ADDED RISK VERSUS EXTRA RISK
Thus far, it has been noted that the regulatory upper-bound potency measures (like q1*) based on the linearized multistage model tend to overstate the risks more than the multistage models maximum likelihood estimates and that these maximum likelihood estimates may even overstate the risks corresponding to the observed data at the lower doses. Although the discussion is moving toward a newer and better characterization of the observed dose-response information and risk, it is perhaps useful to digress slightly in order to more precisely define the terms added risk and extra risk and to indicate the advantages of discussing risk in terms of the added risk.
The mathematical definitions of added risk and extra risk are given in Figure 9. Namely, if
P(d) = Probability of an adverse health effect when the dose is d,
then the added risk at dose d is defined as
Added Risk (d) = P(d) - P(0)
which is simply the increase in the probability at dose d above the background probability (P(0)) at dose 0. On the other hand, the extra risk at dose d is defined as
Extra Risk (d) =
[ Added Risk (d) ] / [ 1 - P(0) ]
= [ P(d) - P(0) ] / [ 1 - P(0) ]
which is the increase in the probability of an adverse health effect above the background probability of an adverse health effect given the condition that the individual would not have had the adverse health effect at the background dose (dose 0).
Although the U.S. Environmental Protection Agency (EPA) default practice has been to quantify dose-response characteristics in terms of the extra risk instead of added risk, there are important advantages to using added risk instead of extra risks.
If the dose-response characteristic is defined in terms of added risk, then the dose-response characteristic refers to the whole population. This makes the communication of dose-response characteristics based on added risk more straightforward and the relevant population clearer. Furthermore, if two different substances have the same added risk and the same number of individuals are exposed to each substance, then the increased number of individuals expected to develop the specified adverse health effect are the same for both substances. On the other hand, if the dose-response characteristic is defined in terms of extra risk, then the dose-response characteristic only refers to part of the population (a subset of the population) and not necessarily the whole population. This makes the communication of dose-response characteristics based on extra risk less straightforward and the relevant population less clear. Furthermore, if two different substances have the same extra risk and the same number of individuals are exposed to each substance, then the increased number of individuals expected to develop the specified adverse health effect is not necessarily the same for both substances.
>> Figure 9 |