PRINCIPLES OF TOXICOLOGY

Rboth = 1– (1 – Rchemical A) × (1 – Rchemical B)
When the probabilities are small, this reduces to simply
18.7 EVALUATING RISK FROM CHEMICAL MIXTURES 467
Rboth = Rchemical A + Rchemical B
This approach is considered to be useful in summing a series of small component risks, but does not
work well when one or more of the risks is large. In practice, response addition is used primarily in
developing estimates of total cancer risks from more than one chemical or from chemical exposure by
more than one route.
Each of the above mentioned approaches to combining risks assumes no interaction among
chemicals. This is not always the case. It is possible that in some instances one chemical might
antagonize or inhibit the toxicity of another. In this situation, the combination of chemicals would
produce less-than-additive toxicity. This could conceivably occur through a variety of means depending
on the mechanism(s) of toxicity of the chemicals and their toxicokinetics. Examples include effects to
decrease toxicant absorption, increase its elimination or decrease its bioactivation, competition for
receptor binding, or production of an opposing biochemical or physiological effect. Chemicals in
combination can also produce greater-than-additive effects. When both chemicals are capable of
Figure 18.8 Isobologram of effects of two chemicals administered in varying dose combinations. The response
obtained from chemical A alone is on the y axis, and the response from chemical B alone is plotted on the x axis.
When there is no interaction between the chemicals, the responses from doses comprised of varying proportions of
chemicals A and B will fall on a straight line connecting the response for 100% chemical A to 100% chemical B
(squares in the figure). If there is antagonism between the chemicals, responses to combinations of the chemicals
will lie below and to the left of this line (triangles), and synergistic responses will lie above and to the right of the
line (circles).