Low-dose extrapolation using the power family of response functions
The power family of response functions is introduced for modeling low-dose binary response data. These functions may be expressed in terms of the incomplete gamma function indexed by a shape parameter, and they include as special cases the probit, gamma, extreme-value, double exponential, and uniform response functions. Although these response functions do not have a closed form, we show that maximum likelihood estimates (MLEs) of the parameters are easily obtained by using a Bounded Algorithm given by Devidas and George (Statist. Med. 12(9) (1999) 881892). The efficacy of the power family for estimating low-dose responses, is illustrated by analyzing the ED01 data of Farmer et al. (J. Environ. Path. Toxicol. 3 (1979) 5568).
incomplete gamma function probit ed01 data