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Generalized logistic models for low—dose response data
Author(s) -
Devidas Meenakshi,
George E. Olusegun,
Zelterman Daniel
Publication year - 1993
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.4780120907
Subject(s) - extrapolation , logistic regression , generalization , statistics , logistic function , mathematics , function (biology) , a priori and a posteriori , medicine , econometrics , biology , mathematical analysis , philosophy , epistemology , evolutionary biology
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.