On a generalization of the logistic distribution

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(- theta - beta'x)]-alpha, where alpha > 0. This function coincides with the usual logistic response when the shape parameter alpha 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.