Generalized logistic models for low—dose response data


We discuss a generalization of the logistic response function of the form Pr(y = 1|x) = {1 + exp( − θ − β'x)}−α, where α > 0. This function coincides with the usual logistic response when the shape parameter α is equal to one. We describe the use of this model for analysing cancer rates in mice for low‐dose exposure to a known carcinogen. When estimating the low‐dose responses, the errors associated with extrapolation are reduced when a priori knowledge about the rates among unexposed individuals is incorporated into the fitting procedures. Copyright © 1993 John Wiley & Sons, Ltd.

Publication Title

Statistics in Medicine