Multihit dose response

K. Rai, and J. Van Rysin (1979), A generalized multihit dose/response model for low-dose extrapolation, Biometrics, 37, 341. 

Pharmacokinetic models involving nonlinear kinetics of the Michaelis-Menten form have the important extrapolation characteristic of being linear at low dose levels. This low dose linearity contrasts with the low dose nonlinearity of the multihit and Weibull models. Each model, pharmacokinetic, multihit, and Ifeibull, has the desirable ability to describe either convex (upward curvature) or concave (downward curvature) dose-response relationships. Other models, stich as the log normal or multistage, are not consistent with concave relationships. However, the pharmacokinetic model differs from the multihit and Heibull in that it does not assume the nonlinear behavior observed at high dose levels will necessarily correspond to the sane nonlinear behavior at low dose levels. 

It might be thought that the basis for selection of one particular model over the others would be provided by the observed dose-response. However, this is often not the case, as many dose-response models appear similar to one another over the range of observable response rates. Tables II and III compare the dose-response relationships of the more commonly used models Table II compares the log normal, log logistic and single-hit models Table III compares the multihit, Weibull and multistage models. 

Table III. Comparison of Dose-Response Relationships Over Range of Observable and Extrapolated Rates Multihit, Weibull, and Multistage Models...

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