POTENCY

Potencies are frequently used to loosely characterize dose-response models. For example, when the time of the occurrence of a specified response is being ignored, then a dose-response model evaluated at a dose d is the probability, say P(d), that the specified response will occur at dose d.  The added risk from being at dose d instead of dose 0 is P(d)-P(0) -- the increased probability above the background probability, P(0).  This added risk can be calculated directly from the dose-response model.  However, such added risks are frequently approximated (overstated) by straight-line representations of the dose-response curve or upper bounds on the dose-response curve.  The slopes of these straight lines are called potencies.

For example, in Figure 3 a straight line has been drawn between the fitted dose-response models estimated probability of the specified response at dose d=MTD/2 (one half of the maximum tolerated dose (MTD)) and the corresponding probability at dose d=0.  The slope of such a straight line is frequently called the potency or even more loosely called the low-dose potency even though it may have been determined from the fitted model at relatively high doses (or determined from upper bounds on the response probabilities at relatively high doses).  Such a slope is often used to approximate (mischaracterize, overstate) the added risks at lower doses.  For example, even at a dose like MTD/4 (which would usually be quite high relative to environmental exposures), the added risk according to the estimated dose-response model is significantly less than the added risk inferred from the potency and the corresponding straight-line representation of the dose-response curve.   The overstatement of the added risk at MTD/4 inferred from the potency instead of the maximum likelihood estimate from the fitted multistage dose-response model is indicated in Figure 3.

>> Figure 3