthwhile to assess or re-assess EF distributions for different situations (e.g., intra- and interspecies) where usable datasets are much harder to find. Using the benchmark approach a larger fraction of the available datasets could be used to derive an EF distribution. Furthermore, the distribution can probably be established more accurately compared to one based on the NOAEL approach.
The main conclusion of this study is that the benchmark (or CED) ratio approach is a better approach for assessing a distribution for a particular EF: the improvement achieved is sufficient to warrant the extra time needed for the analysis. Using the benchmark approach, more accurate (and less conservative) AFs can be derived in general compared to those based on NOAEL ratios.
ACKNOWLEDGMENTS
This work was performed within the EU funded CASCADE Network of Excellence (Contract No.: FOOD-CT-2004-506319).
REFERENCES
Baird, S. J. S., Cohen, J. T., Graham, J. D., Shlyakhter, A. I., and Evans, J. S. (1996). Noncancer risk assessment: A probabilistic alternative to current practice. Human Ecolog. Risk Assess. 2, 79–102.
Brand, K. P., Rhomberg, L., and Evans, J. S. (1999). Estimating noncancer uncertainty factors: Are ratios NOAELs informative Risk Anal. 19, 295–308.
Crump, K. S. (1984). A new method for determining allowable daily intakes. Fundam. Appl. Toxicol. 4, 854–871.
Dekkers, S., de Heer, C., and Rennen, M. A. (2001). Critical effect sizes in toxicological risk assessment: A comprehensive and critical evaluation. Environ. Toxicol. Pharmacol. 10, 33–52.
EC (1988). Testing Method B.30, Chronic Toxicity Test, Commission Directive 88/302/EEC. Official Journal of the European Communities L 133.
EC (2001). Testing Method B.26, Sub-chronic oral toxicity test. Repeated dose 90-day oral toxicity study in rodents, Commission Directive 2001/59/EC. Official Journal of the European Communities L 225.
Edler, L., Poirier, K., Dourson, M., Kleiner, J., Mileson, B., Nordmann, H., Renwick, A., Slob, W., Walton, K., and Wurtzen, G. (2002). Mathematical modelling and quantitative methods. Food Chem. Toxicol. 40, 283–326.
Kalberlah, F., and Schneider, K. (1998). Quantification of extrapolation factors. Final report of the research project no. 1116 06 113 of the Federal Environmental Agency. Schriftenreihe der Bundesanstalt fuer Arbeitsschutz und Arbeitsmedizin Dortmund, pp. 177–189, Bremerhaven: Wirtschaftsverlag NW.
Kramer, H. J., vandenHam, W. A., Slob, W., and Pieters, M. N. (1996). Conversion factors estimating indicative chronic no-observed- adverse-effect levels from short-term toxicity data. Regul. Toxicol. Pharmacol. 23, 249–255.
McNamara, B. P. (1976). Concepts in health evaluation of commercial and industrial chemicals. In Advances in Modern Technology, Vol. 1, Part 1: New Concepts in Safety Evaluation (M. A. Mehlman, R. E. Shapiro, and H. Blumenthal, Eds.), pp. 61–140. Hemisphere, Washington, DC.
Moerbeek, M., Piersma, A. H., and Slob, W. (2004). A comparison of three methods for calculating confidence intervals for the benchmark dose. Risk Anal. 24, 31–40.
OECD (1981). Guideline 452, Chronic Toxicity Studies (adopted 12 May 1981). In OECD Guidelines for the Testing of Chemicals, Section 4: Health Effects. Organisation for Economic Cooperation & Development, Paris.
OECD (1998). Guideline 408, Repeated Dose 90-Day Oral Toxicity Study in Rodents (Updated Guideline, adopted 21st September 1998). In OECD Guidelines for the Testing of Chemicals, Section 4: Health Effects. Organisation for Economic Cooperation & Development, Paris.
Pieters, M. N., Kramer, H. J., and Slob, W. (1998). Evaluation of the uncertainty factor for subchronic-to-chronic extrapolation: Statistical analysis of toxicity data. Regul. Toxicol. Pharmacol. 27, 108–111.
Rulis, A. M., and Hattan, D. G. (1985). FDA's priority-based assessment of food additives. II. General toxicity parameters. Regul. Toxicol. Pharmacol. 5, 152–174.
Slob, W. (2002). Dose-response modeling of continuous endpoints. Toxicol. Sci. 66, 298–312.
Slob, W., and Pieters, M. N. (1998). A probabilistic approach for deriving acceptable human intake limits and human health risks from toxicological studies: General framework. Risk Anal. 18, 787–798.
Vermeire, T., Stevenson, H., Pieters, M. N., Rennen, M., Slob, W., and Hakkert, B. C. (1999). Assessment factors for human health risk assessment: A discussion paper. Crit. Rev. Toxicol. 29, 439–490.(Bas G. H. Bokkers, and Wo)
National Institute of Public Health and the Environment (RIVM), P.O. Box 1, 3720 BA Bilthoven, The Netherlands
ABSTRACT
One approach to derive a data-based assessment factor (AF) for subchronic-to-chronic extrapolation is to determine ratios between the NOAELsubchronic and NOAELchronic for the same compounds. Instead of using ratios of NOAELs, the distribution can also be estimated by ratios of subchronic and chronic Benchmark Doses (or Critical Effect Doses, CEDs, for continuous data). In this study 314 dose-response datasets on body weights and liver weights of mice and rats were selected providing dose-response information after both subchronic and chronic exposure. NOAEL ratios could be derived in only 68 of these datasets, while CED ratios could be derived in 189 datasets. When only the (53) datasets suitable for both approaches were evaluated the variation of the CED ratio distribution (GSD [geometric standard deviation]: 2.9) was smaller than the one of the NOAEL ratio distribution (GSD: 3.3). After correcting for the estimation error of the individual CED ratios the GSD of the CED distribution decreased to 2.3. The geometric means (GMs) of the NOAEL and CED distributions were similar (1.2 and 1.6, respectively). Comparing the NOAEL distribution based on all 68 datasets suitable for deriving NOAEL ratios with the CED distribution based on the 189 ratios suitable for deriving CED ratios resulted in similar GMs (1.5 and 1.7, respectively), but the GSDs differed considerably (5.3 and 2.3 respectively). It is concluded that usage of the CED approach results in less wide distributions. Furthermore, a larger fraction of available datasets is useful to inform the ratio distribution. This results in more accurate, and less conservative distributions of AFs in general compared to the distributions based on NOAEL ratios that have been proposed so far.
Key Words: benchmark dose; NOAEL; critical effect dose; subchronic-to-chronic extrapolation; assessment factor; extrapolation factor.
INTRODUCTION
Regulatory agencies establish health-based acceptable exposure limits, like the Reference Dose and Acceptable Daily Intake, to protect the human population from adverse health effects in a situation of life-long exposure to non-genotoxic agents. Therefore, these limits are preferably based on chronic toxicity studies. If available, a No-Observed-Adverse-Effect-Level (NOAELchronic) is derived from these studies. The NOAELchronic is divided by assessment factors (AFs, also called uncertainty factors) accounting for interspecies and intraspecies variation to derive an exposure limit. If toxicity data after chronic exposure are not available subchronic toxicity data must be used to estimate a NOAELchronic.
A possible approach of deriving a NOAELchronic from a NOAELsubchronic is to apply another AF to the subchronic NOAEL. By default, a factor for subchronic to chronic extrapolation (AFsubchronic) of 10 is typically applied (Vermeire et al., 1999). Attempts have been made to find a data-based value for the AFsubchronic by taking a certain percentile (mostly the 95th percentile, P95) from the distribution of NOAELsubchronic/NOAELchronic ratios established for a number of compounds (McNamara, 1976; Pieters et al., 1998; Rulis and Hattan, 1985).
In the standard procedure for deriving limit values, various AFs are multiplied to obtain an overall AF. However, multiplication of point values of AFs implies a piling-up of worst-case assumptions. Therefore, the more extrapolation steps are taken into account, the higher the level of conservatism. The piling-up of worst-case assumptions can be avoided by using a probabilistic approach. Slob and Pieters (1998) introduced the term extrapolation factor (EF), which refers to the ratio of the "true" but unknown No-Adverse-Effect-Levels (NAELs) in a (in this case) subchronic and chronic study. The EF varies between different chemicals, resulting in an EF distribution where the AF is a certain chosen point (e.g., P95) of this distribution.
In this method each EF is considered uncertain and characterized as a random variable with a distribution. Multiplying all EF distributions yields a distribution for the overall EF (Baird et al., 1996; Slob and Pieters, 1998).
To obtain an EF distribution NOAELs could be used as a measure for the "true" NAEL. However, as various authors have already stated, there are some problems associated with the approach of deriving NOAELs (Brand et al., 1999; Crump, 1984; Edler et al., 2002; Kalberlah and Schneider, 1998; Kramer et al., 1996; Slob, 2002; Slob and Pieters, 1998; Vermeire et al., 1999). An important argument against the approach is the fact that a NOAEL is only an estimate of the "true" NAEL in the animal, and depends heavily on the particular experimental conditions (including sample size, dose spacing, scatter in the data). Thus, a NOAEL ratio can easily deviate from unity, even if the dose-response relationships related to both situations (associated with numerator and denominator) were in reality identical. The NOAELs are subject to substantial errors, and the error in the NOAEL ratios is even larger. When the error in the NOAEL is ignored, uncertainty distributions that are estimated from ratios of NOAELs will tend to be unnecessarily wide, i.e., the percentile (P95) of the distribution of NOAEL ratios overestimates the percentile of the "true" NAEL ratios (Slob, 2002).
In this article the benchmark approach is used to estimate Critical Effect Doses (CEDs) (Slob, 2002). The CED is defined as the dose associated with a certain "critical" effect size (CES) in continuous endpoints, e.g., 5% change in organ weight or 20% reduction of AChE activity. A CED is an alternative to a NOAEL and CED ratios are an alternative for informing the EFsubchronic distribution.
One possible approach of establishing a CED or NOAEL ratio distribution is to assess an overall CED or overall NOAEL for each of the two exposure durations, and determine their ratios for each compound. To be able to do that, data on the full set of endpoints (body weights, organ weights, hematology, clinical chemistry, urinalysis, necropsy findings, and histopathology) as described in the appropriate guidelines for chemical testing (EC, 1988, 2001; OECD, 1981, 1998) is needed for both the subchronic and the chronic study. Unfortunately, most studies evaluated in the present article report only a subset of these endpoints, in particular for chronic exposure. Because of the incompleteness of the data set no attempt was made to assess an overall CED and an overall NOAEL. Furthermore, since there is no consensus about the setting of a CES for each endpoint (Dekkers et al., 2001) deriving a subchronic/chronic ratio based on CEDs derived for two different endpoints may cause discussion. When one of the CESs of both endpoints would be changed, the ratio of CEDs would also change.
To avoid these problems, two endpoints were chosen which were reported in the majority of the studies, viz. body weight at necropsy and liver weight (absolute and relative). In this case the choice of CES does not have implications for the subchronic/chronic ratio, as is shown in the statistical analysis section. Per endpoint both the CED ratios and the NOAEL ratios were assessed. The distributions of all CED ratios and NOAEL ratios were compared. Theoretically, the NOAEL distribution contains more error than the CED distribution. Further, in contrast to the NOAEL approach, the error in the CED can be quantified. When the EF distribution is based on NOAEL ratios it may result in an unnecessarily conservative (wide) distribution. Using the CED approach may result in a more appropriate and precise EF distribution. These theoretical notions are further explored in the present analysis. The purpose of this analysis is to discuss the methodology of how to derive an EF distribution in general rather than to establish or propose a specific subchronic-to-chronic EF distribution.
DATA SELECTION
The toxicological dose-response data were retrieved from the technical reports (TRs) produced by the U.S. National Toxicology Program (NTP, http://ntp.niehs.nih.gov/index.cfmobjectid=084 801F0-F43F-7B74-0BE549908B5E5C1C). The NTP provides a sufficiently large number of studies allowing the comparison of subchronic to chronic exposure. An additional positive feature of the NTP studies is that they are performed at the same location with the same rat (F344/N) and/or mouse (B6C3F1) strains.
Only data from animals that were orally exposed by gavage, via food or drinking water were used. By default, for a given compound the same exposure route was used in the subchronic and chronic study. Many TRs contain a 13-week study, which is generally regarded as a subchronic study (EC, 2001; OECD, 1998) in rats and mice. Since no sufficient data on body weights and organ weights were available at the end of the two-year study (in most cases only the number of lesions was reported) the 15-month interim evaluation of the two-year study was used as the chronic study. According to testing guidelines the duration of a chronic test in mice and rats should be at least 12 months (EC, 1988; OECD, 1981).
Of each TR the following data were collected: doses (in mg/kg body weight/day), species (mouse or rat), duration of exposure, and sex. Furthermore, means, standard errors of means (SEM), and the sample sizes for total body weight (at necropsy) and liver weight (absolute and relative) were included. Datasets were only used when at least three doses of the compound and a control were available per exposure duration and per sex for a certain species.
Doses given in ppm (feed) and mg/ml (drinking water) were converted to mg/kg body weight/day, while correcting for animal growth. When feed consumption in the 13-week study was given in grams feed per kg body weight as an average of 13 weekly measurements, the dose was calculated as follows:
When feed consumption was given in grams feed per animal in week 1 and week 13, the dose was calculated as the mean of the doses from week 1 and 13. The same approach was used when the animals were exposed via drinking water:
where i refers to week number 1 or 13. In the two-year studies, the doses (in mg/kg bw/day) of every few weeks were listed in the TRs. The mean of these doses in the first 15 months (approximately 66 weeks) were taken as the chronic dose in mg/kg bw/day.
Some TRs deviated slightly from the terms set above. Occasionally, subchronic exposure durations were longer than 13 weeks (14 weeks in TR 493 and 445, 17 weeks in TR 384). Or chronic exposure duration was shorter than 15 months (12 months in TR 493).
The final database consisted of data from 31 TRs (Table 1), several of which contain both rat and mouse data (Table 2). After chronic (15 months) exposure, liver neoplasms were reported in mice in TRs 384 and 443. These studies are included in the present analysis. Using the 53 pairs of studies, a total of (53 x 2 sexes x 3 endpoints – 4 due to insufficient data =) 314 datasets were created that were theoretically suitable for deriving a ratio of NOAELs and CEDs. A dataset in this article consists of dose-response data for a particular compound/species/sex/endpoint with both subchronic and chronic exposure. An example of a particular dataset is given in Figure 1.
STATISTICAL ANALYSIS
Lowest-Observed-Adverse-Effect-Levels (LOAELs) were determined by taking the lowest dose showing a statistically significantly different ( = 0.05) effect, according to an ANOVA followed by pairwise t-tests. The NOAEL was set at the applied dose below the LOAEL, if possible. When a LOAEL could not be established (and consequently no NOAEL could be derived) the subchronic or chronic study was labelled as "no LOAEL."
The subchronic/chronic NOAEL ratios were assumed to be drawn from a lognormal distribution. Lognormal probability plots were constructed to check this assumption (see Results).
The CEDs were determined by dose-response analysis using the software PROAST (PROAST v8.9 or PROAST.gui.00) written in the S-language. A model was simultaneously fitted to the data associated with the four groups (malesubchronic, malechronic, femalesubchronic, and femalechronic) within a species. The following models were used:
Model 1: y = a with a > 0
Model 2: y = a exp(x/b) with a > 0
Model 3: y = a exp(±(x/b)d) with a > 0, b > 0, d 1
Model 4: y = a [c – (c – 1)exp(–x/b)] with a > 0, b > 0, c > 0
Model 5: y = a [c – (c – 1)exp(–x/b)d] with a > 0, b > 0, c > 0, d 1
These models are designed such that their fits can be compared using the likelihood ratio test (Slob, 2002). Variable y is any continuous endpoint, and x denotes the dose. In all models the parameter a represents the level of the endpoint at dose zero, b can be considered as the parameter reflecting the efficacy of the chemical, c can be interpreted as the maximum (or minimum) relative change, and d as an extra shape parameter. By being larger or equal to 1 parameter d prevents the slope of the function to be infinitive at dose zero.
The parameters a and b, as well as the residual variance were allowed to be dependent on sex and/or exposure duration if such resulted in a significant ( = 0.05) improvement of the fit. Otherwise these parameters were assumed equal between sexes and/or exposure durations. As an exception, parameter b was never assumed equal for both exposure durations: when the bs are equal, the CEDs are as well, while we are interested in the best estimate of the ratio of CEDs between exposure durations. As an example, Figure 1 shows the absolute liver weight for female mice after subchronic and chronic exposure observed in one of the NTP studies. Model 2 was fitted to both data sets simultaneously, allowing for parameters a, b, and the residual variance to be different between exposure durations. The data for both durations appear to be adequately described by this model. In this example, the CEDs associated with a 5% increase of the absolute liver weight in the subchronic and chronic study were 350 and 217 mg/kg body weight/day respectively, which gives a ratio of 1.6. When the CES is set at 10% the same ratio is found (685/423 = 1.6), illustrating that the ratio of CEDs does not depend on the value of CES in this model approach. The ratio can also be calculated by the ratio of the parameters b for both exposure durations (71.8/44.4 = 1.6). Thus, the difference in "sensitivity" between these two durations can be expressed by a single factor, that holds for any effect size in these models.
To determine the uncertainty of a CED the 90%-confidence interval was calculated with the likelihood-ratio method (Moerbeek et al., 2004). When the likelihood profile had a shape that strongly deviated from a parabolic shape the bootstrap method (500 runs) was applied to assess the confidence interval (Moerbeek et al., 2004; Slob and Pieters, 1998).
The CED ratios were assumed to be drawn from a lognormal distribution. Lognormal probability plots were constructed to check this assumption (see Results). The lognormal distributions for the CED and NOAEL ratios were characterized by the median and the geometric standard deviation (GSD). The median of the lognormal distribution is estimated by the geometric mean (GM). The GSD is a measure of the variation of the distribution and is defined as the backtransformed SD of the data on log-scale.
The estimation error of an individual CED ratio (on log-scale) was estimated by
where L05 is the lower and L95 the upper confidence bound of the CED, and 1.645 is the 95th percentile of the standard normal distribution. The corrected variance of the distribution of CED ratios (on log-scale) may then be roughly estimated by
where is the observed variance of all log-ratios. The corrected GSD of the CED ratio distribution then follows from
The log-transformed subchronic NOAELs or CEDs were plotted against their corresponding log-transformed chronic NOAELs or CEDs. In fitting a straight line, both variables were treated as random variables, with different errors, i.e., the intercept (a) and slope (b) were estimated by minimizing the sum of products,
where xi and yi are the subchronic and chronic NOAELs (or CEDs) of ratio i, respectively. Note that the fitted line
is equivalent with
where =10a. When b = 1, then the estimate of is equivalent to the GM of the chronic-to-subchronic ratios.
RESULTS
From the 314 datasets, 246 were not suitable for deriving a NOAEL ratio because no NOAEL could be assessed in the subchronic and/or chronic dataset (Table 3). NOAELs could not be derived when the lowest dose tested was a LOAEL or when no LOAEL could be assessed at all. The distribution of the remaining 68 NOAEL ratios (Table 4, first row) showed a GM of 1.5 and a GSD of 5.3. Figure 2 (left panel) shows the lognormal probability plot of the ratios. The linear relation indicates that the NOAEL ratios are approximately lognormally distributed.
When the log-transformed chronic NOAELs were plotted against the log-transformed subchronic NOAELs, the fitted line through these 68 data points had an intercept of –0.35, and a slope of 1.09. The correlation coefficient was 0.59 (Figure 3, left panel).
Although the quantification of a LOAEL-to-NOAEL extrapolation factor is without justification, it gives information about dose spacing rather than being a precisely quantified factor (Pieters et al., 1998; Vermeire et al., 1999), a factor of 10 is commonly used. By applying this factor of 10 to the studies resulting in a LOAEL for the lowest dose, the number of NOAEL ratios could be increased to 189. By including these ratios the variation (GSD) of the distribution increased to 9.6 (Table 4, second row).
To determine the CEDs, a dose-response model was selected from the family of models mentioned above by the log-likelihood criterion. In all cases model 1, 2, or 4 was selected. For several datasets the accuracy of the dose response data was doubtful (Table 5), the data points (i.e., average responses) were highly scattered. Furthermore, in 30 of the 314 datasets the subchronic study did not give any information about the response in the chronic study. For example, in 16 datasets there was no response after subchronic exposure, while after chronic exposure a response was found. In other datasets no CEDs, and thus no ratios, could be derived because there was no significant response (model 1 could not be significantly improved). For a total of 125 datasets no CED ratio was assessed for one of these reasons.
The resulting distribution of the remaining 189 CED ratios is reported in Table 4 (third row). Taking all studies and endpoints together, the GM of the subchronic/chronic CED ratios was 1.7 with a GSD of 2.9. By taking the estimation errors of the individual ratios into account, the GSD decreased to 2.3. Figure 2 (right panel) presents the lognormal probability plot of the CED ratios. The linear relation indicates that the CED ratios are approximately lognormally distributed. Log-transformed chronic CEDs were plotted against the log-transformed subchronic CEDs (Figure 3, right panel). The regression line through these data points has an intercept of –0.34 and a slope of 1.05. The correlation coefficient was 0.82.
Since the criteria for selecting ratios to be included in the NOAEL or CED distributions are different, both distributions are based on different datasets. For 53 datasets both approaches could be properly applied. The NOAEL distribution based on only these 53 datasets showed a GM of 1.2 and a GSD of 3.3. The CED distribution based on the same 53 datasets hardly changed, the GM was 1.6 and the corrected GSD was 2.3 (Table 4).
CED (Table 6) and NOAEL (data not shown) ratio distributions showed similar GMs and GSDs when comparing individual endpoints, species, and sexes. The distributions of the ratios based on drinking water studies appear to deviate from distributions of gavage and feed studies. However, the large confidence interval of the GM of the CED ratios for the drinking water studies indicates that the small number of ratios might have led to an unfortunate point estimate of the GM.
DISCUSSION
Since NOAELs may be expected to contain considerable error, it was hypothesized that a distribution of the CED ratios will have a smaller variation than one based on NOAEL ratios. In this study, distributions of NOAEL and CED ratios were assessed using the same dose-response data to evaluate this hypothesis. To that end, NOAELs and CEDs were derived from dose-response data relating to body weights and (absolute and relative) liver weights in (male and female) rats and mice, orally exposed by gavage, feed, or drinking water. The separate distributions of the subchronic-to-chronic ratios for these individual endpoints, sexes, species, and routes of exposure did not reveal clearly deviating subgroups (Table 6). Therefore, ratios of all datasets were taken together in a single NOAEL or CED distribution.
A straight line was fitted to the log-transformed chronic CEDs and NOAELs plotted against the log-transformed subchronic CEDs and NOAELs respectively (Fig. 3). Fortunately, the slope turned out to be close to unity, otherwise the use of a single AF, independent from the level of the NOAEL (or CED), would have been a doubtful practice.
The NOAEL distribution was based on 68 ratios while theoretically a number of 314 ratios could have been derived from the available datasets. In many cases no NOAEL or no LOAEL could be derived, resulting in a quite drastic drop of number of useable datasets. To increase the number of datasets LOAELs were converted into NOAELs by dividing them by 10. It is stressed that this factor, although widely used, is not quantified properly. When the LOAELs were nonetheless divided by 10 and included in the data set, the variation in the data set became even larger (GSD = 9.6). In this situation the number of ratios (189) is the same as the number of CED ratios, but this is coincidental (the underlying set of datasets was not identical).
The GMs of the CED (1.7) and NOAEL (1.5) ratios were virtually the same. But, the variation (GSD = 2.9) of the CED ratio distribution was considerably smaller than the GSD (5.3) of the NOAEL ratio distribution. The variation of the CED distribution can even be reduced (to 2.3) by correcting it for the estimation errors in the individual ratios. The reduction is only possible in case of the CED approach, since it is not possible to determine standard errors of NOAELs.
With the NOAEL approach only a small fraction of available datasets can be used to assess an EF distribution. This is a considerable disadvantage especially when only a few datasets are available. With the NOAEL approach about 80% of the available datasets was not useful in informing the ratio distribution. With the CED approach this percentage (about 40%) was much smaller. Out of this 40% datasets, 10% (30 datasets) contained subchronic studies that did not give any information about the response in the chronic study. This indicates that in several occasions the effect of chronic exposure to the compound could not be predicted by the subchronic study.
When exactly the same (53) datasets were evaluated the NOAEL and CED distributions were more similar (Table 4). The uncorrected GSD of the CED ratios (2.9) was still smaller than the GSD of the NOAEL ratios (3.3). This confirms the hypothesis that a distribution of CED ratios contains less error than a NOAEL ratio distribution, although the difference was not large. However, when corrected for the estimation error of the individual CED ratios the GSDcorrected became considerably smaller (2.3) than the GSD of the NOAEL ratios. The GSD (and GM) of the CED distribution stayed the same when the ratio sample size decreased from 189 to 53, indicating the CED ratio distribution to be independent of the sample of datasets. The NOAEL ratio distribution did change considerable, however, indicating that poor datasets (i.e., with scattered data) caused the larger GSD in the NOAEL distribution based on the 68 ratios.
In an evaluation where only the NOAEL approach would have been used, the NOAEL distribution derived from the 68 ratios would have been assessed. In that situation the GSD of the NOAEL distribution would have been estimated at a much higher value than when estimated from the 189 CED ratios. As a consequence of the larger GSD of the NOAEL distribution the P95 of this distribution is 3.3 times higher than the one derived from the CED distribution. In other words, when an AF (as a point estimate) is based on the 95th percentile of a NOAEL ratio distribution its value may be unnecessarily large. Using probabilistic risk assessment methods the resulting probabilistic RfD also would be unnecessarily conservative.
These results indicate that it is worthwhile to assess or re-assess EF distributions for different situations (e.g., intra- and interspecies) where usable datasets are much harder to find. Using the benchmark approach a larger fraction of the available datasets could be used to derive an EF distribution. Furthermore, the distribution can probably be established more accurately compared to one based on the NOAEL approach.
The main conclusion of this study is that the benchmark (or CED) ratio approach is a better approach for assessing a distribution for a particular EF: the improvement achieved is sufficient to warrant the extra time needed for the analysis. Using the benchmark approach, more accurate (and less conservative) AFs can be derived in general compared to those based on NOAEL ratios.
ACKNOWLEDGMENTS
This work was performed within the EU funded CASCADE Network of Excellence (Contract No.: FOOD-CT-2004-506319).
REFERENCES
Baird, S. J. S., Cohen, J. T., Graham, J. D., Shlyakhter, A. I., and Evans, J. S. (1996). Noncancer risk assessment: A probabilistic alternative to current practice. Human Ecolog. Risk Assess. 2, 79–102.
Brand, K. P., Rhomberg, L., and Evans, J. S. (1999). Estimating noncancer uncertainty factors: Are ratios NOAELs informative Risk Anal. 19, 295–308.
Crump, K. S. (1984). A new method for determining allowable daily intakes. Fundam. Appl. Toxicol. 4, 854–871.
Dekkers, S., de Heer, C., and Rennen, M. A. (2001). Critical effect sizes in toxicological risk assessment: A comprehensive and critical evaluation. Environ. Toxicol. Pharmacol. 10, 33–52.
EC (1988). Testing Method B.30, Chronic Toxicity Test, Commission Directive 88/302/EEC. Official Journal of the European Communities L 133.
EC (2001). Testing Method B.26, Sub-chronic oral toxicity test. Repeated dose 90-day oral toxicity study in rodents, Commission Directive 2001/59/EC. Official Journal of the European Communities L 225.
Edler, L., Poirier, K., Dourson, M., Kleiner, J., Mileson, B., Nordmann, H., Renwick, A., Slob, W., Walton, K., and Wurtzen, G. (2002). Mathematical modelling and quantitative methods. Food Chem. Toxicol. 40, 283–326.
Kalberlah, F., and Schneider, K. (1998). Quantification of extrapolation factors. Final report of the research project no. 1116 06 113 of the Federal Environmental Agency. Schriftenreihe der Bundesanstalt fuer Arbeitsschutz und Arbeitsmedizin Dortmund, pp. 177–189, Bremerhaven: Wirtschaftsverlag NW.
Kramer, H. J., vandenHam, W. A., Slob, W., and Pieters, M. N. (1996). Conversion factors estimating indicative chronic no-observed- adverse-effect levels from short-term toxicity data. Regul. Toxicol. Pharmacol. 23, 249–255.
McNamara, B. P. (1976). Concepts in health evaluation of commercial and industrial chemicals. In Advances in Modern Technology, Vol. 1, Part 1: New Concepts in Safety Evaluation (M. A. Mehlman, R. E. Shapiro, and H. Blumenthal, Eds.), pp. 61–140. Hemisphere, Washington, DC.
Moerbeek, M., Piersma, A. H., and Slob, W. (2004). A comparison of three methods for calculating confidence intervals for the benchmark dose. Risk Anal. 24, 31–40.
OECD (1981). Guideline 452, Chronic Toxicity Studies (adopted 12 May 1981). In OECD Guidelines for the Testing of Chemicals, Section 4: Health Effects. Organisation for Economic Cooperation & Development, Paris.
OECD (1998). Guideline 408, Repeated Dose 90-Day Oral Toxicity Study in Rodents (Updated Guideline, adopted 21st September 1998). In OECD Guidelines for the Testing of Chemicals, Section 4: Health Effects. Organisation for Economic Cooperation & Development, Paris.
Pieters, M. N., Kramer, H. J., and Slob, W. (1998). Evaluation of the uncertainty factor for subchronic-to-chronic extrapolation: Statistical analysis of toxicity data. Regul. Toxicol. Pharmacol. 27, 108–111.
Rulis, A. M., and Hattan, D. G. (1985). FDA's priority-based assessment of food additives. II. General toxicity parameters. Regul. Toxicol. Pharmacol. 5, 152–174.
Slob, W. (2002). Dose-response modeling of continuous endpoints. Toxicol. Sci. 66, 298–312.
Slob, W., and Pieters, M. N. (1998). A probabilistic approach for deriving acceptable human intake limits and human health risks from toxicological studies: General framework. Risk Anal. 18, 787–798.
Vermeire, T., Stevenson, H., Pieters, M. N., Rennen, M., Slob, W., and Hakkert, B. C. (1999). Assessment factors for human health risk assessment: A discussion paper. Crit. Rev. Toxicol. 29, 439–490.(Bas G. H. Bokkers, and Wo)