LINEARIZED MULTISTAGE MODEL

The overstatement of added risks by potencies is made even worse when the potencies are not determined from the maximum likelihood estimate of the dose-response model but instead are inferred from upper bounds on the dose-response model.  The most common set of regulatory upper bounds is the linearized multistage model.  The linearized multistage model is not really a dose-response model at all; that is, it is not one curve fit to data.  Instead, the linearized multistage model is a set of upper bounds on the probabilities of the specified response at the different dose levels.  As suggested in Figure 4, the linearized multistage model upper-bound value on the risk at each dose corresponds to the largest added risk that can be obtained from any multistage model that can not be rejected as providing a fit that is too inferior relative to the fit of the MLE of the multistage model.  For most doses, the linearized multistage model upper-bound value at a dose corresponds to the largest added risk that can be obtained by making the linear term in the multistage models as large as possible.  Usually the linear term in the multistage model is denoted by q₁ and the much larger values in the linearized multistage model at low doses are denoted by q₁^*.  The linearized multistage models q₁^* upper bound on the slope of the extra risk is the potency most often used to overstate the added risks implied by the multistage dose-response model (Figure 5).

>> Figure 4

>> Figure 5