An Increasing Failure Rate Approach to Low-Dose Extrapolation

Abstract

SUMMARY A new method for conservative low-dose extrapolation is introduced. The method does not depend on a particular parametric model of carcinogenesis, but only that the dose response relation be described by an increasing failure rate function. Use of the method, which is linear in dose for low doses, is described and comparisons are made with existing models. Many of the low-dose extrapolation techniques applied to cancer studies in use today rely on models of carcinogenesis as a basis for analysis. Using the assumption that the dose response function is an increasing failure rate (IFR) function, we present a technique for conservative low-dose extrapolation that is linear in dose for low doses (low-dose linear), is not based on any particular carcinogenesis model, and encompasses many of the models currently in use. Formally, the response is expressed as a right-continuous function F, with 0 0 with F(O-) = 0 and limd oF(d) = 1. Further, we assume that the failure rate of F, defined by r(d) = F'(d)/[ 1 - F(d)], is increasing in d. This is the IFR property. Intuitively, this is equivalent to assuming that each additional dose unit causes an increase in the proportion of tumorless subjects to develop tumors. In a carcinogenesis experiment, a situation like this may be encountered when the toxic substance under study accumulates in the subject before producing tumors. For IFR dose response functions the following result holds (see Barlow and Proschan, 1975). Let do be any fixed dose with F(do) = po. Then we have