The U.S. National Toxicology Program (NTP) recently evaluated the relative potency of dioxin-like compounds with respect to toxicity and carcinogenicity endpoints (NTP, 2006a
). They studied 2,3,7,8-tetrachlorodibenzo-p
-dioxin (TCDD), 3,3′,4,4′,5-pentachlorobiphenyl (PCB126), 2,3,4,7,8-pentachlorodibenzofuran (PeCDF), and a TEF-based mixture of the three. We used a subset of these data (Online Supplement
) to illustrate several concepts introduced earlier. Specifically, we focused on the activity of cytochrome P
450 1A1-associated 7-ethoxyresorufin-O
-deethylase (EROD) as measured in liver tissue of female Harlan Sprague-Dawley rats treated by oral gavage for 53 weeks (Toyoshiba et al, 2004
). There were 8 rats per dose for each chemical, though dose levels and numbers of doses varied across chemicals. To illustrate our ideas, we treated the mixture as a fourth chemical, ignoring its composition.
We used SAS Proc NLIN (version 9.00, SAS Institute Inc., Cary, NC, USA) to fit Hill models to log-transformed EROD activity using unweighted least squares. Initially, we fit an unrestricted model, with four parameters for each of the four chemicals (). Individual Hill models appeared to fit the data well, as evidenced by the proximity of the estimated dose-response curves to the dose-specific mean EROD levels ().
Parameter estimates (standard errors) by chemical under unrestricted, partially similar, and fully similar Hill-model dose-response curves for the NTP liver enzyme (EROD) activity data.
Figure 5 EROD-activity dose-response data and estimated Hill-model dose-response curves for four chemicals. Panels: (a) TCDD, (b) PCB126, (c) PeCDF, and (d) their TEF-based mixture. Symbols: individual response (open circle), and dose-specific average response (more ...)
We assessed similarity by allowing each dose-response curve to have a distinct ED50 but restricting the lower response limits, upper response limits and shape parameters to be the same across chemicals (). Chemical-specific dose-response curves estimated after enforcing similarity did not fit the data as well as the unrestricted curves (); the hypothesis that all four chemicals had similar dose-response curves with respect to EROD activity was rejected (F test of fit, p < 10−15). The poor fit under full similarity is likely due to the PeCDF responses not reaching a plateau, which led to a large (and variable) estimate of the upper response limit (). When considered in pairs, TCDD and PCB126 appear to have similar dose-response curves (p = 0.65), but TCDD and PeCDF (p < 0.001) and TCDD and the mixture (p = 0.02) do not.
Following convention, we treated TCDD as the reference and estimated the relative potency functions of the other chemicals compared to TCDD. In accord with the preceeding results, the Hill models for PeCDF and the mixture were unrestricted, but those for TCDD and PCB126 were constrained to produce similar dose-response curves (, ). We estimated relative potency functions by substituting the parameter estimates from the fitted Hill models into the appropriate formulae (Appendix
Figure 6 Estimated Hill-model dose-response curves for TCDD, PCB126, PeCDF, and their TEF-based mixture and corresponding relative potency functions (relative to TCDD). Hill models were fit separately for PeCDF and the mixture but were constrained by assuming (more ...)
Because TCDD and PCB126 were forced to have similar dose-response curves, relative potency functions for those chemicals were constant () and equal to the ratio of their ED50
= 0.19, 95% CI: 0.16, 0.22), indicating that PCB126 is less potent than TCDD. The chemicals allowed to have non-similar dose-response curves had estimated relative potency functions that deviated substantially from constant functions.
If one considers the differences between the lower and upper response limits for these chemicals as intrinsic to the comparison, attention should focus on ρμ
(μ) or one of the ρdi
) ( displays ρ d0
) but not ρ d1
)). For the mixture compared to TCDD, the estimated relative potency functions μ
(μ) and d0
), exceeded the null value of 1 for every μ and d0,
respectively, suggesting the mixture is more potent than TCDD. In fact, the value of either μ
(μ) or d0
) closest to 1 was μ
= 1.73, which occurred at μ
= 1115 and d0
= 7.67, respectively. On the other hand, for PeCDF relative to TCDD, μ
(μ) and d0
) each crossed the equipotency line (ρ
= 1) at two places (μ
= 159 and 1886; d0
= 0.88 and 58.15), suggesting PeCDF could be more potent or less potent than TCDD, depending on the mean response or dose considered. The geometric mean values of μ
(μ) were ρ̆μ
= 0.19 over 34.5 <μ
< 1984, ρ̆μ
= 0.86 over 77.2 <μ
< 1984, and ρ̆μ
= 3.79 over 70.9 <μ
< 1984 for PCB126, PeCDF and the mixture, respectively, relative to TCDD. The upper limit of integration was the same in each case, as the reference TCDD had the lowest value of U
, but the lower limit of integration varied, as TCDD did not have the highest value of L
. Because μ
(μ) and d0
) for the three test chemicals cross each other only near edges of the range of integration, the ordering of these averages agrees with the general appearance of the curves, with the relative potency curve for the mixture lying above that for PeCDF, which in turn lies above that for PCB126.
On the other hand, if one considers the differences between the lower and upper response limits as extrinsic to the comparison, attention should focus on ρπ
(π) . Only for PCB126 does π
(π) fail to cross the equipotency line, though the crossing point for PeCDF at π
= 0.001 is near the edge of the range. For either PCB126 or PeCDF, π
(π) suggests that the respective compounds are less potent than TCDD, whereas π
(π) for the mixture crosses the equipotency line at π
= 0.2, with a negative slope, suggesting that the mixture is more potent than TCDD at low quantiles of response but less potent at higher quantiles. The average values of π
(π) over the interval 0 < π
< 1 were ρ̆π
= 0.19, 0.05, and 0.76 for PCB126, PeCDF and the mixture, respectively, relative to TCDD, in qualitative agreement with the ordering suggested by the curves themselves. The qualitative ordering of the chemicals based on π
(π) differs from that based on μ
(μ) or d0
) , so the issue of whether evident differences in the response limits are intrinsic or extrinsic to the potency comparison has a definite impact.