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Appendix C Analysis of a Mixture of Five Phthalates: A Case Study The objective of this appendix is to provide details on an approach to the evaluation of âlow-doseâ mixture effects (see discussion in Chapter 5) by using data on a mixture of phthalates. There are many ways of conceptualizing a criti- cal dose of each chemical in a mixture associated with âno observable effect,â such as no-observed-adverse-effect levels (NOAELs) or benchmark doses (BMDs). For illustration purposes, a BMD associated with a benchmark re- sponse (BMR) of 5% is estimated for each chemical in a mixture of phthalates and is used to determine a âmixture BMDâ for a specified mixing ratio, assum- ing dose addition. The choice of a 5% BMR is for illustration only; other values may be selected. The mixture BMD depends on the mixing ratio of the compo- nents, and a tiered analysis strategy is described to determine critical doses of the chemicals in the mixture. Howdeshell et al. (2008) reported on the effect that a mixture of five phthalate esters (BBP, DBP, DEHP, DIBP, and DPP) had on fetal testicular tes- tosterone production. The mixture was selected so that the dose of each phthal- ate was proportional to a dose that yielded about equal reduction in testosterone when the components were given alone; that is, they used BBP, DBP, DEHP, and DIBP each at one dose and DPP at one-third that dose. Single-chemical data were used to predict the effect of the mixture at the specified ratio assuming dose addition; the observed fixed-ratio mixture dose-response data were com- pared with the dose-response predicted under dose addition. However, Howde- shell et al. did not use the dose-addition formula given in Chapter 4 (Equation 1) but rather an approximate approach to dose addition that used the average of the Hill slopes for the individual chemicals. The analytic method used in this ap- pendix is based on a more general dose-additive model than and a somewhat different dose-response model from that used by Howdeshell et al. (2008). Here, dose addition is performed by using the formula from Chapter 4 (Equation 1) with the different slopes of the dose-response curves of the mixture components, and equality of the slopes is tested. Specifically, a nonlinear logistic dose- 147
148 Phthalates and Cumulative Risk Assessment: The Tasks Ahead response model is used to facilitate a point estimate of a BMDâcorresponding to a BMR of 5%âfor each chemical alone. A mixture BMD is estimated from the dose-additive model and compared with that estimated from the observed mixture data at the specified mixing ratio. Furthermore, the dose-additive model is used to demonstrate that the mixture BMD is not constant across mixing ra- tios. That is, the point estimate of the mixture BMD predicted under dose addi- tion is shown to be numerically different if observed and hypothetical mixing ratios of the five chemicals are used. The illustration is concluded with a de- scription of a tiered analytic strategy for mixtures. METHODS Data were kindly provided by Earl Gray, Jr., in the Reproductive Toxicol- ogy Division, National Health and Environmental Effects Research Laboratory, Office of Research and Development, Environmental Protection Agency, Re- search Triangle Park, NC. Experimental Data. Pregnant Sprague-Dawley rats were dosed by gavage on gestation day (GD) 8-18 with either vehicle control (dose, 0), a dose of one of the chemicals, or a dose of the mixture of five phthalates (BBP, DBP, DEHP, DIBP, and DPP) in a mixing ratio of 3:3:3:3:1. DEP was also evaluated in the single-chemical studies but showed no effect; the DEP data have been retained because they provide additional information on variability. Both single-chemical and mixture studies were conducted in blocks (incomplete block design) with one or two dams per treatment per block with two to four blocks per chemical for a total of 166 litters across chemicals and doses. Testosterone was extracted on GD 18 from the testes of the first three males in each litter and measured with radioimmunoassay. Details are given in Howdeshell et al. (2008). The average of the two measurements (one per testis) for each fetus was used in the analysis herein. Initial Statistical Analysis. A mixed-effects analysis of variance was used to test for differences in control-group means while adjusting for intralitter correlated data. There was a significant difference in the control-group means of testoster- one (in nanograms per milliliter of medium) between studies and a significant block effect, so the data from all studies were adjusted by the average control- group value per block (giving percent of control). Construction of an Additivity Model. The general strategy for the analysis of the data was to use the single-chemical data to fit a nonlinear logistic model of the mean (Âµ) testosterone concentration (percent of control) for the five single chemicals and for the fixed-ratio mixture (in terms of total dose), that is,
Appendix C 149 (1 â Î± i )[1 + exp(â Î² 0i )] Âµi = Î± i + , 1 + exp[â( Î² 0i + Î² i x )] where x is the dose, Î±i is the parameter associated with the maximum effect for the ith chemical or mixture, Î²i is the (negative) parameter associated with the slope for the ith chemical or mixture, and Î²0i is the parameter associated with the shape of the curve. The term [1 + exp(â Î² 0i )] was included in the numerator to force the mean to equal 1 for the control group (x = 0). It was assumed that the observed relative testosterone concentration differed from the model mean, ï¬Âµ, by additive independent zero-mean normally distributed random terms representing between-pup (within-litter) and between-litter variations (that is, a nonlinear mixed-effects model was used with a linear random-effect, adjusting for intrali- ter correlations). Preliminary analyses demonstrated that the sample variances among chemicals, doses, and litters increased with the sample means; this sug- gested that the within-litter variation is proportional to the mean. When the within-litter values were adjusted for the dose-group mean, the variation was relatively similar and suggested a common interlitter variance. The model adopted therefore set the within-litter variance to be proportional to the pre- dicted mean and set the between-litter standard deviation to be constant. The model was estimated with all three parameters per chemical and mixture (18 mean parameters and two parameters for the standard deviations). When the model dose-response curve is inverted, the dose, EDi(Âµ0), of the ith chemical that is required to produce a given mean, Âµ0, is â¡ ( Âµ0 â Î± i ) â¤ ln â¢ â¥ â Î² 0i â£ 1 â Âµ0 + (1 â Î± i ) exp(â Î² 0i ) â¦ EDi ( Âµ0 ) = . Î²i Therefore, if component doses of a mixture are given by ai tadd , where the ai are fixed proportions and tadd is the total mixture dose, then the general dose- additive model (see Altenburger et al. 2000 and Gennings et al. 2004) gives the dose-response curve for this fixed-proportion mixture as â1 â¡ 5 ai â¤ tadd = â¢ â â¥ â£ i =1 EDi ( Âµ0 ) â¦ â1 â¡ â¤ â¢ â¥ â¢ â¥ â¢ 5 ai â¥ = â¢â â¥ . â¢ i =1 â¡ ( Âµ0 â Î± i ) â¤ â¥ â¢ ln â¢1 â Âµ + (1 â Î± ) exp(â Î² ) â¥ â Î² 0i â¥ â¢ â£ 0 i 0i â¦ â¥ â¢ â£ Î²i â¥ â¦
150 Phthalates and Cumulative Risk Assessment: The Tasks Ahead The mixture data were also fitted to a nonlinear model of the same form, in terms of total dose, as used for the components. The mixture BMD with a 5% BMR was estimated from the mixture model and from the dose-additive model.1 For comparison, an independent-action model based on percentage of re- sponse to individual chemicals (Ïi) was estimated, where2 Âµi â Î± i 1 + exp(â Î² 0i ) Ïi = = . 1 â Î±i 1 + exp â¡ â ( Î² 0i + Î² i x ) â¤ â£ â¦ If Ï measures the fraction of the maximum response, then 5 Ï ind = âÏ . i =1 i It is important to note that the independent-action model as used here is not a probabilistic model; it makes the conceptual leap of substituting fractional effect (the fraction of the maximum response) for probability of occurrence (see Chapter 4). It is not based on the assumption of statistical independence. More- over, there is no way to estimate the maximum effect by using independent ac- tion; here, for illustration, it is assumed that the maximum effect is 100% sup- pression of testosterone because the maximum likelihood estimate for DEHP alone has a maximum effect of 100% suppression. RESULTS Preliminary analyses indicated significant differences in mean testosterone concentrations among the vehicle control groups and a significant difference in the means among the blocks within control groups. Therefore, the later analyses were based on percent control values, which were calculated by dividing the average testosterone concentration per pup by the corresponding intrablock av- erage control mean. The nonlinear logistic mixed-effects model was fitted to the dose-response data from each single chemical and to the mixture data in terms of total dose; the model allowed intralitter correlated data. All five slope parameters were nega- tive and significant, indicating that as the dose increases, there is a significant decrease in testosterone concentration. The five slope parameters were statisti- 1 The model parameters were estimated by maximizing the likelihood of the observa- tions, and confidence limits were estimated with the profile likelihood method. All calcu- lations were performed in an Excel spreadsheet with components coded in Visual Basic for Applications. 2 Recall that response in this case is the reduction in testosterone concentration and that there is a maximum response.
Appendix C 151 cally inhomogeneous (p = 0.03, likelihood ratio test) with point estimates rang- ing from â0.002 to â0.040 per milligram per kilogram per day. Figure C-1 pro- vides the observations and model-predicted dose-response curves (for the mean response, at the maximum likelihood) for the five phthalates. In general, the data are adequately represented by the nonlinear logistic model. Figure C-2 presents the observed mixture data in terms of total dose. The solid curve is the model fit based on the nonlinear logistic model, which adequately represents the observed data. The dashed curve (Figure C-2A) is the dose-response model for the mix- ture under the assumption of additivity. For comparison, the predicted independ- ent-action dose-response curve is provided in Figure C-2B. In this case, the ex- perimentally observed mixture data are adequately approximated by both the dose-additive model and the independent-action model. In most cases, mixture data are not available to make such a comparison, and single-chemical data are used to approximate the mixture through an additivity model; in this case, dose addition is a reasonable default to use when mixture data are not available. It is of interest to determine a critical dose for the mixture of five phthal- ates and compare the adjusted critical doses of the individual components with their unadjusted critical doses. When the mixing ratio of the chemicals is speci- fied, a BMD can be estimated for the mixture by using dose addition. BMD es- timates for each of the five chemicals are provided in Table C-1 with lower one- sided 95% confidence limits. BMDs for the mixture (with a specified mixing ratio) and as predicted under additivity for the same mixing ratio (with the pro- portion of the ith chemical denoted by ai) were estimated with the single- chemical and mixture models (Table C-1). Specifically, the BMD for the mix- ture (with fixed mixing ratio) under additivity is estimated as â1 â1 â 5 ai â â 0.23 0.23 0.23 0.08 0.23 â tadd = ââ â = â + + + + â = 52 mg/kg-d. â i =1 BMDi â â 116 30 49 25 126 â The mixture BMD as predicted by dose addition depends on the mixing ratios of the chemicals. To illustrate that point, consider three mixing ratios of the five phthalates for which single-chemical data are available (from the study by Howdeshell et al. 2008). Table C-2 includes the mixing proportions for each case and the corresponding concentrations of each chemical in such mixtures at the mixture BMD (assuming dose addition). Such mixture BMDs depend on the mixing ratio of the chemicals. A tiered analytic strategy is suggested by consid- eration of the following and other cases. â Case 1 is based on a mixture in which the mixing ratio for each single- chemical component concentration is proportional to the BMD for each single chemical. The single-chemical component concentrations in the BMD mixture correspond to dividing each BMD by the number of active chemicals in the mix- tureâhere, five. The single-chemical component concentrations in the BMD mixture can be considered as adjusted critical valuesâany mixture that contains
152 Phthalates and Cumulative Risk Assessment: The Tasks Ahead single-chemical component concentrations that are each less than or equal to their adjusted critical values3 will (under dose addition) invoke a response less than the BMR. In case 1, the mixture BMD is 69 mg/kg-d under additivity, and the adjusted critical values for the five chemicals range from 5 mg/kg-d for DPP to 25 mg/kg-d for DIBP (Table C-2). This case is especially simple because the adjusted critical values are just one-fifth of the single-chemical BMDs (Table C- 1). When the exposure concentration of each single chemical in some mixture is below the adjusted critical value (for any mixing ratio), the response to the mix- ture is associated with a lower BMR than that used to construct the adjusted critical values (here, the BMR is 5%). â Cases 2 and 3 are based on exposure data presented in Table 2-2; data on DPP as a parent compound were not included, and it is omitted from these two cases. Table 2-2 presents urinary concentrations of metabolites of the parent compounds, but the fraction of the parent diester that ends up in the urine varies widely among the phthalates. For example, 5-10% of DEHP is excreted as TABLE C-1 Estimated BMDs Associated with 5% BMRa for Single Chemicals and Mixture Data Based on Nonlinear Logistic Model and Estimated with Mixed-Effects Model Accounting for Intralitter Correlated Datab Lower One-Sided 95% Chemical BMD (mg/kg-d) Confidence Limit (mg/kg-d) BBP 116 66 DBP 30 20 DEHP 49 31 DPP 25 10 DIBP 126 47 Mixture 74 39 Mixture (additivity) 52 39 a The response evaluated here is the fractional reduction of testosterone concentration relative to the testosterone concentration at zero dose. Other definitions could be contem- plated, such as the change relative to the maximum reduction achievable or, in view of the variation observed in average testosterone concentrations at zero dose between differ- ent groups of animals, some change related to a measure of the width of the distribution of those zero-dose testosterone concentrations. The choice here has been arbitrarily se- lected for demonstration purposes. b The mixture components are each at 23% except DPP, which is 8% of the mixture. Study details are included in Howdeshell et al. (2008). 3 Any particular set of adjusted critical values have to be treated together as a set for a particular mixing ratio of the components. There must be no mixing and matching of adjusted critical values obtained from different mixtures.
Appendix C 153 TABLE C-2 Three Mixtures to Illustrate an Approach to Calculating Adjusted Critical Doses for Single Chemicals in a Mixturea Mixing Ratios That Sum to 1 Mixture BMD, (Single-Chemical Dose [mg/kg] in Mixture BMD, Assuming Additivity Assuming Additivity)b (mg/kg) BBP DBP DEHP DPP DIBP Case a1 a2 a3 a5 a6 tadd 1 0.336 0.086 0.143 0.072 0.363 (23.3) (6.0) (9.9) (5.0) (25.2) 69.3 2 0.13 0.19 0.66 0.02 (6.2) (9.0) (31.4) â (1.0) 47.6 3 0.02 0.38 0.48 0.12 (0.8) (16.1) (20.3) â (5.1) 42.4 a Case 1 corresponds to dividing each single chemical BMD by 5 (the number of active chemicals in the mixture). Case 2 is based on the relative proportion of the parent com- pound from its metabolites at the 50th percentile as evaluated in the NHANES study for the five chemicals (see Table 2-2). Case 3 is based on the relative proportion of the parent compound from its metabolites at the 50th percentile as evaluated in the Wittassek et al. (2007) study (see Table 2-2). The mixture BMD depends on the mixing ratio. b The single-chemical doses for the mixture BMD under additivity sum to the mixture BMD in the last column. MEHP, whereas more than 90% of DBP is excreted as MBP. For this example, we assumed that the sum of MEHP, MECPP, MEOHP, and MEHHP (DEHP metabolites) represents 50% of parent DEHP. Because less is known about the excretion of BBP, DBP, and DIBP as measured by the listed metabolites, we assumed that the excretion of the corresponding metabolites is roughly similar to the exposure to the parent compound. So, for illustration only, the mixing pro- portions of the four parent compounds were calculated on the basis of the pro- portion of the sum across the metabolites (using the 50th percentile values) for the four parent compounds, with the DEHP metabolites doubled. Case 2 corre- sponds to the values from the National Health and Nutrition Examination Sur- vey (NHANES); case 3 corresponds to the German study values (see Table 2-2). For case 2, the mixture BMD is 48 mg/kg under dose addition, and the adjusted critical values for the remaining four chemicals range from 1 mg/kg for DIBP to 31 mg/kg for DEHP (Table C-2). For case 3, the mixture BMD is 42 mg/kg un- der additivity, and the adjusted critical values for the remaining four chemicals range from 1 mg/kg for BBP to 20 mg/kg for DEHP (Table C-2). In contrast with the evaluation of single chemicals, the critical dose (here, 69, 48, and 42 mg/kg for the three cases considered) of a mixture and the ad- justed critical values for the components clearly depend on the mixing ratio. How should adjusted critical doses be specified for individual chemicals in a mixture when exposure information is not available (that is, the doses and mix-
154 Phthalates and Cumulative Risk Assessment: The Tasks Ahead ing ratios of the chemicals in the mixture are not known or are not constant)? The committee suggests that a tiered approach be considered. â First, determine whether the single-chemical doses in the exposure of concern are all below the adjusted critical value specified by dividing the critical values (here, the BMD associated with a fixed BMR) of the single chemicals by the number of active chemicals in the mixture (case 1 in Table C-2). If so, the response to the mixture is less than the BMR, assuming general dose addition. There is no need to go any further. â Second, if one or more of the single-chemical doses in the exposure of concern exceeds the adjusted critical value specified for the mixture in step 1, determine the mixing ratio of the exposure of concern and recalculate the critical dose for the specific mixture ratio (for example, cases 2 and 3 in Table C-2). If all single-chemical exposures are below the adjusted critical doses for the mix- ture of concern, the response to the mixture is less than the BMR, assuming gen- eral dose addition. In Table C-2 for cases 2 and 3, assumptions would be made to determine doses of a parent compound on the basis of metabolite concentrations. If, for example, the calculated dose of DEHP exceeds 10 mg/kg (from case 1), a more refined estimate of an adjusted critical dose could be based on the mixing ratios obtained from exposure estimates (case 2 or 3). That is, the exposure to DEHP may be increased if exposures to other chemicals are lower than considered in case 1. If the exposure to each chemical is below the single-chemical adjusted critical value for the specified mixture ratio (case 2 or 3), the response could be claimed to be less than the selected BMR. DISCUSSION The additivity model described here was based on a nonlinear logistic model with the potential for a maximum effect other than zero testosterone. Howdeshell et al. (2008) used the nonlinear Hill model, assuming that the maximum effect was complete suppression of testosterone, and approximated the dose-addition procedure by using an average Hill slope for the mixture. The analyses of each model included similar figures (Figure C-2 here; Figure 2B in Howdeshell et al. 2008) that compared the mixture data, the nonlinear model fit to mixture data, and the model predicted by dose addition. Both showed that the dose-additive model fell below the mixture model. Howdeshell et al. did not make a statistical comparison of the two models; they claimed that a dose- additive relationship adequately represented the data. As seen in Figure C-2, the dose-additive model used here is similar to the observed mixture model; a for- mal statistical comparison of the two curves was not conducted. The point of the analysis illustrated here was to determine a mixture BMD by using dose addition and to show that its value depends on the mixing ratio.
Appendix C 155 That required an estimation of a BMD for each component in the mixture; a nonlinear logistic model was used here for illustration. A comparison of the re- sults that would be obtained with other models was not conducted. The devel- opment and dissemination of methods that result in inference that does not de- pend on a specific model constitute an important field of research. Bayesian approaches have been suggested in which the resulting inferences include the uncertainty associated with model selection, as well as parameter uncertainty. In accordance with the discussion in Chapter 5, the evaluation of critical doses in this illustration was based on BMDs. Nyribihizi et al. (2008) compare BMDs for experimentally observed mixture data with a fixed mixing ratio and the corresponding BMD under additivity. Their approach is similar to that used here. Other approaches, such as the use of NOAELs, are possible; the limitations of the use of NOAELs have been discussed extensively (see, for example, EPA 2000). The illustration in this appendix included the use of approximate mixing ratios of the chemicals estimated from urinary concentrations. Such estimates required many simplifying assumptions. The availability of the supporting data relating urinary metabolites and parent compound exposure concentrations var- ies among the chemicals. Exposures probably differ between infants, children, and adultsâa variation not considered in our calculations. However, the ap- proach is generic and can be repeated for different mixing ratios to account for observed exposures. A BBP 1.6 1.4 Testosterone (fraction of control) . 1.2 1 0.8 0.6 0.4 0.2 0 0 100 200 300 400 500 600 700 800 900 1000 Dose (mg/kg-d)
156 Phthalates and Cumulative Risk Assessment: The Tasks Ahead B DBP 1.6 1.4 Testosterone (fraction of control) . 1.2 1 0.8 0.6 0.4 0.2 0 0 100 200 300 400 500 600 700 Dose (mg/kg-d) C DEHP 1.6 1.4 Testosterone (fraction of control) . 1.2 1 0.8 0.6 0.4 0.2 0 0 100 200 300 400 500 600 700 800 900 1000 Dose (mg/kg-d)
Appendix C 157 D DPP 1.6 1.4 Testosterone (fraction of control) . 1.2 1 0.8 0.6 0.4 0.2 0 0 50 100 150 200 250 Dose (mg/kg-d) E DIBP 1.4 1.2 Testosterone (fraction of control) . 1 0.8 0.6 0.4 0.2 0 0 100 200 300 400 500 600 700 800 900 1000 Dose (mg/kg-d) FIGURE C-1 Average testosterone concentration (as percent of control) per pup (*) vs dose of five single chemicals with maximum likelihood dose-response curves used in additivity model.
158 Phthalates and Cumulative Risk Assessment: The Tasks Ahead A MIXTURE 1.4 1.2 Testosterone (fraction of control) . 1 0.8 0.6 0.4 0.2 0 0 200 400 600 800 1000 1200 1400 Dose (mg/kg-d) Model Data Dose addition Data mean and 90% confidence interval B MIXTURE 1.4 1.2 Testosterone (fraction of control) . 1 0.8 0.6 0.4 0.2 0 0 200 400 600 800 1000 1200 1400 Dose (mg/kg-d) Model Data Independent action FIGURE C-2 (A) Observed (*) and model-predicted dose-response curves for mixture of five phthalates based on the nonlinear logistic model for the mixture data (solid curve) and as predicted under additivity (dashed curve). The mixing ratio of the five phthalates was 3:3:3:3:1 for BBP, DBP, DEHP, DIBP, and DPP, that is, 0.23, 0.23, 0.23, 0.23, and 0.08 of the mixture. (B) For comparison, the prediction using an independent-action model based on percentage of response.
Appendix C 159 REFERENCES Altenburger, R., T. Backhaus, W. Boedeker, M. Faust, M. Scholze, and L.H. Grimme. 2000. Predictability of the toxicity of multiple chemical mixtures to Vibrio fischeri: Mixtures composed of similarly acting chemicals. Environ. Toxicol. Chem. 19(9):2341-2347. EPA (U.S. Environmental Protection Agency). 2000. Benchmark Dose Technical Guidance Document. External Review Draft. EPA/630/R-00/001. Risk Assessment Forum, U.S. Environmental Protection Agency, Washington, DC [online]. Available: http://www.epa.gov/ncea/pdfs/bmds/BMD-External_10_13_2000.pdf [accessed July 25, 2008]. Gennings, C., W.H. Carter, Jr., E.W. Carney, G.D. Charles, B.B. Gollapudi, and R.A. Carchman. 2004. A novel flexible approach for evaluating fixed ratio mixtures of full and partial agonists. Toxicol. Sci. 80(1):134-150. Howdeshell, K.L., V.S. Wilson, J. Furr, C.R. Lambright, C.V. Rider, C.R. Blystone, A.K. Hotchkiss, and L.E. Gray, Jr. 2008. A mixture of five phthalate esters inhibits fetal testicular testosterone production in the Sprague-Dawley rat in a cumulative, dose- additive manner. Toxicol. Sci. 105(1):153-165. Nyirabahizi, E., C. Gennings, W.W. Piegorsch, S. Yeatts, M.J. DeVito, and K.M. Crof- ton. 2008. Benchmark doses for chemical mixtures: Evaluation of a mixture of 18 PHAHs. Toxicologist 102(S-1):242 [Abstract No. 1177]. Wittassek, M., G.A. Wiesmuller, H.M. Koch, R. Eckard, L. Dobler, J. Muller, J. Angerer, and C. Schluter. 2007. Internal phthalate exposure over the last two decadesâa retrospective human biomonitoring study. Int. J. Hyg. Environ. Health 210(3- 4):319-333.