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Application of qualitative and quantitative uncertainty assessment tools in developing ranges of plausible toxicity values for 2,3,7,8‐tetrachlorodibenzo‐p‐dioxin

Abstract Increasing interest in characterizing risk assessment uncertainty is highlighted by recent recommendations from the National Academy of Sciences. In this paper we demonstrate the utility of applying qualitative and quantitative methods for assessing uncertainty to enhance risk‐based decision‐making for 2,3,7,8‐tetrachlorodibenzo‐p‐dioxin. The approach involved deconstructing the reference dose (RfD) via evaluation of the different assumptions, options, models and methods associated with derivation of the value, culminating in the development of a plausible range of potential values based on such areas of uncertainty. The results demonstrate that overall RfD uncertainty was high based on limitations in the process for selection (e.g., compliance with inclusion criteria related to internal validity of the co‐critical studies, consistency with other studies), external validity (e.g., generalizing findings of acute, high‐dose exposure scenarios to the general population), and selection and classification of the point of departure using data from the individual studies (e.g., lack of statistical and clinical significance). Building on sensitivity analyses conducted by the US Environmental Protection Agency in 2012, the resulting estimates of RfD values that account for the uncertainties ranged from ~1.5 to 179 pg/kg/day. It is anticipated that the range of RfDs presented herein, along with the characterization of uncertainties, will improve risk assessments of dioxins and provide important information to risk managers, because reliance on a single toxicity value limits the information needed for making decisions and gives a false sense of precision and accuracy.

U is analogous to the factor of 1/UF in Equation 1: e.g., U = 1/3 to divide the POD by the standard UF of 3 representing inter-individual variability.
In the Bayesian approach, both the POD and U are considered probabilistically, as random variables obeying some known or estimated distributions. The RfD then also has a distribution, which can be characterized. 1 The distribution of the POD is intended to represent uncertainty in the estimated POD, if known.
In this analysis, a single distribution representing POD uncertainty was not derived. Rather, uncertainty was estimated qualitatively by comparing various PODs derived under various assumptions: e.g., various possible threshold levels where a specific neonatal TSH value (i.e., 5 uU/mL or 10 uU/mL) was linked to a specific exposure metric, which in this case would be maternal TCDD or maternal TEQ. Consequently, in this analysis, PODs were not represented by a distribution, but were treated as exact values. If a range of maternal TCDD and/or TEQ blood concentrations were available, the POD could be treated probabilistically.
The distribution of U is intended to represent the actual uncertainty or variability in the UF. For example, if U represents inter-individual variability, then the distribution should reflect the population distribution of sensitivity. If the POD is derived from human data, then the median individual would probably see adverse effects at a dose approximately equal to the POD (U = 1). Some people will be less sensitive and would see adverse effects only at a dose much higher than the POD (U > 1). Some people will be more sensitive and would see adverse effects at a dose much lower than the POD (U < 1). If U = 1/3 is protective of, say, 97.5% of the population, then 97.5% of the distribution should be above 1/3. Standard UFs are not linked to detailed data that could characterize an empirical distribution for U. Therefore, this analysis followed the approach used in NAS (2014) and Simon et al. (2016), assuming that the factor U obeys a log-normal distribution. The median of this distribution is set equal to 1, reflecting the assumption that the median individual would probably see adverse effects at a dose approximately equal to the POD (U = 1). To reflect the idea that a factor of 1/UF (where UF is some standard uncertainty factor) should be protective of 97.5% of the population, a log-scale standard deviation is chosen to ensure that the 2.5 th percentile of the distribution corresponds to 1/UF. For example, the distribution representing a standard Under the assumption that a POD is an exact value, and it is multiplied by an uncertainty factor U obeying a log-normal distribution (i.e., log U obeys a normal distribution with mean 0 and standard deviation equal to sU), then the resulting RfD obeys the following distribution on the log scale: Under some circumstances, a traditional UF approach requires dividing the POD by two (or more) UFs. For example, if the POD is considered to be a LOAEL, then a UF of 10 is applied to represent uncertainty in converting from LOAEL to NOAEL, and then a UF of 3 is applied to represent inter-individual variability. In this Bayesian uncertainty-propagation framework, this situation can be represented as a POD successively multiplied by two uncertainty factors.
where log U1 obeys a normal distribution with mean 0 and standard deviation s1, and log U2 obeys a normal distribution with mean 0 and standard deviation s2. If U1 and U2 are uncorrelated, and if the POD is taken as an exact value (as before), then the resulting RfD obeys the following distribution on the log scale: log RfD ~ Normal 3µ = log POD, s=4s 0 2 + s 2 2 6 (Equation 5) The traditional UF example described above might apply a single combined UF of 30, because successively dividing by 10 and then by 3 is equivalent to simply dividing by 30. However, in the Bayesian framework, applying a single log-normal distribution representing a combined uncertainty factor U1U2 is not equivalent to successively applying two log-normal distributions representing U1 and then U2, as in Equation 5. For example, consider the case where U1 represents the LOAEL-NOAEL conversion factor (2.5 th percentile should be 1/10, so s1 = 1.175), and U2 represents inter-individual variability (2.5 th percentile should be 1/3, so s2 = 0.561). A single combined UF of 30 would be represented by a distribution whose 2.5 th percentile was 1/30, i.e. sU = 1.735. By contrast, applying the two uncertainty factors in succession (as in Equation 5) leads to a log-normal distribution, with sU = 4s 0 2 + s 2 2 = 1.302, and 2.5 th percentile = 1/12.5 rather than 1/30. In fact, for this log-normal distribution (with sU = 1.302), 1/30 is the 1 st percentile. This fact reflects the compounding of conservatism that occurs when a single combined UF is used. Because UFs can typically be assumed to represent uncorrelated sources of uncertainty or variability in the RfD, combining two UFs that are each intended to be conservative at a 97.5% level ultimately yields a single UF that is actually conservative at the 99% level.

Determination of POD values
The Bayesian approach was applied to derive distributions for RfDs corresponding to both maternal TCDD and maternal TEQ, associated with neonatal TSH threshold values of both 5 µU/mL and 10 µU/mL.
Because the only POD data provided by the USEPA was that for TCDD associated with a threshold value for neonatal TSH of 5uU/mL, PODs had to be determined for TCDD associated with a threshold of 10 uU/mL, as well as TEQ-based PODs associated with both neonatal TSH thresholds. To do so, the Bacarelli regression analyses were reproduced for both neonatal TSH vs. maternal LASC TCDD, and neonatal TSH vs. maternal LASC TEQ. The data in Baccarelli Figure 2A (TCDD) and Figure 2D (TEQ) were digitized using Web Plot Digitizer software, and regression analysis (log neonatal TSH vs. log maternal LASC) was carried out using R (R Core Team, 2017). Using these regression models, inverse predictions were made of the maternal LASC TCDD and TEQ corresponding to neonatal TSH of 5 µU/mL and 10 µU/mL. where b0 = -8.534e-1; b1 = 5.433e-2; and b2 = 1.441e-4.
The ad hoc estimated relationship was used to predict the doses corresponding to maternal LASC TCDD and TEQ corresponding to neonatal TSH of 5 µU/mL and 10 µU/mL. These equivalent doses were treated as PODs.
The Bayesian approach described above was then applied to each of these four PODs under two assumptions: first, that the POD represented a NOAEL (i.e., only applying a factor representing inter-individual variability), and second, that the POD represented a LOAEL (i.e., successively applying two factors: one representing LOAEL-NOAEL extrapolation, and one representing inter-individual variability). The resulting RfD distributions are illustrated in Figure 6 in the main manuscript. To characterize the "reasonable worst-case scenario" from each of the RfD distributions, the 2.5 th percentile was calculated for each distribution (representing an RfD that is conservative at the 97.5% level).
The results of each stage of this analysis are summarized in Supplemental * RfD lower-bound (2.5 th percentile) values corresponding to various combinations of assumptions on threshold neonatal TSH, maternal exposure metric, and whether POD is treated as a NOAEL or LOAEL. Also provided: the maternal LASC corresponding to the given neonatal TSH value and maternal exposure metric; and the corresponding POD (i.e., the equivalent dose).