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Statistical methodology to determine kinetically derived maximum tolerated dose in repeat dose toxicity studies
Regulatory Toxicology and Pharmacology 63 (2012) 344–351
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Regulatory Toxicology and Pharmacology journal homepage: www.elsevier.com/locate/yrtph
Statistical methodology to determine kinetically derived maximum tolerated dose in repeat dose toxicity studies Lisa G. McFadden, Michael J. Bartels, David L. Rick, Paul S. Price, Donald D. Fontaine, Shakil A. Saghir ⇑ Toxicology and Environmental Research and Consulting, The Dow Chemical Company, Midland, MI 48674, United States
a r t i c l e
i n f o
Article history: Received 2 December 2011 Available online 2 April 2012 Keywords: Toxicokinetics TK Nonlinearity Statistical approach Nonlinear systemic dose increase
a b s t r a c t Several statistical approaches were evaluated to identify an optimum method for determining a point of nonlinearity (PONL) in toxicokinetic data. (1) A second-order least squares regression model was fit iteratively starting with data from all doses. If the second order term was significant (a < 0.05), the dataset was reevaluated with successive removal of the highest dose until the second-order term became nonsignificant. This dose, whose removal made the second order term non-significant, is an estimate of the PONL. (2) A least squares linear model was fit iteratively starting with data from all doses except the highest. The mean response for the omitted dose was compared to the 95% prediction interval. If the omitted dose falls outside the confidence interval it is an estimate of the PONL. (3) Slopes of least squares linear regression lines for sections of contiguous doses were compared. Nonlinearity was suggested when slopes of compared sections differed. A total of 33 dose–response datasets were evaluated. For these toxicokinetic data, the best statistical approach was the least squares regression analysis with a second-order term. Changing the a level for the second-order term and weighting the second-order analysis by the inverse of feed consumption were also considered. This technique has been shown to give reproducible identification of nonlinearities in TK datasets. Ó 2012 Elsevier Inc. All rights reserved.
1. Introduction Toxicokinetic (TK) analysis is the evaluation of kinetic data to assess systemic exposure to understand the relationship between observed toxicity and administered doses. The TK evaluation of the degree of systemic exposure to a chemical across doses and/ or life-stages requires collection of biological samples from test animals and analysis for parent and/or metabolite(s) of interest (EMA, 1994; Health Canada, 1994; Goehl, 1997; Schwartz, 2001; Baldrick, 2003; Barton et al., 2006; Creton et al., 2012; Saghir et al., 2006, 2011). Nonlinearities in TK are determined by observation of a disproportional increase or decrease in the biomarker (test material and/or metabolite) in the central compartment (blood, sera, and plasma) and/or excreta (usually urine) across doses relative to the ingested test material over 24 h (Saghir et al., 2006, 2011). These nonlinearities in TK parameters may indicate saturation of test material absorption and/or elimination in the test species with increasing dose. This nonlinearity of data in subchronic/ chronic studies can be used to derive a Kinetically-Derived Maximum Dose (KMD) for subsequent toxicity studies (ECHA, 2008; Creton et al., 2012; Saghir et al., 2009, 2011). Currently, nonlinear⇑ Corresponding author. Current address: Syngenta Crop Protection, Inc., 410 Swing Rd, Greensboro, NC 27409, United States. Fax: +1 336 632 7581. E-mail address: [email protected] (S.A. Saghir). 0273-2300/$ - see front matter Ó 2012 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.yrtph.2012.03.013
ities in TK are mostly determined visually (subjectively) by comparing the increase in the biomarker concentration versus the test material intake (Sweatman, 1980; Saghir et al., 2006, 2009, 2011). Although, visual interpretation of the dose–response curves may be satisfactory a statistical method for the determination of nonlinearity will provide the means for reproducible interpretations of a point of nonlinearity (PONL). Lack of any firm statistical method to define PONL can result in potential bias in deriving KMD levels for long-term studies. Overestimation of the KMD could result in conduct of subsequent toxicity studies at too high of dose levels that could introduce artifactual biological effects (Goehl, 1997; Baldrick, 2003). One of the remedies to the current subjective methods for selection of the PONL level(s) from TK datasets is to devise a statistical method that determines the probability (i.e., p-values) above which dose–response becomes nonlinear in order to choose an appropriate, statistically-derived KMD. A number of researchers have looked at various statistical approaches to evaluate questions encompassing TK sampling and data analysis including sparse sampling from different animals to complete the time-course blood concentration profiles and estimating deviation of the data from linearity (Beatty and Piegorsch, 1997; Hing et al., 2002; Igarashi and Sekido, 1996; Nedelman et al., 1995). None, however, have described a detailed method for the analysis of deviation from linearity. Igarashi (1995) focused on the need for a log transformation of the concentration data before
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the analysis and later Igarashi and Sekido (1996) analyzed their data using simple linear regression with cut-off regression coefficients of 0.7 and 1.3 for the data to be considered linear without any formal statistical technique. Their techniques for the analysis of TK data have limitations that prohibit their universal use and can only be used for certain study designs and data. For example chemicals, other than human pharmaceutics, where data are generated from the same animals over a 24 h period to estimate daily systemic dose at different times during exposure and typically use three treated groups and a control are not suited for their analytical approach. Thus a new approach is needed. In this paper, several promising statistical methods are examined and discussed which are appropriate for a typical toxicity study conducted in a chemical industry with as little as three doses and a control. The use of control data in the PONL analysis is necessary as at least three dose levels are required for statistical analysis; therefore, log transformation of the data as described by Igarashi (1995) was not possible as this would exclude the control data. The goal of this paper is to develop a robust statistical method that has the ability to analyze a variety of TK datasets and accurately and objectively estimate the PONL, especially for chemicals where toxicity studies are conducted at limited doses (mostly at low, mid and high doses plus control) as warranted by the regulatory agencies (e.g., OECD, 1981; EEC, 1988; US EPA, 1998; JMAFF, 2000) at doses orders of magnitude different from the expected human exposure through environment (e.g., pesticides).
2. Materials and methods 2.1. Data Data from four different compounds were analyzed from various study types. A total of 33 variable dose–response datasets (four chemicals, two species, genders, dietary and inhalation exposures, levels in milk and nursing pups) were analyzed. Tables 1 and 2 list the study information. The X11422208 (rat [plasma AUC24h] and mouse [plasma concentration, total in urine) and two isomers (X517131 and X513999) of X574175 (rat [plasma AUC24h]) studies had four doses including controls. The X574175 mouse (plasma concentration) and 1,3-dichloropropene (rat plasma concentration) had five doses including controls. The 2,4-D (2,4-dichlorophenoxyacetic acid) study had six doses for most of the experiments. There were seven doses for day (D) 29 females (29 days of exposure), five for lactation day (LD) 21 pups and adult females D 95, four for postnatal day (PND) 28 and PND 35 pups. Data were comprised of plasma AUC24h in all adult rats and PND 35 pups and concentration of 2,4-D in milk and plasma of all other pups.
2.2. Statistical analyses In order to assess with appropriate (statistical) sensitivity the point at which nonlinearity occurred, three methods were examined. All statistical analysis was performed using SAS computer software (SAS Institute Inc., Cary NC), see Supplemental Tables 1–3 for the codes used to run these analyses. The control dose was included in all three models which allowed the method to be applicable to a standard toxicity test with three treated groups and a control. The actual measured ingested or inhaled dose for each individual animal was used whenever available; targeted dose was used when actual dose information was not available. For ease of reporting, doses were coded numerically starting with 1 for the control dose. An example of the coding for the typical study; 2 was code for the low dose, 3 for the mid dose and 4 for the high dose.
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2.3. Statistical method 1 The first method was a least squares regression analysis where responses were regressed against dose with a second-order term (squared value of dose, also known as a quadratic term) added to the model in order to test for nonlinearity (Neter et al., 1990). See Supplemental Table 1 for SAS codes used to run the analysis. A significant second-order term (a 6 0.05) indicated that the model was encountering nonlinearity in the dose–response curve. For this method, the model containing all dose groups was run first followed by dropping the highest dose in subsequent iterations (if previous iteration indicated nonlinearity) until the PONL was found or only three doses (control and two doses) were left. As with any test evaluating linearity, there needs to be at least three doses in the model to test for a second-order effect. If the model with all doses had a significant second-order effect and the next model after deleting the high dose did not, there was nonlinearity due to the high dose. A few datasets were encountered where the dose–response appeared linear visually but had a significant second-order effect. For such scenarios, two approaches were considered: (1) the a level was lowered to 0.025; and (2) the a level was kept at 0.05 and a weighted analysis was performed with the inverse of feed consumption as the weighting factor. 2.4. Statistical method 2 In the second method a least squares linear model was fit to the data using a range of doses. See Supplemental Table 2 for SAS codes used to run the analysis. This model was used to predict the linear response for the next consecutive dose left out of the model and a 95% prediction interval (PI) was calculated around the predicted value (Neter et al., 1990). The actual mean response from the data for the model that included that next consecutive dose was then compared to the prediction interval. If the actual response fell within the interval it was considered linear. If it did not, then this suggested nonlinearity in the actual response. 2.5. Statistical method 3 The third method compared slopes of least squares linear regression lines (Kleinbaum and Kupper, 1978) where responses were regressed against dose. See Supplemental Table 3 for SAS codes used to run the analysis. The first comparison had all doses in the regression model compared to the model with all doses but the highest included. The next, compared a model with all doses except the highest to a model with all doses except the two highest. This was continued sequentially. Also compared were different segments in which all doses were represented between the two models with splits being made at consecutively higher doses. For data with 6 doses, the first comparison compared the slope of the regression line that included doses one and two to the slope of the regression line that included doses three to six. The next comparison was between the slope for the line with doses one to three and the slope for the line with doses four to six. The slopes of the different models were compared at a 6 0.05. In this case if the slopes differed, it suggested a possible nonlinearity between the models since the slopes were not parallel. 3. Results and discussion 3.1. Visual inspection of the data In order to compare the three statistical methods and choose the most appropriate test for the determination of PONL from linearity, 33 sets of data were analyzed (Table 2). Out of those 33
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Table 1 Detailed information of the studies listing compounds, species, doses and relationship of statistical method with the observed data. Compound
Study
Sample type
Dosesa
Visual PONLb
Statistical methods used for PONLc 1
2
3
X11422208
28-day diet in rats
Male plasma AUC24h Female plasma AUC24h
4 4
None None
None None
None 3
4,3 None
X11422208
90-day diet in mice
Male plasma conc Female plasma conc Male total in urine Female total in urine
4 4 4 4
4 4 4 4
None 4 4 4,3
4 4 4 4
4 4 4,3 4,3
X574175
28-day diet in rats
Male plasma AUC24h (isomer J) Male plasma AUC24h (isomer L)
4 4
4,3 4
4,3 3
3 4,3
4,3 4,3
X574175
28-day diet in mice
Male plasma conc (isomer J) Male plasma conc (isomer L) Female plasma conc (isomer J) Female plasma conc (isomer L)
5 5 5 5
5 5 5 5
5,4 5 5 5
5,4,3 None 5,4 5
5,4,3 5,4,3 5,4,3 5,4,3
1,3-DCP
3-h inhalation in rats
Male plasma conc (cis isomer) Male plasma conc (trans isomer)
5 5
5 5
5 5
5,4 5
5,4 5,4,3
2,4-D
1-gen. diet in rats
Male plasma AUC24h D-28 Male plasma AUC24h D-71 Female plasma AUC24h D-29 Female plasma AUC24h D-95 Female plasma AUC24h GD-17 Female plasma AUC24h LD-4 Female plasma AUC24h LD-14 Milk conc LD-4 Milk conc LD-14 Male pup plasma conc LD-4 Male pup plasma conc LD-14 Male pup plasma conc LD-21 Male pup plasma conc PND-28
6 6 7 5 6 6 6 6 6 6 6 5 4
6 6,5 7,6,5,4 5,4 6 6,5,4 6,5 6 None 6,5,4 6,5,4 5 4
6 5 7,6,5,4 5,4 5,4 4 6,5 5 3 4 5,4 5 None
6 5 7,6,4,3 5,4,3 6,5,4,3 6,4,3 5,3 5 5,3 4 4,3 5,3 3
6,5,4 5 7,6,5,3 5,4,3 6,5,4,3 6,5,4,3 6,5,4,3 6,5,4 6,5,4 5,4 6,5,4,3 5,4,3 4,3
1,3-DCP, 1,3-dichloropropene; 2,4-D, 2,4-dichloro-phenoxyacetic acid; gen., generation; D, days after exposure; GD, gestational day; LD, lactational day; PND, postnatal day; PONL, point of nonlinearity; AUC, area under the curve 24 h; conc, concentration. a Number of doses animals were exposed to including control. b Visual determination of doses where nonlinearity was observed. c Statistically significant doses suggesting nonlinearity in each method. 1. A least squares regression model with a quadratic term. 2. A least squares linear model for a predicted response and prediction. 3. A comparison of slopes of least squares linear regressions.
Table 2 Summary of the compound, study types and samples analyzed for the determination of nonlinearity using the three proposed statistical methods. Compound
Study type
Data type
Datasets
X11422208 X11422208 X574175 X574175 1,3-DCP 2,4-D
Rat 28-day diet Mouse 90-day diet Rat 28-day diet Rat 28-day diet Rat 3-hour inhalation Rat 1-generation diet
Plasma AUC24h (M and F) Plasma concentration and total in urine (M and F) Plasma AUC24h (M) two isomers Plasma concentration (M and F) two isomers Plasma concentration (M) two isomers Plasma AUC24h P1 (M) D 28 and D 71 Plasma AUC24h P1 (F) D 29, D 95, GD 17, LD 4 and LD 14 Milk concentration P1 (F) LD 4 and LD 14 Plasma concentration F1 (M and F) LD 4, LD 14, LD 21, PND 28 Plasma AUC24h F1(M and F) PND 35
2 4 2 4 2 2 5 2 8 2
M, male; F, female, P1, parental-1; F1, filial-1; D, days after exposure; GD, gestational day; LD, lactational day; PND, postnatal day. AUC, area under the curve 24 h; 1,3-DCP, 1,3-dichloropropene; 2,4-D, 2,4-dichloro-phenoxyacetic acid.
datasets, the most data rich sets are presented here as examples to show the pros and cons of each of the three statistical tests used to determine PONL. To do this, an expert opinion was obtained for each of the 33 data sets on whether a PONL existed and its value. The statistical method results were then examined to see if they demonstrated concordance with those opinions (Table 1). The numbers of the doses where nonlinearity occurred are listed for the visual inspection and each statistical method. Fig. 1 is a graph used in visual inspection of the observed daily systemic dose, as measured by the plasma AUC24h, for the male and
female rats across doses after 4 weeks of dietary exposure to 2,4-D along with the trend lines showing expected AUC24h values as dose levels are increased. The expected daily systemic doses (AUC24h) (indicated by trend lines) were calculated using the actual ingestion of the 2,4-D through the test material fortified diet at the lowest dose level and extrapolating through the origin ‘‘0’’ to the higher doses. Visual inspection of the data revealed that only the highest dose in males was very different in response than the other doses. However, the four higher doses in females were very different in response (Fig. 1). The deviation between the observed and
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1400
Plasma AUC24 h of 2,4-D (µg h ml-1)
1200
Observed Male Expected Male Observed Female Expected Female
1000
800
600
400
200
0 0
10
20
30
40
50
60
70
80
90
100
2,4-D dose (mg/kg/day) Fig. 1. Systemic exposure of 2,4-D to male and female rats, as measured by the plasma AUC24h across doses after 4 weeks of dietary exposure along with the expected systemic dose based on the difference in the test material intake across doses showing points of nonlinearity.
expected values provided the visual determination of the PONL; in this case it was P 69 mg/kg/day for the male and P 14 mg/kg/day for the female rats (Fig. 1). Fig. 2 shows the systemic exposure (plasma concentration) of the two isoforms of X574175 to male and female mice as measured after 4 weeks of dietary exposure to X574175. The expected systemic doses based on the difference in the test material intake across doses showed points of nonlinearity in male (P19 mg/kg/ day for X517131 and P23 mg/kg/day for X513999) and female (none for X517131 and P32 mg/kg/day for X513999) mice. It is interesting to note from these graphs that the concentration of X517131 was higher than expected from a dose-proportional increase in the male mice and was dose-proportional in female mice. In contrast to this, the concentration of X513999 was less than the expected dose-proportional increase at the highest dose in both male and female mice (Fig. 2). Another important observation is that the dietary intake of X574175 was higher in the female mice; however, either the absorption was lower or elimination was higher by the female mice, relative to males, resulting in a lower plasma concentration at each dose level (Fig. 2). Fig. 3 shows the plasma concentration and 24 h urinary elimination of X11422208 by male and female mice after 13 weeks of dietary exposure. The plasma concentrations of X11422208 were dose-proportional only up to the middle dose for both male and female mice. In the case of males, the systemic exposure became supra-linear between the middle and high doses. However, in females, the plasma concentration remained almost unchanged between the middle and the high doses, being sub-linear relative to expected proportionality (Fig. 3). Total elimination of X11422208 in 24 h urine remained dose proportional only up to the middle dose and showed less than a dose proportional increase at the highest dose, both in male and female mice (Fig. 3). The PONL for both male and female mice was much lower than the highest doses, closer to the middle (P92 mg/kg/day for males and P227 mg/kg/day for females) doses. Taken together, the directions of the PONLs for plasma versus that for urine values suggested that in the case of males, elimination of X11422208 from plasma was saturated at the highest dose; whereas, for females, absorption of X11422208 from the gastrointestinal (GI) tract was saturated at the highest dose. These inter-
pretations were supported by a higher than expected increase in the liver weight along with histopathological changes in male mice at the highest dose. On the other hand, no additional changes in the liver weight or histopathology was observed in the female mice after 13 weeks of dosing when compared to a 4 week dietary study (unpublished data). Plasma concentrations of X11422208 remained linear in the 4 week dietary study at 3- to 4-fold higher doses than that used in the 13 week study (unpublished data). In some or even most cases visual inspection of the observed and expected daily systemic dose data may lead to a reasonable value of PONL. However, this method may induce human bias resulting in an incorrect assessment of the PONL. 3.2. Second-order model (Method 1) Table 3 shows the results from fitting a second-order model to the representative 2,4-D data. Dose levels were coded numerically starting with 1 for the control group. The models tested have the doses listed along with the p-value of the second-order term. An asterisk denotes significance and indicates deviation from linearity. The 2,4-D males showed deviation from linearity only in the complete model which showed the deviation occurred after the fifth dose. The sixth dose did not fit the linear model. The 2,4-D females showed deviation from linearity down to the fourth dose which means deviation occurred after the third dose. Only the first three doses fit the linear model for females, which is consistent with the PONL based on the visual observation. 3.3. Prediction interval (Method 2) Results of the prediction interval method are presented in Table 4. This table lists the doses in the model used to calculate the prediction interval, the prediction interval, the next higher dose it based the prediction on, and the actual mean response of the next higher dose. An asterisk denotes that the mean response is outside the prediction interval indicating possible deviation from linearity. The prediction interval results for the male 2,4-D data (Table 4) matched the second-order model results (presented in Table 3) as well as the visual interpretation. The mean response for the sixth dose did not fall within the prediction interval for the model con-
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8000
Plasma concentration of X517131 (ng/ml)
7000 6000 5000 4000 3000 Observed Male
2000
Expected Male Observed female
1000
Expected Female 0
Plasma concentration of X513999 (ng/ml)
12000
0
20
40
60
80
100
120
140
160
180
200
10000
8000
6000
4000 Observed Male Expected Male 2000
Observed female Expected Female
0 0
10
20
30
40 50 60 Dose (mg/kg/day)
70
80
90
100
Fig. 2. Systemic exposure of two components (X517131 and X513999) of X574175 to male and female mice as measured by the plasma concentration across doses after 4 weeks of dietary exposure along with the expected systemic dose based on the difference in the test material intake across doses showing points of nonlinearity.
taining the five doses, which suggested possible deviation from linearity (Table 4). Similarly, the second-order term was significant for the model containing all six doses, which confirmed a deviation from linearity at or above the fifth dose (Table 3). The female data were not as clear from the prediction interval runs. The models found doses 7, 6, 4 and 3 deviated from linearity as they did not have mean responses within the prediction interval. The results for doses 7, 6 and 4 matched the second-order model results. However, the results did not match for doses 5 and 3. Dose 3 was outside the prediction interval but appears linear. The lower variability at these low doses contributed to this finding. Dose 5 appears nonlinear and is found to be so by the second-order method, but fell within the prediction interval due to the very large amount of variability at this dose. 3.4. Comparison of slopes (Method 3) The comparison of slopes from linear regression lines are presented in Table 5. The first column lists the doses included in the
first model with the second column being the slope corresponding to that model. The third column lists the doses included in the second model and the fourth column is the slope corresponding to the second model. The slopes of these two models were compared and if they were different an asterisk was placed on the slope in column 4. In this table only two comparisons were not statistically different. The first instance was in males, the models with only the first two doses (control and first treated dose, slope 2.50) and the first three doses (control and the first two treated doses, slope 2.83). The second instance was in females, the models with the first three doses (slope 32.99) and the first four doses (slope 32.88). This method was too sensitive, finding differences between slopes that were very small. For example, the test indicated that the slope of 32.88 (from doses 1,2,3, and 4) was not different from 32.99 (of doses 1,2, and 3) which was a reasonable subjective conclusion but the slopes of 32.56 and 32.99 were different (Table 5) even though the reasonable conclusion would have been that they were not different. Similarly, in the males, the deviation from linearity only occurred after the fifth dose by visual inspection and by the
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90
Concentration of X11422208 in plasma (µg/g)
Observed Male 80
Expected Male Observed female
70
Expected Female
60 50 40 30 20 10 0 7000
Amount of X11422208 in 24 h urine (µg)
Observed Male Expected Male
6000
Observed female Expected Female 5000
4000
3000
2000
1000
0
0
100
200
300
400
500
600
Dose (mg/kg/day) Fig. 3. Systemic exposure of X11422208 to male and female mice as measured by the plasma concentration across doses after 13 weeks of dietary exposure and the urinary elimination (lg over 24 h) of the daily ingested dose along with the expected systemic dose based on the difference in the test material intake across doses showing points of nonlinearity.
Table 3 Testing second-order model for the statistical determination of the point of nonlinearity using daily systemic dose (plasma AUC24h) of 2,4-D across doses in adults of both genders after reaching steady-state systemic exposure (4 weeks of continuous dietary exposure).
*
Model dosesa
Sex
p-value of quadratic term
All doses (6,5,4,3,2,1) 5,4,3,2,1 4,3,2,1 3,2,1 All doses (7,6,5,4,3,2,1) 6,5,4,3,2,1 5,4,3,2,1 4,3,2,1 3,2,1
Male Male Male Male Female Female Female Female Female
0.0145* 0.3734 0.9971 0.9492 0.0022* 0.0028* 0.0019* 0.0324* 0.7036
Table 4 Testing prediction interval for response from the next dose for the statistical determination of the point of nonlinearity using daily systemic dose (plasma AUC24h) of 2,4-D across doses in adults of both genders after reaching steady-state systemic exposure (4 weeks of continuous dietary exposure).
Statistically significant at p 6 0.05. a Doses coded numerically with control dose being 1.
second-order test; therefore, expectations were that the slope for the model of 1,2,3,4,5 would not be different from the slope for the model of 1,2,3,4 but the slope comparison test found these slopes different. The slope differences were due to the lines not
*
Doses in modela
Prediction intervalb
Next dose
Mean responsec
Males 1,2,3,4,5 1,2,3,4 1,2,3 1,2
108–337 171–293 75.8–158 35.0–70.7
6 5 4 3
579* 179 147 60
Females 1,2,3,4,5,6 1,2,3,4,5 1,2,3,4 1,2,3 1,2
1121–2665 319–562 234–457 86.1–151 29.2–64.4
7 6 5 4 3
3113* 1139* 310 223* 68*
Mean response outside the prediction interval. Doses coded numerically with control dose being 1. b Prediction interval for response from the next dose. c Actual mean response for model with next dose included. a
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Table 5 Testing comparison of slopes for the statistical determination of the point of nonlinearity using daily systemic dose (plasma AUC24h) of 2,4-D across doses in adults of both genders after reaching steady-state systemic exposure (4 weeks of continuous dietary exposure).
*
Doses 1a
Slope 1
Doses 2a
Slope 2
Males All (6,5,4,3,2,1) 5,4,3,2,1 4,3,2,1 3,2,1 1,2 1,2,3 1,2,3,4
5.59 2.75 3.42 2.83 2.5 2.83 3.42
5,4,3,2,1 4,3,2,1 3,2,1 2,1 3,4,5,6 4,5,6 5,6
2.75* 3.42* 2.83* 2.5 6.95* 8.69* 16.27*
Females All (7,6,5,4,3,2,1) 6,5,4,3,2,1 5,4,3,2,1 4,3,2,1 3,2,1 1,2 1,2,3 1,2,3,4 1,2,3,4,5
30.59 20.96 31.77 32.88 32.99 32.56 32.99 32.88 31.77
6,5,4,3,2,1 5,4,3,2,1 4,3,2,1 3,2,1 2,1 3,4,5,6,7 4,5,6,7 5,6,7 6,7
20.96* 31.77* 32.88* 32.99 32.56* 36.80* 39.84* 45.87* 43.27*
Slope 2 is statistically different from slope 1. Doses coded numerically with control dose being 1.
a
being parallel and did not need the slopes to change direction as much as a nonlinear change would have required to be significant. The sensitivity of the test is greater than needed for determining nonlinearity and found deviations that are not biologically relevant. 3.5. Comparison of the statistical models Comparing the three methods to the graphs further demonstrates the positive and negative aspects of the methods. For the male data, the second-order method and prediction interval matched the graph well with the highest dose not in line with the lower dose groups. The comparison of slopes however had only the 1,2 slope the same as the 1,2,3 slope. If it were to match the other methods, it would also have had the 1,2,3 slope the same as the 1,2,3,4 slope and the 1,2,3,4 slope the same as the 1,2,3,4,5
slope, but the method detected small differences in slopes. For the females, the second-order method matched the graph picking up the difference between the first 3 doses and the rest of the data. The prediction interval showed that dose 6 and 7 were out of line with the lower doses and was apparent in the graph. When the first 4 doses were fit, the prediction interval found the fifth dose to be in line with this fit. This matched the graph in that dose 4 pulled up the slope of the line so that dose 5 fits. Going to the doses of 1,2,3 and comparing them to dose 4 gave dose 4 being out of line with the first 3 doses. This was a break in the graph, although not as dramatic as the break after dose 5. Table 1 summarizes the 3 statistical methods and their agreement with the visual inspection of the observed data. The PONL determined form visual inspection was listed along with the PONL found from each method. Method 1 was not done iteratively in this table, meaning that doses were excluded and the next model run regardless of whether there was nonlinearity determined at a higher dose. This was done in order to make a more direct comparison to the other methods. Method 1 had the best relationship between the observed data and the results of the statistical analysis, followed by method two. Method 3 found more possible nonlinearities than existed. There were three instances where Method 1 did not find nonlinearity and did not match the visual interpretation (2,4-D data for male pup PND28 and female LD21, and X11422208 male mice plasma). For 2,4-D female LD21 the highest dose was lower than the second to highest dose. The second to highest dose increased greatly from the dose below it. Method 1 placed the regression line between the highest and second highest dose and determined it was linear. This is not really reflective of what occurred, there were two points of nonlinearity. For the other two occurrences, there was a large spread in data points at the highest dose with one point pulling down the regression line.
3.6. Second-order model at a = 0.025 Dropping the a level to 0.025 was considered to address the possibility of the second-order model being too sensitive after 2 additional datasets were encountered that appeared linear visually but had a significant second-order effect. One of these datasets is
Concentration of X11422208 in Plasma (µg/ml)
18 16 14 12 10 8 6 4 2 0 0
5
10
15
20
25
30
35
40
Dose (mg/kg/day) Fig. 4. Analysis of X11422208 plasma concentration in adult female rats in two-generation toxicity study by dropping the a level to 0.025 to reconcile the discrepancy of appearing linear visually and nonlinear by the statistical analysis.
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shown in Fig. 4. The lowering of the a level did work for the 2 newer datasets. Comparing a at 0.025 to a at 0.05, the results found in Table 3 would still flag significance at 0.025 in all but one analysis, the female 4,3,2,1 regression. The fourth dose does appear to be second-order so would be missed by the lower a level. Results from the other initial analyses were in agreement with 29 out of 31 significant findings. For the two that did not match, one was for the analysis after the high dose was dropped and nonlinearity was not readily obvious but the other did look nonlinear. 3.7. Weighted second-order model at a = 0.05 Weighting the second-order analysis with the inverse of the variance of feed consumption was also considered to address a dataset that looked linear but had a second-order effect significant at a = 0.05. There was more variability in the feed data as the doses increased so weighting by the inverse of the variance for feed consumption would lessen the reliance of the analysis on the more variable results at the higher doses. One dataset was run and did result in the second-order effect no longer being significant (i.e., there was no deviation from linearity). Not all data were re-analyzed using the weighted analysis, but this analysis is an option to be considered in the future. The second-order model worked the best for most datasets and is an easy method to implement. However, on occasion, we encountered datasets in which the method indicated nonlinearity while the data visually looked linear. In those cases, lowering the a level or using a weighted analysis with the inverse of the variance for feed consumption as the weighting factor did help. Conflict of interest The authors work for the company at which the substances used as examples are produced. Acknowledgments The authors wish to thank the Industrial Task Force II on 2,4-D Research Data for allowing the data collected in the extended onegeneration dietary toxicity study to be analyzed in this manner. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.yrtph. 2012. 03.013. References Baldrick, P., 2003. Toxicokinetics in preclinical evaluation. Drug Discovery Today 8, 127–133. Barton, H.A., Pastoor, T.P., Baetcke, K., Chambers, J.E., Diliberto, J., Doerrer, N.G., Driver, J.H., Hastings, C.E., Iyengar, S., Krieger, R., Stahl, B., Timchalk, C., 2006.
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The acquisition and application of absorption, distribution, metabolism, and excretion (ADME) data in agricultural chemical safety assessments. Crit. Rev. Toxicol. 36, 9–35. Beatty, D.A., Piegorsch, W.W., 1997. Optimal statistical design for toxicokinetic studies. Stat. Methods Med. Res. 6, 359–376. Creton, S., Saghir, S.A., Bartels, M.J., Billington, R., Davies, W., Dent, M.P., Hawksworth, G.H., Parry, S., Travis, K.Z., 2012. Use of TK to support chemical evaluation: informing high dose selection and study interpretation. Regul. Toxicol. Pharmacol. 62, 241–247. ECHA (European Chemicals Agency), 2008. Guidance on information requirements and chemical safety assessment Chapter R.7c: Endpoint specific guidance. May.. EEC (Official Journal of the European Communities), 1988. Methods for the Determination of Toxicity, 1988. Part B. (Combined chronic toxicity/ carcinogenicity test), Directive 87/302/EEC. EMA (European Medicines Agency), 1994. Toxicokinetics: A Guidance for Assessing Systemic Exposure in Toxicology Studies. November. Goehl, T.J., 1997. Toxicokinetics in the national toxicology program. In: Rapaka, R.S., Chiang, N., Martin, B.R. (Eds.), Pharmacokinetics, Metabolism, and Pharmaceutics of Drugs of Abuse. National Institute on Drug Abuse Research Monograph 173, Rockville, MD, pp. 273–304. Health Canada, 1994. Guidance for Industry: Note for Guidance on Toxicokinetics: The Assessment of Systemic Exposure in Toxicity Studies (ICH Topic S3A). . Hing, J.P., Woolfrey, S.G., Greenslade, D., Wright, P.M.C., 2002. Distinguishing animal subsets in toxicokinetic studies: comparison of non-linear mixed effects modeling with non-compartmental methods. J. Appl. Toxicol. 22, 437–443. Igarashi, T., 1995. The rationale for using logarithmic transformation of concentration data in toxicokinetic studies. J. Toxicol. Sci. 20, 67–72. Igarashi, T., Sekido, T., 1996. Case studies for statistical analysis of toxicokinetic data. Regul. Toxicol. Pharmacol. 23, 193–208. JMAFF (Japanese Ministry of Agriculture, Forestry and Fisheries), 2000. Testing Guidelines for Toxicology Studies, 2000 (Combined Chronic Toxicity/ Oncogenicity Study). Kleinbaum, D.G., Kupper, L.L., 1978. Applied Regression Analysis and Other Multivariable Methods. Duxbury Press, Boston, Massachusetts, pp. 95–101. Nedelman, J.R., Gibiansky, E., Lau, D.T.W., 1995. Applying Bailer’s method for AUC confidence intervals to sparse sampling. Pharm. Res. 12, 124–128. Neter, J., Wasserman, W., Kutner, M.H., 1990. Applied Linear Statistical Models: Regression, Analysis of Variance, and Experimental Designs, third ed. Richard D. Irwin, Inc. Homewood, IL. OECD (Organisation for Economic Co-Operation and Development), 1981. OECD Guideline for the Testing of Chemicals, Guideline 453 (Combined Chronic Toxicity/Carcinogenicity Studies). Saghir, S.A., Mendrala, A.L., Bartels, M.J., Day, S.J., Hansen, S.C., Sushynski, J.M., Bus, J.S., 2006. Strategies to assess systemic exposure of chemicals in subchronic/ chronic diet and drinking water studies. Toxicol. Appl. Pharmacol. 211, 245– 260. Saghir, S.A., Marty, M.S., Clark, A.J., Zablotny, C.L., Bus, J.S., Perala, A.W., Yano, B.L., Neal, B.H., 2009. A dietary dose range-finding and toxicokinetic (TK) study of 2,4-dichlorophenoxyacetic acid (2,4-D) in adult CRL:CD(SD) rats and their offspring: I. Toxicokinetics. The Toxicologist, 108(S1), abstract No. 1161, p. 242. Saghir, S.A., Bartels, M.J., Rick, D.L., McCoy, A.T., Billington, R., Bus J.S., 2011. Assessment of diurnal systemic dose (toxicokinetics) of agrochemicals in regulatory toxicity testing – an integrated approach without additional animals use. Regul. Toxicol. Pharmacol. (submitted as a package of three manuscripts along with this). Schwartz, S., 2001. Providing toxicokinetic support for reproductive toxicology studies in pharmaceutical development. Arch. Toxicol. 75, 381–387. Sweatman, T.W., Renwick, A.G., 1980. The tissue distribution and pharmacokinetics of saccharin in the rat. Toxicology and Applied Pharmacology 55, no. 1 (August): 18–31. US EPA (United States Environmental Protection Agency), 1998. Health Effects Test Guidelines, OPPTS 870.4300 (Combined Chronic Toxicity/Carcinogenicity) EPA712-C-98-212.
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Regulatory Toxicology and Pharmacology journal homepage: www.elsevier.com/locate/yrtph
Statistical methodology to determine kinetically derived maximum tolerated dose in repeat dose toxicity studies Lisa G. McFadden, Michael J. Bartels, David L. Rick, Paul S. Price, Donald D. Fontaine, Shakil A. Saghir ⇑ Toxicology and Environmental Research and Consulting, The Dow Chemical Company, Midland, MI 48674, United States
a r t i c l e
i n f o
Article history: Received 2 December 2011 Available online 2 April 2012 Keywords: Toxicokinetics TK Nonlinearity Statistical approach Nonlinear systemic dose increase
a b s t r a c t Several statistical approaches were evaluated to identify an optimum method for determining a point of nonlinearity (PONL) in toxicokinetic data. (1) A second-order least squares regression model was fit iteratively starting with data from all doses. If the second order term was significant (a < 0.05), the dataset was reevaluated with successive removal of the highest dose until the second-order term became nonsignificant. This dose, whose removal made the second order term non-significant, is an estimate of the PONL. (2) A least squares linear model was fit iteratively starting with data from all doses except the highest. The mean response for the omitted dose was compared to the 95% prediction interval. If the omitted dose falls outside the confidence interval it is an estimate of the PONL. (3) Slopes of least squares linear regression lines for sections of contiguous doses were compared. Nonlinearity was suggested when slopes of compared sections differed. A total of 33 dose–response datasets were evaluated. For these toxicokinetic data, the best statistical approach was the least squares regression analysis with a second-order term. Changing the a level for the second-order term and weighting the second-order analysis by the inverse of feed consumption were also considered. This technique has been shown to give reproducible identification of nonlinearities in TK datasets. Ó 2012 Elsevier Inc. All rights reserved.
1. Introduction Toxicokinetic (TK) analysis is the evaluation of kinetic data to assess systemic exposure to understand the relationship between observed toxicity and administered doses. The TK evaluation of the degree of systemic exposure to a chemical across doses and/ or life-stages requires collection of biological samples from test animals and analysis for parent and/or metabolite(s) of interest (EMA, 1994; Health Canada, 1994; Goehl, 1997; Schwartz, 2001; Baldrick, 2003; Barton et al., 2006; Creton et al., 2012; Saghir et al., 2006, 2011). Nonlinearities in TK are determined by observation of a disproportional increase or decrease in the biomarker (test material and/or metabolite) in the central compartment (blood, sera, and plasma) and/or excreta (usually urine) across doses relative to the ingested test material over 24 h (Saghir et al., 2006, 2011). These nonlinearities in TK parameters may indicate saturation of test material absorption and/or elimination in the test species with increasing dose. This nonlinearity of data in subchronic/ chronic studies can be used to derive a Kinetically-Derived Maximum Dose (KMD) for subsequent toxicity studies (ECHA, 2008; Creton et al., 2012; Saghir et al., 2009, 2011). Currently, nonlinear⇑ Corresponding author. Current address: Syngenta Crop Protection, Inc., 410 Swing Rd, Greensboro, NC 27409, United States. Fax: +1 336 632 7581. E-mail address: [email protected] (S.A. Saghir). 0273-2300/$ - see front matter Ó 2012 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.yrtph.2012.03.013
ities in TK are mostly determined visually (subjectively) by comparing the increase in the biomarker concentration versus the test material intake (Sweatman, 1980; Saghir et al., 2006, 2009, 2011). Although, visual interpretation of the dose–response curves may be satisfactory a statistical method for the determination of nonlinearity will provide the means for reproducible interpretations of a point of nonlinearity (PONL). Lack of any firm statistical method to define PONL can result in potential bias in deriving KMD levels for long-term studies. Overestimation of the KMD could result in conduct of subsequent toxicity studies at too high of dose levels that could introduce artifactual biological effects (Goehl, 1997; Baldrick, 2003). One of the remedies to the current subjective methods for selection of the PONL level(s) from TK datasets is to devise a statistical method that determines the probability (i.e., p-values) above which dose–response becomes nonlinear in order to choose an appropriate, statistically-derived KMD. A number of researchers have looked at various statistical approaches to evaluate questions encompassing TK sampling and data analysis including sparse sampling from different animals to complete the time-course blood concentration profiles and estimating deviation of the data from linearity (Beatty and Piegorsch, 1997; Hing et al., 2002; Igarashi and Sekido, 1996; Nedelman et al., 1995). None, however, have described a detailed method for the analysis of deviation from linearity. Igarashi (1995) focused on the need for a log transformation of the concentration data before
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the analysis and later Igarashi and Sekido (1996) analyzed their data using simple linear regression with cut-off regression coefficients of 0.7 and 1.3 for the data to be considered linear without any formal statistical technique. Their techniques for the analysis of TK data have limitations that prohibit their universal use and can only be used for certain study designs and data. For example chemicals, other than human pharmaceutics, where data are generated from the same animals over a 24 h period to estimate daily systemic dose at different times during exposure and typically use three treated groups and a control are not suited for their analytical approach. Thus a new approach is needed. In this paper, several promising statistical methods are examined and discussed which are appropriate for a typical toxicity study conducted in a chemical industry with as little as three doses and a control. The use of control data in the PONL analysis is necessary as at least three dose levels are required for statistical analysis; therefore, log transformation of the data as described by Igarashi (1995) was not possible as this would exclude the control data. The goal of this paper is to develop a robust statistical method that has the ability to analyze a variety of TK datasets and accurately and objectively estimate the PONL, especially for chemicals where toxicity studies are conducted at limited doses (mostly at low, mid and high doses plus control) as warranted by the regulatory agencies (e.g., OECD, 1981; EEC, 1988; US EPA, 1998; JMAFF, 2000) at doses orders of magnitude different from the expected human exposure through environment (e.g., pesticides).
2. Materials and methods 2.1. Data Data from four different compounds were analyzed from various study types. A total of 33 variable dose–response datasets (four chemicals, two species, genders, dietary and inhalation exposures, levels in milk and nursing pups) were analyzed. Tables 1 and 2 list the study information. The X11422208 (rat [plasma AUC24h] and mouse [plasma concentration, total in urine) and two isomers (X517131 and X513999) of X574175 (rat [plasma AUC24h]) studies had four doses including controls. The X574175 mouse (plasma concentration) and 1,3-dichloropropene (rat plasma concentration) had five doses including controls. The 2,4-D (2,4-dichlorophenoxyacetic acid) study had six doses for most of the experiments. There were seven doses for day (D) 29 females (29 days of exposure), five for lactation day (LD) 21 pups and adult females D 95, four for postnatal day (PND) 28 and PND 35 pups. Data were comprised of plasma AUC24h in all adult rats and PND 35 pups and concentration of 2,4-D in milk and plasma of all other pups.
2.2. Statistical analyses In order to assess with appropriate (statistical) sensitivity the point at which nonlinearity occurred, three methods were examined. All statistical analysis was performed using SAS computer software (SAS Institute Inc., Cary NC), see Supplemental Tables 1–3 for the codes used to run these analyses. The control dose was included in all three models which allowed the method to be applicable to a standard toxicity test with three treated groups and a control. The actual measured ingested or inhaled dose for each individual animal was used whenever available; targeted dose was used when actual dose information was not available. For ease of reporting, doses were coded numerically starting with 1 for the control dose. An example of the coding for the typical study; 2 was code for the low dose, 3 for the mid dose and 4 for the high dose.
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2.3. Statistical method 1 The first method was a least squares regression analysis where responses were regressed against dose with a second-order term (squared value of dose, also known as a quadratic term) added to the model in order to test for nonlinearity (Neter et al., 1990). See Supplemental Table 1 for SAS codes used to run the analysis. A significant second-order term (a 6 0.05) indicated that the model was encountering nonlinearity in the dose–response curve. For this method, the model containing all dose groups was run first followed by dropping the highest dose in subsequent iterations (if previous iteration indicated nonlinearity) until the PONL was found or only three doses (control and two doses) were left. As with any test evaluating linearity, there needs to be at least three doses in the model to test for a second-order effect. If the model with all doses had a significant second-order effect and the next model after deleting the high dose did not, there was nonlinearity due to the high dose. A few datasets were encountered where the dose–response appeared linear visually but had a significant second-order effect. For such scenarios, two approaches were considered: (1) the a level was lowered to 0.025; and (2) the a level was kept at 0.05 and a weighted analysis was performed with the inverse of feed consumption as the weighting factor. 2.4. Statistical method 2 In the second method a least squares linear model was fit to the data using a range of doses. See Supplemental Table 2 for SAS codes used to run the analysis. This model was used to predict the linear response for the next consecutive dose left out of the model and a 95% prediction interval (PI) was calculated around the predicted value (Neter et al., 1990). The actual mean response from the data for the model that included that next consecutive dose was then compared to the prediction interval. If the actual response fell within the interval it was considered linear. If it did not, then this suggested nonlinearity in the actual response. 2.5. Statistical method 3 The third method compared slopes of least squares linear regression lines (Kleinbaum and Kupper, 1978) where responses were regressed against dose. See Supplemental Table 3 for SAS codes used to run the analysis. The first comparison had all doses in the regression model compared to the model with all doses but the highest included. The next, compared a model with all doses except the highest to a model with all doses except the two highest. This was continued sequentially. Also compared were different segments in which all doses were represented between the two models with splits being made at consecutively higher doses. For data with 6 doses, the first comparison compared the slope of the regression line that included doses one and two to the slope of the regression line that included doses three to six. The next comparison was between the slope for the line with doses one to three and the slope for the line with doses four to six. The slopes of the different models were compared at a 6 0.05. In this case if the slopes differed, it suggested a possible nonlinearity between the models since the slopes were not parallel. 3. Results and discussion 3.1. Visual inspection of the data In order to compare the three statistical methods and choose the most appropriate test for the determination of PONL from linearity, 33 sets of data were analyzed (Table 2). Out of those 33
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Table 1 Detailed information of the studies listing compounds, species, doses and relationship of statistical method with the observed data. Compound
Study
Sample type
Dosesa
Visual PONLb
Statistical methods used for PONLc 1
2
3
X11422208
28-day diet in rats
Male plasma AUC24h Female plasma AUC24h
4 4
None None
None None
None 3
4,3 None
X11422208
90-day diet in mice
Male plasma conc Female plasma conc Male total in urine Female total in urine
4 4 4 4
4 4 4 4
None 4 4 4,3
4 4 4 4
4 4 4,3 4,3
X574175
28-day diet in rats
Male plasma AUC24h (isomer J) Male plasma AUC24h (isomer L)
4 4
4,3 4
4,3 3
3 4,3
4,3 4,3
X574175
28-day diet in mice
Male plasma conc (isomer J) Male plasma conc (isomer L) Female plasma conc (isomer J) Female plasma conc (isomer L)
5 5 5 5
5 5 5 5
5,4 5 5 5
5,4,3 None 5,4 5
5,4,3 5,4,3 5,4,3 5,4,3
1,3-DCP
3-h inhalation in rats
Male plasma conc (cis isomer) Male plasma conc (trans isomer)
5 5
5 5
5 5
5,4 5
5,4 5,4,3
2,4-D
1-gen. diet in rats
Male plasma AUC24h D-28 Male plasma AUC24h D-71 Female plasma AUC24h D-29 Female plasma AUC24h D-95 Female plasma AUC24h GD-17 Female plasma AUC24h LD-4 Female plasma AUC24h LD-14 Milk conc LD-4 Milk conc LD-14 Male pup plasma conc LD-4 Male pup plasma conc LD-14 Male pup plasma conc LD-21 Male pup plasma conc PND-28
6 6 7 5 6 6 6 6 6 6 6 5 4
6 6,5 7,6,5,4 5,4 6 6,5,4 6,5 6 None 6,5,4 6,5,4 5 4
6 5 7,6,5,4 5,4 5,4 4 6,5 5 3 4 5,4 5 None
6 5 7,6,4,3 5,4,3 6,5,4,3 6,4,3 5,3 5 5,3 4 4,3 5,3 3
6,5,4 5 7,6,5,3 5,4,3 6,5,4,3 6,5,4,3 6,5,4,3 6,5,4 6,5,4 5,4 6,5,4,3 5,4,3 4,3
1,3-DCP, 1,3-dichloropropene; 2,4-D, 2,4-dichloro-phenoxyacetic acid; gen., generation; D, days after exposure; GD, gestational day; LD, lactational day; PND, postnatal day; PONL, point of nonlinearity; AUC, area under the curve 24 h; conc, concentration. a Number of doses animals were exposed to including control. b Visual determination of doses where nonlinearity was observed. c Statistically significant doses suggesting nonlinearity in each method. 1. A least squares regression model with a quadratic term. 2. A least squares linear model for a predicted response and prediction. 3. A comparison of slopes of least squares linear regressions.
Table 2 Summary of the compound, study types and samples analyzed for the determination of nonlinearity using the three proposed statistical methods. Compound
Study type
Data type
Datasets
X11422208 X11422208 X574175 X574175 1,3-DCP 2,4-D
Rat 28-day diet Mouse 90-day diet Rat 28-day diet Rat 28-day diet Rat 3-hour inhalation Rat 1-generation diet
Plasma AUC24h (M and F) Plasma concentration and total in urine (M and F) Plasma AUC24h (M) two isomers Plasma concentration (M and F) two isomers Plasma concentration (M) two isomers Plasma AUC24h P1 (M) D 28 and D 71 Plasma AUC24h P1 (F) D 29, D 95, GD 17, LD 4 and LD 14 Milk concentration P1 (F) LD 4 and LD 14 Plasma concentration F1 (M and F) LD 4, LD 14, LD 21, PND 28 Plasma AUC24h F1(M and F) PND 35
2 4 2 4 2 2 5 2 8 2
M, male; F, female, P1, parental-1; F1, filial-1; D, days after exposure; GD, gestational day; LD, lactational day; PND, postnatal day. AUC, area under the curve 24 h; 1,3-DCP, 1,3-dichloropropene; 2,4-D, 2,4-dichloro-phenoxyacetic acid.
datasets, the most data rich sets are presented here as examples to show the pros and cons of each of the three statistical tests used to determine PONL. To do this, an expert opinion was obtained for each of the 33 data sets on whether a PONL existed and its value. The statistical method results were then examined to see if they demonstrated concordance with those opinions (Table 1). The numbers of the doses where nonlinearity occurred are listed for the visual inspection and each statistical method. Fig. 1 is a graph used in visual inspection of the observed daily systemic dose, as measured by the plasma AUC24h, for the male and
female rats across doses after 4 weeks of dietary exposure to 2,4-D along with the trend lines showing expected AUC24h values as dose levels are increased. The expected daily systemic doses (AUC24h) (indicated by trend lines) were calculated using the actual ingestion of the 2,4-D through the test material fortified diet at the lowest dose level and extrapolating through the origin ‘‘0’’ to the higher doses. Visual inspection of the data revealed that only the highest dose in males was very different in response than the other doses. However, the four higher doses in females were very different in response (Fig. 1). The deviation between the observed and
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1400
Plasma AUC24 h of 2,4-D (µg h ml-1)
1200
Observed Male Expected Male Observed Female Expected Female
1000
800
600
400
200
0 0
10
20
30
40
50
60
70
80
90
100
2,4-D dose (mg/kg/day) Fig. 1. Systemic exposure of 2,4-D to male and female rats, as measured by the plasma AUC24h across doses after 4 weeks of dietary exposure along with the expected systemic dose based on the difference in the test material intake across doses showing points of nonlinearity.
expected values provided the visual determination of the PONL; in this case it was P 69 mg/kg/day for the male and P 14 mg/kg/day for the female rats (Fig. 1). Fig. 2 shows the systemic exposure (plasma concentration) of the two isoforms of X574175 to male and female mice as measured after 4 weeks of dietary exposure to X574175. The expected systemic doses based on the difference in the test material intake across doses showed points of nonlinearity in male (P19 mg/kg/ day for X517131 and P23 mg/kg/day for X513999) and female (none for X517131 and P32 mg/kg/day for X513999) mice. It is interesting to note from these graphs that the concentration of X517131 was higher than expected from a dose-proportional increase in the male mice and was dose-proportional in female mice. In contrast to this, the concentration of X513999 was less than the expected dose-proportional increase at the highest dose in both male and female mice (Fig. 2). Another important observation is that the dietary intake of X574175 was higher in the female mice; however, either the absorption was lower or elimination was higher by the female mice, relative to males, resulting in a lower plasma concentration at each dose level (Fig. 2). Fig. 3 shows the plasma concentration and 24 h urinary elimination of X11422208 by male and female mice after 13 weeks of dietary exposure. The plasma concentrations of X11422208 were dose-proportional only up to the middle dose for both male and female mice. In the case of males, the systemic exposure became supra-linear between the middle and high doses. However, in females, the plasma concentration remained almost unchanged between the middle and the high doses, being sub-linear relative to expected proportionality (Fig. 3). Total elimination of X11422208 in 24 h urine remained dose proportional only up to the middle dose and showed less than a dose proportional increase at the highest dose, both in male and female mice (Fig. 3). The PONL for both male and female mice was much lower than the highest doses, closer to the middle (P92 mg/kg/day for males and P227 mg/kg/day for females) doses. Taken together, the directions of the PONLs for plasma versus that for urine values suggested that in the case of males, elimination of X11422208 from plasma was saturated at the highest dose; whereas, for females, absorption of X11422208 from the gastrointestinal (GI) tract was saturated at the highest dose. These inter-
pretations were supported by a higher than expected increase in the liver weight along with histopathological changes in male mice at the highest dose. On the other hand, no additional changes in the liver weight or histopathology was observed in the female mice after 13 weeks of dosing when compared to a 4 week dietary study (unpublished data). Plasma concentrations of X11422208 remained linear in the 4 week dietary study at 3- to 4-fold higher doses than that used in the 13 week study (unpublished data). In some or even most cases visual inspection of the observed and expected daily systemic dose data may lead to a reasonable value of PONL. However, this method may induce human bias resulting in an incorrect assessment of the PONL. 3.2. Second-order model (Method 1) Table 3 shows the results from fitting a second-order model to the representative 2,4-D data. Dose levels were coded numerically starting with 1 for the control group. The models tested have the doses listed along with the p-value of the second-order term. An asterisk denotes significance and indicates deviation from linearity. The 2,4-D males showed deviation from linearity only in the complete model which showed the deviation occurred after the fifth dose. The sixth dose did not fit the linear model. The 2,4-D females showed deviation from linearity down to the fourth dose which means deviation occurred after the third dose. Only the first three doses fit the linear model for females, which is consistent with the PONL based on the visual observation. 3.3. Prediction interval (Method 2) Results of the prediction interval method are presented in Table 4. This table lists the doses in the model used to calculate the prediction interval, the prediction interval, the next higher dose it based the prediction on, and the actual mean response of the next higher dose. An asterisk denotes that the mean response is outside the prediction interval indicating possible deviation from linearity. The prediction interval results for the male 2,4-D data (Table 4) matched the second-order model results (presented in Table 3) as well as the visual interpretation. The mean response for the sixth dose did not fall within the prediction interval for the model con-
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8000
Plasma concentration of X517131 (ng/ml)
7000 6000 5000 4000 3000 Observed Male
2000
Expected Male Observed female
1000
Expected Female 0
Plasma concentration of X513999 (ng/ml)
12000
0
20
40
60
80
100
120
140
160
180
200
10000
8000
6000
4000 Observed Male Expected Male 2000
Observed female Expected Female
0 0
10
20
30
40 50 60 Dose (mg/kg/day)
70
80
90
100
Fig. 2. Systemic exposure of two components (X517131 and X513999) of X574175 to male and female mice as measured by the plasma concentration across doses after 4 weeks of dietary exposure along with the expected systemic dose based on the difference in the test material intake across doses showing points of nonlinearity.
taining the five doses, which suggested possible deviation from linearity (Table 4). Similarly, the second-order term was significant for the model containing all six doses, which confirmed a deviation from linearity at or above the fifth dose (Table 3). The female data were not as clear from the prediction interval runs. The models found doses 7, 6, 4 and 3 deviated from linearity as they did not have mean responses within the prediction interval. The results for doses 7, 6 and 4 matched the second-order model results. However, the results did not match for doses 5 and 3. Dose 3 was outside the prediction interval but appears linear. The lower variability at these low doses contributed to this finding. Dose 5 appears nonlinear and is found to be so by the second-order method, but fell within the prediction interval due to the very large amount of variability at this dose. 3.4. Comparison of slopes (Method 3) The comparison of slopes from linear regression lines are presented in Table 5. The first column lists the doses included in the
first model with the second column being the slope corresponding to that model. The third column lists the doses included in the second model and the fourth column is the slope corresponding to the second model. The slopes of these two models were compared and if they were different an asterisk was placed on the slope in column 4. In this table only two comparisons were not statistically different. The first instance was in males, the models with only the first two doses (control and first treated dose, slope 2.50) and the first three doses (control and the first two treated doses, slope 2.83). The second instance was in females, the models with the first three doses (slope 32.99) and the first four doses (slope 32.88). This method was too sensitive, finding differences between slopes that were very small. For example, the test indicated that the slope of 32.88 (from doses 1,2,3, and 4) was not different from 32.99 (of doses 1,2, and 3) which was a reasonable subjective conclusion but the slopes of 32.56 and 32.99 were different (Table 5) even though the reasonable conclusion would have been that they were not different. Similarly, in the males, the deviation from linearity only occurred after the fifth dose by visual inspection and by the
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90
Concentration of X11422208 in plasma (µg/g)
Observed Male 80
Expected Male Observed female
70
Expected Female
60 50 40 30 20 10 0 7000
Amount of X11422208 in 24 h urine (µg)
Observed Male Expected Male
6000
Observed female Expected Female 5000
4000
3000
2000
1000
0
0
100
200
300
400
500
600
Dose (mg/kg/day) Fig. 3. Systemic exposure of X11422208 to male and female mice as measured by the plasma concentration across doses after 13 weeks of dietary exposure and the urinary elimination (lg over 24 h) of the daily ingested dose along with the expected systemic dose based on the difference in the test material intake across doses showing points of nonlinearity.
Table 3 Testing second-order model for the statistical determination of the point of nonlinearity using daily systemic dose (plasma AUC24h) of 2,4-D across doses in adults of both genders after reaching steady-state systemic exposure (4 weeks of continuous dietary exposure).
*
Model dosesa
Sex
p-value of quadratic term
All doses (6,5,4,3,2,1) 5,4,3,2,1 4,3,2,1 3,2,1 All doses (7,6,5,4,3,2,1) 6,5,4,3,2,1 5,4,3,2,1 4,3,2,1 3,2,1
Male Male Male Male Female Female Female Female Female
0.0145* 0.3734 0.9971 0.9492 0.0022* 0.0028* 0.0019* 0.0324* 0.7036
Table 4 Testing prediction interval for response from the next dose for the statistical determination of the point of nonlinearity using daily systemic dose (plasma AUC24h) of 2,4-D across doses in adults of both genders after reaching steady-state systemic exposure (4 weeks of continuous dietary exposure).
Statistically significant at p 6 0.05. a Doses coded numerically with control dose being 1.
second-order test; therefore, expectations were that the slope for the model of 1,2,3,4,5 would not be different from the slope for the model of 1,2,3,4 but the slope comparison test found these slopes different. The slope differences were due to the lines not
*
Doses in modela
Prediction intervalb
Next dose
Mean responsec
Males 1,2,3,4,5 1,2,3,4 1,2,3 1,2
108–337 171–293 75.8–158 35.0–70.7
6 5 4 3
579* 179 147 60
Females 1,2,3,4,5,6 1,2,3,4,5 1,2,3,4 1,2,3 1,2
1121–2665 319–562 234–457 86.1–151 29.2–64.4
7 6 5 4 3
3113* 1139* 310 223* 68*
Mean response outside the prediction interval. Doses coded numerically with control dose being 1. b Prediction interval for response from the next dose. c Actual mean response for model with next dose included. a
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Table 5 Testing comparison of slopes for the statistical determination of the point of nonlinearity using daily systemic dose (plasma AUC24h) of 2,4-D across doses in adults of both genders after reaching steady-state systemic exposure (4 weeks of continuous dietary exposure).
*
Doses 1a
Slope 1
Doses 2a
Slope 2
Males All (6,5,4,3,2,1) 5,4,3,2,1 4,3,2,1 3,2,1 1,2 1,2,3 1,2,3,4
5.59 2.75 3.42 2.83 2.5 2.83 3.42
5,4,3,2,1 4,3,2,1 3,2,1 2,1 3,4,5,6 4,5,6 5,6
2.75* 3.42* 2.83* 2.5 6.95* 8.69* 16.27*
Females All (7,6,5,4,3,2,1) 6,5,4,3,2,1 5,4,3,2,1 4,3,2,1 3,2,1 1,2 1,2,3 1,2,3,4 1,2,3,4,5
30.59 20.96 31.77 32.88 32.99 32.56 32.99 32.88 31.77
6,5,4,3,2,1 5,4,3,2,1 4,3,2,1 3,2,1 2,1 3,4,5,6,7 4,5,6,7 5,6,7 6,7
20.96* 31.77* 32.88* 32.99 32.56* 36.80* 39.84* 45.87* 43.27*
Slope 2 is statistically different from slope 1. Doses coded numerically with control dose being 1.
a
being parallel and did not need the slopes to change direction as much as a nonlinear change would have required to be significant. The sensitivity of the test is greater than needed for determining nonlinearity and found deviations that are not biologically relevant. 3.5. Comparison of the statistical models Comparing the three methods to the graphs further demonstrates the positive and negative aspects of the methods. For the male data, the second-order method and prediction interval matched the graph well with the highest dose not in line with the lower dose groups. The comparison of slopes however had only the 1,2 slope the same as the 1,2,3 slope. If it were to match the other methods, it would also have had the 1,2,3 slope the same as the 1,2,3,4 slope and the 1,2,3,4 slope the same as the 1,2,3,4,5
slope, but the method detected small differences in slopes. For the females, the second-order method matched the graph picking up the difference between the first 3 doses and the rest of the data. The prediction interval showed that dose 6 and 7 were out of line with the lower doses and was apparent in the graph. When the first 4 doses were fit, the prediction interval found the fifth dose to be in line with this fit. This matched the graph in that dose 4 pulled up the slope of the line so that dose 5 fits. Going to the doses of 1,2,3 and comparing them to dose 4 gave dose 4 being out of line with the first 3 doses. This was a break in the graph, although not as dramatic as the break after dose 5. Table 1 summarizes the 3 statistical methods and their agreement with the visual inspection of the observed data. The PONL determined form visual inspection was listed along with the PONL found from each method. Method 1 was not done iteratively in this table, meaning that doses were excluded and the next model run regardless of whether there was nonlinearity determined at a higher dose. This was done in order to make a more direct comparison to the other methods. Method 1 had the best relationship between the observed data and the results of the statistical analysis, followed by method two. Method 3 found more possible nonlinearities than existed. There were three instances where Method 1 did not find nonlinearity and did not match the visual interpretation (2,4-D data for male pup PND28 and female LD21, and X11422208 male mice plasma). For 2,4-D female LD21 the highest dose was lower than the second to highest dose. The second to highest dose increased greatly from the dose below it. Method 1 placed the regression line between the highest and second highest dose and determined it was linear. This is not really reflective of what occurred, there were two points of nonlinearity. For the other two occurrences, there was a large spread in data points at the highest dose with one point pulling down the regression line.
3.6. Second-order model at a = 0.025 Dropping the a level to 0.025 was considered to address the possibility of the second-order model being too sensitive after 2 additional datasets were encountered that appeared linear visually but had a significant second-order effect. One of these datasets is
Concentration of X11422208 in Plasma (µg/ml)
18 16 14 12 10 8 6 4 2 0 0
5
10
15
20
25
30
35
40
Dose (mg/kg/day) Fig. 4. Analysis of X11422208 plasma concentration in adult female rats in two-generation toxicity study by dropping the a level to 0.025 to reconcile the discrepancy of appearing linear visually and nonlinear by the statistical analysis.
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shown in Fig. 4. The lowering of the a level did work for the 2 newer datasets. Comparing a at 0.025 to a at 0.05, the results found in Table 3 would still flag significance at 0.025 in all but one analysis, the female 4,3,2,1 regression. The fourth dose does appear to be second-order so would be missed by the lower a level. Results from the other initial analyses were in agreement with 29 out of 31 significant findings. For the two that did not match, one was for the analysis after the high dose was dropped and nonlinearity was not readily obvious but the other did look nonlinear. 3.7. Weighted second-order model at a = 0.05 Weighting the second-order analysis with the inverse of the variance of feed consumption was also considered to address a dataset that looked linear but had a second-order effect significant at a = 0.05. There was more variability in the feed data as the doses increased so weighting by the inverse of the variance for feed consumption would lessen the reliance of the analysis on the more variable results at the higher doses. One dataset was run and did result in the second-order effect no longer being significant (i.e., there was no deviation from linearity). Not all data were re-analyzed using the weighted analysis, but this analysis is an option to be considered in the future. The second-order model worked the best for most datasets and is an easy method to implement. However, on occasion, we encountered datasets in which the method indicated nonlinearity while the data visually looked linear. In those cases, lowering the a level or using a weighted analysis with the inverse of the variance for feed consumption as the weighting factor did help. Conflict of interest The authors work for the company at which the substances used as examples are produced. Acknowledgments The authors wish to thank the Industrial Task Force II on 2,4-D Research Data for allowing the data collected in the extended onegeneration dietary toxicity study to be analyzed in this manner. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.yrtph. 2012. 03.013. References Baldrick, P., 2003. Toxicokinetics in preclinical evaluation. Drug Discovery Today 8, 127–133. Barton, H.A., Pastoor, T.P., Baetcke, K., Chambers, J.E., Diliberto, J., Doerrer, N.G., Driver, J.H., Hastings, C.E., Iyengar, S., Krieger, R., Stahl, B., Timchalk, C., 2006.
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