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ERRATA—Replaces page 101 oŁ EPA/630/R-00/002
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Scenarios 1 and 3 are not quite as simple. Because these scenarios are identical except
for the direction of the interaction (and hence the WOE weighting factors), only scenario 1 will
be examined in detail. If each of the chemicals in the mixture is present in equitoxic amounts,
then all the Hazard Quotients are equal. Equation 4-15 yields an adjusted HI five times greater
than the HI based on additivity. Note that hi this simple case, both By = 1 and 6^ = 1. Assuming
that M is set to 5 (the proposed scenario says each chemical is known to potentiate the other by a
factor of 5), then Equation 4-15 reduces to:
Thus, if the HI based on additivity were 1, the HI considering interactions would be 5. The
counterpart, scenario 3, would give an interaction-based HI of 0.2.
Suppose, however, that the mixture of chemicals 1, 2, and 3 was such that the hazard
quotients of each chemical were 0.98, 0.01, and 0.01, respectively. For such a mixture, it would
not seem reasonable to assume as great an interaction as in the equitoxic mixture because the
relative amounts of chemicals 2 and 3 are much smaller than hi the equitoxic mixture. For this
98:1:1 mixture of the three chemicals, 0y < 1 for pairs involving chemical 1, resulting hi a
decrease in the interaction-based HI. For the effect of chemical 2 on chemical 1, using Equation
4-17 gives:
6I2 = (0.98*0.01)'5 / (0.99/2) = 0.2, f,2 = 0.01 / (1.00-0.98) = 0.5
Thus, the partial adjusted hazard quotient for just the effect of chemical 2 on chemical 1 is:
'*= 0.98*0.5*5°-2=0.676
By symmetry, the effect of chemical 3 on chemical 1 would also be 0.676. Thus, the adjusted
hazard quotient for chemical 1 would be 1:35 [=0.676+0.676], a 38% increase over HQj.
By applying the same hazard quotients to the other terms hi Equation 4-15, the adjusted
hazard quotients for chemicals 2 and 3 can be determined. The adjusted hazard quotient for
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