NEED FOR A BETTER DOSE-RESPONSE CHARACTERIZATION
The regulatory upper-bound potency measures (like q1*) based on the linearized multistage model tend to overstate the risks. Sometimes this overstatement may be by several orders of magnitude. Sometimes this overstatement may be in the form of positive risks when the real risks are zero.
The multistage models maximum likelihood estimates tend to overstate risks less than the linearized multistage models upper-bound potency measures (like q1*). However, the multistage models maximum likelihood estimates may still overstate the risks corresponding to the observed data at the lower doses.
As illustrated in Figure 10, the problem is that a linear dose-response relationship like that assumed in the linearized multistage model will always overstate the risks in a sublinear dose-response relationship. This overstatement will be most severe (relatively) at lower doses. Furthermore, a linear or sublinear non-threshold dose-response relationship like that assumed in the multistage model will always overstate the risks at doses below a threshold. A threshold is a dose level below which the probability of response is the same as the probability of response when the dose equals zero. Many biological processes may have a practical threshold in the sense that the probabilities of response at sufficiently low doses are practically the same as the probability of response at dose zero.
Figure 11 illustrates the failure of the multistage models maximum likelihood estimates to reflect dose levels that are likely to be without appreciable risks of deleterious effects during a lifetime. This failure is due to the restrictions implicit in the structure (functional form) of the multistage model and due to the current regulatory restrictions that require the parameters in the multistage model to be greater than or equal to zero. This failure occurs regardless of how large the sample sizes are in the observed data. The failure of the linearized multistage model and its regulatory upper bounds is even worse.
>> Figure 10
>> Figure 11 |