Comparison of the Approaches Taken by EFSA and JECFA to Establish a HBGV for Cadmium 1

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1 EFSA Journal 011;9():006 SCIENTIFIC REPORT OF EFSA Comparison of the Approaches Taken by EFSA and JECFA to Establish a HBGV for Cadmium 1 European Food Safety Authority, 3 European Food Safety Authority (EFSA), Parma, Italy ABSTRACT EFSA received a mandate from the European Commission (EC) to re-assess the elements linked to the establishment of the health-based guidance value in the opinion on cadmium in food of the EFSA s CONTAM panel (EFSA, 009a). The CONTAM Unit asked support from the Assessment Methodology Unit to re-assess the elements leading to the establishment of the health-based guidance value in the opinion taking into account a report established by the Joint FAO/WHO Expert Committee on Food Additives (JECFA, 010) where a different health-based guidance value was concluded. In this scientific report, the methodology used by EFSA and its rationale is described in more detail, and supporting evidence for the need of an adjustment factor to establish a health-based guidance value is provided. A comparison between JECFA and EFSA approaches is presented, as well as a sensitivity analysis in relation to the choice of the toxicodynamic variability function used by JECFA in their approach, to illustrate impact when establishing a health-based guidance value. European Food Safety Authority, 011 KEY WORDS Cadmium, meta-analysis, dose-response model, PK models, benchmark dose, hybrid approach 1 3 On request of EFSA, Question No EFSA-Q , issued on 7 February 011. Correspondence: amu@efsa.europa.eu Acknowledgement: EFSA wishes to thank the members of the Working Group on Cadmium modelling: Billy Amzal, Alan Raymond Boobis, Diane Benford, Clark Carrington, Eugenia Dogliotti, Lutz Edler, Antonio Mutti and Josef Schlatter (chair of the CONTAM Panel) for the critical review on this scientific output and EFSA staff: José Cortiñas Abrahantes for the support provided to this scientific output. This scientific output, published on the 10th of February 011 replaces the the earlier version published on the 8 th of February 011. Suggested citation: European Food Safety Authority; Comparison of the Approaches Taken by EFSA and JECFA to Establish a HBGV for Cadmium. EFSA Journal 011; 9():006. [8pp.] doi:10.903/j.efsa Available online: European Food Safety Authority, 011

2 SUMMARY The CONTAM Unit asked support from the Assessment Methodology Unit to re-assess the elements linked to the establishment of the HBGV in the opinion on cadmium in food of the EFSA s CONTAM panel. The EFSA opinion on Cadmium (EFSA, 009a) needed to be reviewed based on a report established by the Joint FAO/WHO Expert Committee on Food Additives (JECFA, 010) where a different provisional tolerable monthly intake was reported. The EFSA opinion (EFSA, 009a) was based on a meta-analysis of epidemiological studies assessing the concentration-effect relationship between Beta--microglobulin (BM), a biomarker of tubular toxicity, and cadmium in urine which was considered as the most reliable basis on which to determine a critical concentration of cadmium. This meta-analysis was published in a separate report (EFSA, 009b). Based on this analysis the CONTAM Panel derived a group-based BMDL5 of 4 µg cadmium/g creatinine that was further adjusted based on the fact that modelling was done using summary measures (geometric mean and standard deviations) resulting in a reference point of 1 µg cadmium/g creatinine. In the JECFA report a breakpoint of 5.4 (CI: ) µg cadmium/g creatinine was used as a point of departure. In this scientific report the methodology used in the meta-analysis (EFSA, 009b) is described in detail, focussing on how to deal with summary values from the selected studies as no individual data was available to build the concentration-effect model. The rationale behind the approach undertaken is explained and simulation based evidence is provided for the need of an adjustment factor to establish a health-based guidance value. The importance on the selection of the adjustment factor on the final establishment of a health-based guidance value is studied by providing examples of the impact of selecting different percentiles in the calculation of the adjustment factor, recognising that this is in general a policy decision and could be influenced by aspects such as the severity of the effect, the robustness of the data, the nature of the distribution and risk management considerations. A comparison between JECFA and EFSA approaches is presented, illustrating differences between the methods, as well as assumptions made by both approaches, which induces in both methods uncertainties when applying them. The JECFA approach plug-in distributions for the parameters instead of posterior mean values obtained from the posterior distribution when Bayesian inferences were used in the TK modelling (Amzal et al., 009) in order to account for uncertainty. It is shown that by doing that, uncertainties about the right distribution to use are introduced. A sensitivity analysis in relation to the choice of the toxicodynamic variability function used by JECFA in their approach is also undertaken, in order to illustrate the impact of the choice made when establishing health-based guidance value. EFSA Journal 011;9():006

3 TABLE OF CONTENTS Abstract... 1 Summary... Table of contents Introduction The significance and impact of the adjustment factor Statistical model used in the EFSA Opinion BMD Overestimation Issues without adjustment for within dose variability Simulation-based Illustration of BMD Overestimation Issues Adjustment Factor Overview Differences of the Statistical Approaches used by EFSA and JECFA Dose response Modelling EFSA s Piece-wise Linear Model on Log-Log Scale used by JECFA Modelling the Relationship between Urinary Cadmium Concentration and Cadmium Intake Variability in the Biomarker Dose-Response Relationship Sensitivity Analysis in Relation to Assumptions Made by JECFA Original Results Obtained by JECFA Sensitivity Analysis in Relation to the Age Used by JECFA Sensitivity Analysis in Relation to the Toxicodynamic Variability Function Conclusions and recommendations... 6 References... 7 abbreviations... 8 EFSA Journal 011;9():006 3

4 1. Introduction In 009 the EFSA s Panel on Contaminants in the Food Chain (CONTAM Panel) was asked to assess the risks to human health related to the presence of cadmium in foodstuff, the outcome of which is referred to as the Opinion (EFSA 009a). EFSA received a mandate from the European Commission (EC) to re-assess the elements linked to the establishment of a health-based guidance value (HBGV) in the opinion on cadmium in food of the EFSA s CONTAM panel. In particular, in accordance with Art. 9 (1) (a) of Regulation (EC) No 178/00, the European Commission asks EFSA to confirm whether the tolerable weekly intake for cadmium of.5 µg/kg body weight established by the CONTAM Panel in 009 is still considered appropriate or whether any modifications are needed. The Assessment Methodology Unit (AMU) was requested to review the method used in the previous opinion. In its Opinion (EFSA, 009a) EFSA determined a reference point for its hazard characterization using meta-analysis methodology on a selected set of groups of individuals exposed to cadmium, of studies identified in a systematic review to evaluate the concentration-effect relationship between urinary cadmium (U-Cd) and urinary beta--microglobulin (BM). A Hill model was fitted to the concentration-effect relationship between urinary cadmium and BM for subjects over 50 years of age, excluding the population sub-groups exclusively comprised of workers as well as for the whole population. From that modeling, a benchmark dose lower confidence limit for a 5 percent increase of the prevalence of elevated BM (BMDL5) of 4 μg Cd/g creatinine was derived using the hybrid approach, with cut-off points based on relevant biological effects on the target organ and significant statistical changes. An adjustment factor of 3.9 was calculated from the estimated inter-individual variation of urinary cadmium within the groups of the study populations to account for residual uncertainty of the BMDL5 value of 4 μg Cd/g creatinine, due to missing information on individual urinary cadmium and BM values in all groups of the studies used for the BMD analysis. This led to a value of 1.0 μg Cd/g creatinine. The objectives of this report are: to explain in more details the method used by EFSA and its underlying rationale to provide more evidence in supporting the need of an adjustment factor for the derivation of the HBGV as well as information on the underlying calculation to compare the approaches used by EFSA and JECFA in the derivation of the HBGV to perform a sensitivity analysis evidencing the impact of the toxicodynamic variability function used by JECFA to establish the health-based guidance value (HBGV). EFSA Journal 011;9():006 4

5 . The significance and impact of the adjustment factor.1. Statistical model used in the EFSA Opinion Embedded into a meta-analysis, the overall relationship between urinary cadmium and BM was modelled using a Hill model for the whole population as well as for subjects over 50 years of (mean) age, while excluding the population sub-groups exclusively comprised of workers, with an adjustment for ethnicity, to account for differences between Caucasians and Asians (including Japanese). Thereby, a mixed-effects model was fitted using the available group-based geometric means (GM) and geometric standard deviations (GSD) of BM and urinary cadmium levels, under log-normality assumption. More specifically, the statistical model chosen accounts for inter-study variability (between the 35 studies included in the meta-analysis), weighing each group according to its sample size. In probability theory, a log-normal distribution is a probability distribution of a random variable whose logarithm is normally distributed. The inter-individual variability within each group, both, for the urinary cadmium (U-Cd) representing the dose as well as for the BM representing the effect, was part of the mixed effects model described below. Let B M i and UCd i denote the β -microglobulinuria and urinary cadmium concentrations, respectively, for individual (i) in the group in units of µg/g creatinine. The statistical distributions of the observed geometric means ( GM ( BM ) and GM ( UCd ) for group k, k =1,..,165) and geometric standard deviations ( GSD( BM ) and GSD( UCd ) for group k, k =1,..,165), shown in the EFSA (009b) report in the Annex 4 were assumed to be : ln ( ( ) ( UCd ) i UCd = ~ N n i UCd σ UCd ( ( ) ) ~ χ ( n UCd 1) ln GM ln GSD UCd and ( ( BM ) ln GM n UCd ( i ) σ ( ( ) ) ~ BM χ ( nbm 1) ln GSD BM ln BM = k) n i n BM ( BM μ ~ N μ UCd BM σ, n σ, n where n UCd and n BM are the sample sizes of the group k, used to compute the group based summary statistics. Note, in a small number of groups the sample sizes for BM and U-Cd μ UCd and μbm the population group mean dose and mean effect (both on the log scale) in the group k, UCd UCd BM BM were not coinciding due to drop out (see Annex 4 of EFSA, 009b), denote σ UCd and σ BM denote the inter-individual geometric variances of dose and effect, which are assumed to be the same in each group. N and χ denote the Normal and the chi-square EFSA Journal 011;9():006 5

6 distribution, respectively. The chi-square distribution was used to model the log of the geometric variances using results from the Cochran s theorem (Cochran, 1934). Note that k is representing a maximum of 165 groups, depending on the focused populations. When evaluating only groups with mean age > 50 years k is representing 110 dose groups, if workers are also excluded the number of groups remaining are 99. As preferred structural mathematical model linking dose (U-Cd concentration) and effect (β -microglobulinuria), EFSA has chosen the Hill model, relating the two mean parameters of the Normal distributions assumed previously, partially ignoring the individual variation within each group: μ BM = Background + study + ethnicity + amplitude j μ η μ UCd η UCd + ed η 50 where: M μ B and μ UCd stand again for the population means of the β -microglobulinuria and U-Cd level measurements (in units of µg/g creatinine), respectively. study j is a centered normal random effect accounting for the within-study correlation and between-study heterogeneity (j=1,, 35 when all groups are included and j=1,, when the analysis is restricted to subjects over 50 years of (mean) age, and further excluding the worker population). ethnicity is an additive fixed effect adjusting for differences observed in Caucasians versus Asians. This adjustment is merely displacing the curve for Asians parallel to the one for Caucasians (on the log scale) amplitude is an unknown constant representing the difference between the plateaux of the S-shape η is the shape parameter defining the steepness of the S curve ed50 is the dose where 50% of the maximal effect is achieved The model is called mixed model, since it includes fixed effects for background, ethnicity, amplitude together with random effects ( study j ) in the regression model. This model allows for population as well as study-specific effects... BMD Overestimation Issues without adjustment for within dose variability As described in detail in the previous EFSA opinion (EFSA, 009a), inter-individual variability within dose groups ( σ UCd ) has not been fully account for when fitting the concentration-effect model, while the variability between studies was fully accounted for by adding the term study j to the model. In other words, the Hill model uses the estimated true mean dose groups, instead of individual dose values, ignoring then the variability around this EFSA Journal 011;9():006 6

7 mean. The Hill model is basically using less noisy data to estimate the concentration-effect relationship. It is clear that when modeling μ BM in function of μ UCd, the σ UCd has not been k) taken into account, although it has been used to estimate μ. The Hill model focus on the parameters extracted from the distributional assumptions of the observed summary measures, in particular the mean parameters. In the context of normally distributed variables, mean and variance parameters are orthogonal, thus it is fair to say that if the Hill model is based on the mean parameters, the information on inter-individual variability within dose groups ( σ ) input in the model could be considered negligible. One of the largest difficulties facing epidemiological research is that of measurement error in the independent variables when performing regression modelling (Amzal et al., 009; Byar and Gail, 1989; Bashir and Duffy, 1995 and Carrol, Rupert and Stefanski, 1995). Measurement error can lead to substantial bias in either direction, either diluting or exaggerating the apparent effect size (Wong et al. 1999). There is a particular problem in the area of epidemiology, where measuring long-term dietary intake is prone to error, such that most epidemiological studies in this field are potentially subject to very large biases (Wong, Day and Wareham, 1999 and Bingham et al., 003). In order to account for such issue, given the fact that dose groups are entering into the Hill s model with measurement errors (due to the lack of individual data), an adjustment factor was introduced. Not accounting for this inter-individual variance σ within dose groups and basing the BMDL calculation only on group mean U-Cd levels ( μ UCd ), would likely generate overestimated BMDL values. The basis of this argument (overestimation of BMDLs), lies in the fact that nonlinear regressions of effect means ( μ BM ) versus dose means ( μ UCd ) do not account for variability around the means and one expects less variability around the regression line built on aggregated data. That is why one also expects that the BMDL values are going to be overestimated. In other words, due to the use of less noisy data (summary values, geometric means and standard deviations) a confidence band around the concentration-effect model would be narrower than when fitting the model using individual data. Ideally this could be solved by using individual data to fit the concentration-effect model (Hill s or piecewise linear models). Unfortunately, EFSA did not have this information and any reconstruction of the individual data (e.g. using simulation techniques) would be hampered by additional assumptions to be imposed. Thus, it was decided to correct for that uncertainty and possible bias in the estimated BMDL values. Note the modelling described in section.1 only uses the mean values (in total 99) to estimate the functional concentration-effect relationship, thus individual variation around this mean is not fully accounted for. From the available data it is not possible to estimate the fraction of the variability already covered by the modelling. In the case of nonlinear models, to obtain an analytical expression about this fraction is not feasible. In the context of linear models, it is T h, where X h is the vector of covariate values of the mean of interest and X is the design matrix) for the T easy to see that the fraction involve the Hat Matrix ( H = X ( X X) X h model using summary values ( H S ) and the model using individual values ( H I ) and the number of observations of the focused group k ( n UCd ), for which the mean is calculated. The HS n UCd fraction will then be. H I UCd ( UCd 1 UCd EFSA Journal 011;9():006 7

8 .3. Simulation-based Illustration of BMD Overestimation Issues In order to visualize this overestimation issue and to illustrate the role of the adjustment factor used by EFSA, the AMU unit performed a simulation study. The summary values (GM and GSD) for each dose groups of both U-Cd and β -microglobulinuria were used to generate individual data points within each dose groups (Figure 1). First n UCd individual urinary cadmium levels were sampled for each study dose group from a lognormal distribution with the geometric mean and standard deviation matching those recorded in each dose group. Referring to the dataset used in the meta-analysis (99 study dose groups) which generated a total of individual dose observations. In order to generate the matching individual β -microglobulinuria values a piecewise linear relationship (on the log scale) was used to derive individual BM values from the simulated individual U-Cd levels (expected BM levels corresponding to the sampled concentrations). The piecewise linear model was used in this simulation for computational simplicity, since the fits of the Hill model and the piecewise linear model were producing comparable results. n UCd Let Y i denote individual samples for group k (being in total individual doses) from the lognormal distribution with GM ( UCd ) and GSD ( UCd ) from the 99 groups. Then the piecewise linear relationship was used as stated in EFSA (009b) to generate values for β -microglobulin ( Z i ). This implies that the variable Zi will also be a random variable D D ( Zi = β 0 + β1 Yi, where D=1, is used here to differentiate the fact that two different lines are used, bellow and above the breakpoint, intercept and slopes of the lines are based on the estimated values reported in Table 11 from the EFSA 009b report) lognormally distributed with an associated variability ( τ BM ) induce by the relationship imposed, that depends on the GSD ( UCd ) of each group k. Given that this relationship is already inducing some variability on the β -microglobulinuria values ( τ BM ), but not all variability that is observed ( GSD ( BM )) is accounted for, an additional independent error term was introduced, corresponding to the amount of BM variability not yet accounted for. It is important to highlight that both variables in the model are used on the log scale, the variability not accounted for could be computed as the difference between GSD( BM ) and τ BM already induced via the relationship assumed, due to the fact that normally distributed variables are used, it implies to add an independent error term ( ε BM ) that accounts for the extra variation in the observed BM data, thus the final simulated effect will be k) E i = Z i + ε. ( BM EFSA Journal 011;9():006 8

9 B-Microglobulin Dose groups (U-Cd) Figure 1. The graph illustrates how aggregated data (black dots) compare with individual data points (blue dots) for the 99 dose groups. In total individual paired concentrationeffect data were simulated based on summary values from both urinary cadmium and BM levels. Blue dashed lines represent the confidence band around the piecewise linear model fit when using individual values, thick black lines represent confidence bands around the piecewise linear model fit using the summary values, the thin vertical black lines locate the 1, 4 and 5.4 µg/g urinary cadmium levels, the thin horizontal black lines locate the 300 and 1000 µg/g creatinine cut-offs. The short yellow line identifies the confidence interval around the breakpoint. Once the individual data was generated, a piecewise linear model (on the log-log scale) was again fitted and the confidence band around the fit was calculated. It is important to mention that estimated values of the parameters in the model were close to those ones obtained when summary values were used instead (for these simulated data the slope for the low doses interval (below 5.4) was estimated as 0.05 with standard error of (EFSA, 009b reported 0.04), while the slope for high doses interval (above 5.4) was 6.0 with standard error of 0.03 (EFSA, 009b reported 5.99)). This result is expected, given that the simulation exercise is using this type of relationship to generate the β -microglobulinuria values. This graph illustrates what happens when the U-Cd means ( μ UCd ) are used in the concentration-effect model instead of the individual U-Cd values. In other words, this plot visualizes the variability that might have been observed would individual data instead of the EFSA Journal 011;9():006 9

10 aggregated data had been used. Note that this is just a simulation exercise with a number of uncertainties when re-constructing the individual data in order to illustrate the issue related to the variability that is not accounted for, when fitting the concentration-effect model to aggregated data. The simulation exercise showed the need for correction of the calculated BMDL when summary values instead of the individual values are used. It is important to note that in this simulations exercise, the variability observed in the urinary cadmium dose groups ( Y i ) is not the only source of variability in the simulated effects BM ( E i ), since an extra interdose group error ( ε ) was finally introduced. BM.4. Adjustment Factor Overview In order to account for the overestimation issue, that was already illustrated and explained above, an adjustment factor was introduced in the previous opinion (EFSA, 009a). The factor was calculated analogously to the adjustment factor given by WHO (005), where the ratio of a 95 th percentile to a central value (median) of the respective population values (it is referred to the within dose group population) was proposed, 95th Percentile AF = Median Note, WHO (005) refer to the choice of percentiles and explicitly mentions that this would be a policy decision and could be influenced by aspects such as the severity of the effect, the robustness of the data, the nature of the distribution and risk management considerations, thus allowing some freedom in the choice of percentile, according to the problem at hand. In its assessment (EFSA, 009a), the 95 th percentile was chosen given that the data are based on a very heterogeneous set of observational human studies which have a lower grade of evidence than experimental studies, and since BM is an indirect measure of renal damage. It could also be interpreted as to what extent the variability observed in BM values is related to the within dose group variability, and the amount of correction that should be introduced to argue that the variability observed within a dose group should be translated into a variability on the effect (BM). Other percentiles could be used instead, obviously implying different assumptions in relation to the association of the variabilities between the doses and the effects. The influence of the choice of the percentile is discussed at the end of this section. In order to clarify how the formula was used by EFSA, it is important to note that a lognormal distribution is assumed and that geometric standard deviations can be written as a Ln(1 + CV ) function of coefficient of variation in the following way: GSD = e. The (1-α) ( k ) μucd Z α UCd percentile is calculated using the formula, e + 1 σ, where μ ( k ) Ln( Median), UCd = σ = Ln(GSD) UCd and Z1 α is the percentile value from the standardized normal distribution. Substituting this into the generic formula above yields the following adjustment factor: EFSA Journal 011;9():006 10

11 AF (1 α) = (1 α) th ( μ Median UCd ) = e UCd + Z1 α σ UCd Z Z 1 1 α α σ UCd = e = e μ UCd μ e Ln (1 + CV ) By replacing Z1 α by the 95 th percentile of the standardized normal distribution one obtains AF ( 95) = 3.9. The impact of choosing different percentiles to calculate an adjustment factor, was evaluated using percentiles 99.5, 95, 90, 85, 75, and 67.5 to finally assess the effect on the tolerable weekly intake (TWI) obtained when using the one-compartment model estimates (considering the population of non-workers above 50 years of age). The six different percentiles correspond to adjustment factors 8.5, 3.9,.9,.4, 1.8 and 1.5. Figure exhibits the cumulative population distribution of daily cadmium intake values corresponding to the six different choices of the percentiles, which are linked to the reference points (RP) in μg/g (representing the internal dose) 0.5, 1.0, 1.5,.0,.5 and 3 used to plot the cumulative distribution. The values 0.18, 0.36, 0.54, 0.73, 0.91, 1.09 on the x-axis correspond to the 5% percentiles of the cumulative distribution obtained when using the different RPs obtained when we used different percentiles to calculate the adjustment factor. The six different percentiles are here linked to six different adjustment factors, which are used to obtained the RPs and this RPs are finally used to obtained six TWIs as it is shown in the following table. In case that we will choose instead of the 95 th percentile to obtained the (95) AF, we would used the 85 th percentile, the AF =. 4, which will corresponds to a TWI of 5.1μg/kg b.w. Table 1: Reference point, tolerable daily and weekly intake values obtained when using different percentiles to calculate the adjustment factor. Percentiles AF RP TDI TWI EFSA Journal 011;9():006 11

12 Figure. Cumulative population distribution of daily cadmium exposure considering different percentiles to calculate AF. The values 0.18, 0.36, 0.54, 0.73, 0.91, 1.09 on the x- axis correspond to the 5 th percentiles of the cumulative distribution used for deriving the tolerable weekly intake. 3. Differences of the Statistical Approaches used by EFSA and JECFA The EFSA and JECFA evaluations of cadmium have a number of commonalities. 1) They are based on the same data. ) They both have two primary components a toxicokinetic model that relates urinary cadmium concentration to dietary cadmium intake, and a concentrationeffect model that relates urinary cadmium concentration to the urinary concentration of a protein (β-microglobulin) that serves as a marker for renal tubular effects. JECFA is actually using the result obtained by EFSA s approach. 3) They both endeavor to account population variability in the concentration-effect relationship. On the other hand, there are some key differences as well. The main differences are listed below, ample details can be found on EFSA (011). The parameter selected as the reference point to derive the HBGV. The statistical approach to account for the variability and uncertainty of the marker of exposure (urinary cadmium concentration) and the marker of response (BM) in the concentration-effect model. The methodology for transforming urinary cadmium concentrations into dietary intake values. EFSA Journal 011;9():006 1

13 3.1. Dose response Modelling EFSA Scientific Panels and Units are strongly encouraged to adopt the BMD approach as such or as otherwise specified in EFSA Scientific Committee Guidance on the use of the benchmark dose approach in risk assessment (EFSA 009c). If continuous effect data are summarised by means and standard deviations of subgroups and if the samples sizes are known the BMD approach can still be applied although its statistical optimality depends on the assumed distribution of the inter-individual dose and effect data within sub-groups. The application of the BMD approach as developed for a continuous effect using individual data was applicable to the data compiled in the systematic review. Calculation of a RP was therefore based on a hybrid type BMD analysis (see e.g. Sand et al., 003; Suwazono et al., 011) applied to the group summary data from the meta-analysis within a Bayesian framework, using a mixed effects model with cut-off points based on relevant biological changes in the biomarker of renal damage EFSA s Piece-wise Linear Model on Log-Log Scale used by JECFA Ln k) D D k) ( μ ) = β + β Ln( μ ) ( BM 0 1 ( UCd where D is representing that the model parameters depend on whether the dose is below or above the breakpoint (more details can be found in EFSA, 009b). 3.. Modelling the Relationship between Urinary Cadmium Concentration and Cadmium Intake The one-compartment population toxicokinetic (TK) model was fitted to 680 paired data of cadmium intake and urinary cadmium concentrations from the Swedish Mammography Cohort study (Amzal et al., 009). The TK modeling was basically done by EFSA; JECFA simply used the results of the one compartment TK model presented in Amzal et al., (009). It is important to highlight that the evaluation of JECFA s modeling approach was possible, thanks to the collaboration of Clark Carrington, who made available to EFSA the computer programs used to develop JECFA s approach. In order to calculate TDI values JECFA used the following formula, such details are not available in JECFA s monograph, but we could retrieve them from the computer programs made available to EFSA (Equation 1) (ample details can be found in Amzal et al., 009) Cd_UrineInv = Urine/ (fxf/log() *Half_life* (1 - Exp(-Log() *Age)/Half_life) / (1 - Exp(-Log() / Half_life))) (1) Formula is the same as the one used by EFSA, as it is already pointed out before. Differences with respect to EFSA is that EFSA treats all parameters (Urine, fxf, and parameters of the distribution of the Half_life) as fixed, all coming from the TK estimation process, while JECFA is assuming that each parameter in the formula (Urine, EFSA Journal 011;9():006 13

14 fxf and parameters of the distribution of Half_life) is going to be drawn from an assumed distribution taking into account the posterior means and credible intervals for such parameters reported in Amzal et al., 009. Half_life is then drawn from a lognormal distribution, parameters of the distribution (mean and standard deviation) are drawn from triangular distribution, which is defined by minimum, mode and maximum. The parameters of the triangular distributions are taken from Amzal et al., 009. It is important to note that using posterior mean reported in the article as mode and credible limits as minimum and maximum, could have an impact on the shape of the distribution used to be drawn from. EFSA used instead the posterior mean values for the parameters. Age used by JECFA to calculate TDI was 70 years old, while EFSA considered the age to be 5. It is important to highlight that it is not clear the impact of choosing different age values on the final outcome of the approach, due to the exponentiation and the fractions in the formula. fxf is referring to the parameter called Factor ( f f ) in Amzal et al. (009), which is drawn from a triangular distribution (JECFA s approach), with , and as minimum, mode and maximum values, being posterior mean and credible limits reported by Amzal et al In particular fxf used by EFSA was fixed at , which is the upper bound of JECFA s triangular distribution. Now in this case the role of the parameter in the formula is more apparent, thus EFSA has opted for a conservative approach choosing the upper bound, since this value is in the denominator and smaller than 1, thus implying that the whole formula will be multiplied by a smaller number in general than what JECFA was using. Urine is set up by JECFA as the ratio between a value that is drawn from a normal distribution which is centered around the breakpoint (5.4) with standard deviation (0.18) obtained from confidence limits given in EFSA opinion (Table 11 of EFSA, 009a) and a parameter called toxicodynamic variability function (TDVF, details about it are reported below). In the case of EFSA the parameter Urine is just representing the reference point, which is also a ratio of the estimated BMDL and the adjustment factor ( AF ( 95) = 3. 9 ) which is used to account for the lack of individual data to build the concentration-effect model. JECFA used parameter estimates from the EFSA opinion (EFSA, 009a) and Amzal et al. (009) to construct the two-dimensional Monte Carlo simulation. It is important to note that JECFA used a number of ad hoc assumptions, as it was already mentioned above, in their probabilistic approach, while EFSA did not need additional distributional assumptions, using a more deterministic approach. In general parameters such as fxf and those of the distribution of Half_life should not have a major impact, since the range of values of their distributions are rather narrow, thus it is not expected to have a major impact on the establishment of the HBGV. On the other hand the way Urine is considered by both approaches could have a major impact on the final outcome of the process. In order to explore the approach proposed by JECFA a sensitivity analysis in relation with the choices k u EFSA Journal 011;9():006 14

15 made in term of age used, and in relation to the toxicodynamic variability function was carried out (see Section 3.4) Variability in the Biomarker Dose-Response Relationship Both EFSA and JECFA recognized the problem of having a large within group-dose range. However, the approaches used were different. While EFSA went ahead and calculated BMDs and BMDLs, JECFA concluded that it could not be assumed that the observed withingroup variation in response rate would vary in function of the urinary cadmium concentration, and therefore used the EFSA model only to estimate population mean responses. Since JECFA accounted for variability with the use of a separate function instead of estimating a biomarker BMDL from the epidemiological data, it was not considered necessary to use an additional factor. However, from a mathematical point of view, this function could be considered as an adjustment function to account for the lack of individual data when estimating posterior parameters from the concentration-effect model. The basis of the evaluation of JECFA s approach, as it was mentioned earlier, is the code provided by Clark Carrington, and it is clear that for most parameters a triangular distribution was assumed. The implication of this assumption is illustrated by a generic example of a triangular distribution (Figure 3) as used by JECFA. Probability densisty function (b a) a c (a + b + c) 3 b X Figure 3. Probability density function of a triangular distributed random variable with parameters a,b and c. EFSA Journal 011;9():006 15

16 When using a triangular distribution, the centered value c basically represents the mode of the triangular distribution. JECFA used values from Table of Amzal et al. (009), which are reported as posterior mean estimates of the parameters in the one compartment model. Minimum and maximum values a and b used by JECFA are lower and upper bounds of the credible interval reported in Amzal et al. (009). When using triangular distributions, the mean value could be calculated as the average of the values a, b and c which characterize the distribution completely. If posterior distributions are unimodal and symmetric, then mean, mode and median will coincide, but once the distribution is not symmetric, they tend to differ. For some of the parameters from the one compartment Bayesian model used by Amzal et al. (009) one must assume that this latter case might hold, for example for population mean for half time parameter, 11.6 (credible interval:10.1;14.7). It is clear, that any assumptions made in relation with the distribution of the parameters, could have an implication when calculating the dietary Cd intake corresponding to the respective urinary Cd levels. In any case we believe that this would not have a major impact, since the ranges of values of their distributions are rather narrow Sensitivity Analysis in Relation to Assumptions Made by JECFA. It is important to highlight that the choice of the age and toxicodynamic variability function (TDVF) used can play an important role when establishing the HBGV. In order to explore the impact of the choice made, a pilot sensitivity analysis was performed in which the age used by EFSA and the age used by JECFA, while all other parameters remained as they were, when they were used in the approach proposed by JECFA, in order to clarify the impact on the establishment of the HBGV. Also as the TDVF function used by JECFA has not been used earlier in the context of establishment of HBGV, and not references are provided to support its used, the impact on the choice of this function will be explored as well in a sensitivity study Original Results Obtained by JECFA. Using the computer program provided to EFSA the proposed JECFA approach was used, keeping all assumptions made by JECFA to run the model (original outcome of JECFA). The results obtained are presented in Figure 4. It can be seen that the average provisional tolerable monthly intake (PTMI) obtained is 35.4 with a confidence interval (3.3, 5.8). EFSA Journal 011;9():006 16

17 100% 90% Cumulative Population Frequency 80% 70% 60% 50% 40% 30% 0% 10% 0% Dietary CD (μg/kg bw per Month) Figure 4. Dietary cadmium monthly intake, using JECFA s TDVF function, the solid line is representing the average intake, the dashed lines the confidence band around the intake curve and the dotted line representing the 5 th percentile Sensitivity Analysis in Relation to the Age Used by JECFA. Note that the results previously presented correspond to Age equals to 70 years old. If instead, the same procedure is followed for Age equals to 50 years old, as considered by EFSA, the results obtained when the original JECFA approach is used (Figure 5), show a slight decrease in the provisional tolerable monthly intake (35.0 (.4, 49.8)). It can be seen that the average value is smaller when the age of 50 is used, but also that the confidence interval is narrower. It is also important to highlight that the lower bound is now around, also lower than the previously obtained (3.3). EFSA Journal 011;9():006 17

18 100% 90% 80% Cumulative Population Frequency 70% 60% 50% 40% 30% 0% 10% 0% Dietary CD (μg/kg bw per Month) Figure 5. Dietary cadmium monthly intake, using the original JECFA TDVF function but age equal to 50, the solid line is representing the average intake, the dashed lines the confidence band around the intake curve and the dotted line representing the 5 th percentile. Other ages could be as well explored, but given that the interest is in comparing the JECFA and EFSA approach, it is out of the scope of this report, the sensitivity analysis was limited to these two values of Age (50 and 70). The results show that choosing age to be larger tend to produce larger HBGV Sensitivity Analysis in Relation to the Toxicodynamic Variability Function. In order illustrate the choice made by JECFA in their approach, we will first show the TDVF function used. Figure 6 is a graphical representation of the TDVF function proposed by JECFA to establish the HBGV. The function depends on assuming a uniform distribution between 0 and 1 (variable X), which basically constrains the TDVF function to be below 1 when X is below 0.5 and allows the TDVF function to be above 1 only when the variable X is above 0.5, where the TDVF function varies between 1 and 3. It is clear from this plot that few observations are going to have values above. On inspection of the histogram plot from the values produced by the TDVF function in the simulation process (Figure 7), it is clear that 50 % of the values produced by the TDVF function are below 1 and that 95 % of the values produced by the TDVF function used by JECFA are below., reaching values above.6 on only 1% of occasions. It is clear from the function used to establish the HBGV EFSA Journal 011;9():006 18

19 (Equation 1) that the choice of the toxicodynamic variability function is going to play an important role, since it is basically defining the values on the numerator of Equation 1. As it was already explained in the previous section the numerator of Equation 1 is defined as the ratio of the breakpoint and the toxicodynamic variability function (presented here below). Given that the HBGV to be established are based on the percentiles of the outcomes of Equation 1 and that in general, all other parameters in Equation 1 are having rather narrow distributions, the percentiles of the toxicodynamic variability function will drive the percentiles of the outcome function (Equation 1). Toxicodynamic Variability Uniform variable Figure 6. Plot of the values taken by toxicodynamic variability function used by JECFA, which are ranging between 0.33 and 3 and will be used to modify the breakpoint values drawn from the normal distribution with mean 5.4 and standard deviation of This ratio is basically defining the numerator of Equation 1. EFSA Journal 011;9():006 19

20 density Toxicodynamic Variability Figure 7. Histogram plot of the values produced by the TDVF function during the simulation (varying between 0.33 and 3) used by JECFA with vertical red lines indicating 50, 75 and 95 percentile values of the distribution. In order to illustrate the influence of the TDVF function used by JECFA, and the influence of the percentiles of such a function, the same range of values as the one used by JECFA (between 0.33 and 3) was used but a function was chosen in which each value has the same probability of being drawn (a uniform distribution between 0.33 and 3 is used). It is important to note that this modified toxicodynamic variability function (Figure 9) produces larger percentiles values, and thus influencing the final results when establishing the HBGV (see Figure 8), where a median PTMI is estimated as.0 with corresponding CI being 14.8 to This exercise provides evidence of the impact of the choice of the toxicodynamic variability function on the establishment of the HBGV. EFSA Journal 011;9():006 0

21 100% 90% 80% Cumulative Population Frequency 70% 60% 50% 40% 30% 0% 10% 0% Dietary CD (μg/kg bw per Month) Figure 8. Dietary cadmium monthly intake, using the original JECFA approach with TDVF function being a uniform distribution between 0.33 and 3. density Toxicodynamic Variability Figure 9. Histogram of the values produced by the uniform TDVF function proposed with vertical red lines indicating 50, 75 and 95 percentile values of the distribution. EFSA Journal 011;9():006 1

22 If the same function as used by JECFA was used but the function is now allowed to vary only between 1 and 3, meaning that we will be allowing the breakpoint value only to be smaller than what it is estimated (Figure 10), this results in a larger portion of observations having values close to 3. The histogram plot (Figure 11) shows that now 50% of the values produced by the new one-sided TDVF function are around 1.75, with 75 % of the values being below.3, and finally 95 % of the values produced by the new TDVF function between 1 and.9. This approach could be considered as conservative; as all Urine values used in Equation 1 are smaller than the breakpoint value drawn from the normal distribution (the breakpoint value is basically representing the average population). With this function the provisional tolerable monthly intake would have a median value of 1.0 when the JECFA s dimensional Monte-Carlo approach would be used and the confidence interval obtain will be 14.7 to 7.. The result from the D Monte-Carlo approach is shown in Figure 1. Still an other option would be to assume that the TDVF values are coming from a uniform distribution between 1 and 3 (instead of between 0.33 and 3). This results in a provisional tolerable monthly intake (Figure 13) with median of 1.3 and confidence interval of 14.7 to 7.4. In this case, it is assumed again that in each iteration the breakpoint has the same probability of being modified by values between 1 and 3, thus the breakpoint ranging on average from 1.75 up to 5.4. It is important to highlight that the distribution percentiles of these two last TDVF functions are rather similar, thus results obtained for the PTMI are expected to be similar. In order to explore further the impact of the choice of the TDVF function, it is assumed that the TDVF function is a triangular distribution with parameters 1, and 3. The histogram when the triangular distribution was used is shown in Figure 14. It can be seen that the 50 th percentile is located at the value, and that 5 % of the values produced by this function are above.7. The result of the -dimensional Monte Carlo s model proposed by JECFA is shown in Figure 15. The median PTMI obtained is then 1.3 and the confidence limits are 15. and 7.9, respectively. EFSA Journal 011;9():006

23 Toxicodynamic Variability Uniform variable Figure 10. Toxicodynamic variability function varying between 1 and 3. density Toxicodynamic Variability Figure 11. Histogram of values produced by TDVF proposed function. EFSA Journal 011;9():006 3

24 100% 90% 80% Cumulative Population Frequency 70% 60% 50% 40% 30% 0% 10% 0% Dietary CD (μg/kg bw per Month) Figure 1. Dietary cadmium monthly intake, using proposed TDVF function (Figure 10). 100% 90% 80% Cumulative Population Frequency 70% 60% 50% 40% 30% 0% 10% 0% Dietary CD (μg/kg bw per Month) Figure 13. Dietary cadmium monthly intake, using a TDVF that could take values from 1 to 3 with the same probability. EFSA Journal 011;9():006 4

25 density Toxicodynamic Variability Figure 14. Histogram plot of the values produced by the triangular TDVF function proposed with vertical red lines indicating 50, 75 and 95 percentile values of the distribution. 100% 90% 80% Cumulative Population Frequency 70% 60% 50% 40% 30% 0% 10% 0% Dietary CD (μg/kg bw per Month) Figure 15. Dietary cadmium monthly intake, using a triangular TDVF function with parameters 1, and 3. EFSA Journal 011;9():006 5

26 It is clear that the choice of the function is playing a crucial role when establishing the HBGV and thus it is crucial to explore several options when choosing a particular TDVF function to establish the HBGV. CONCLUSIONS AND RECOMMENDATIONS EFSA (009a) applied the BMD methodology, when only summary data are available. When using summary values, some of the sources of variability (within dose variability) are not fully accounted for in the concentration-effect model. In the previous EFSA opinion (EFSA, 009a) it was proposed to account for this sources of variability by using an adjustment factor. Although the mixed effects modelling in the Bayesian framework used in EFSA (009a, 009b) accounted for inter-individual variability, both at the BM effect level as well as on the urinary cadmium concentration level, the review of this approach reconfirmed the existence of residual variability at the concentration level which could not be accounted for in the calculation of the BMDL. Therefore, it is concluded that an adjustment factor for the derivation of the HBGV was needed for the cadmium risk assessment of EFSA. It was shown that the size of the adjustment factor critically depends on the approach to define adjustment factors. Concurring with general statistical practice, a 95 th percentile was chosen. A comparison between the approaches taken by EFSA and JECFA was performed in term of assumptions, starting point and methodology. A difference is evidenced in the selection of the reference point (RP), breakpoint by JECFA and the BMDL05 by EFSA. JECFA used the same formula for the TK modeling as EFSA but considered that each parameter in the formula except Age is estimated with uncertainty, thus coming from some distribution. The parameters of the distribution were based on posterior mean estimates and credible intervals reported in Amzal et al. (009). On the other hand, EFSA used a deterministic approach, only considering that the half life parameter was coming from a lognormal distribution but using the posterior mean for all other parameters involved in Equation 1 or the upper bound of the credible interval (as in the case of fxf). A sensitivity analysis was performed in order to explore the impact of the choices of parameters such as Age and toxicodynamic variability function (TDVF) in the formula of the TK modelling (Equation 1). The results showed that the parameter Age was producing a slight difference, but the choice of the toxicodynamic variability function used has a major impact on the outcome, i.e. the TDVF function is basically driving the outcome, and by this the establishment of the provisional tolerable monthly intake. A careful procedure should be followed when choosing the toxicodynamic variability function to be used before drawing final conclusion on the HBGV to be established. EFSA Journal 011;9():006 6