LogisticKadane-class: Reparametrized logistic model

LogisticKadane-classR Documentation

Reparametrized logistic model


This is the logistic model in the parametrization of Kadane et al. (1980).


Let ρ_{0} = p(x_{min}) be the probability of a DLT and the minimum dose x_{min}, and let γ be the dose with target toxicity probability θ, i.e. p(γ) = θ. Then it can easily be shown that the logistic regression model has intercept

(γ logit(ρ_{0}) - x_{min} logit(θ)) / (γ - x_{min})

and slope

(logit(theta) - logit(ρ_{0})) / (γ - x_{min})

The prior is a uniform distribution for γ between x_{min} and x_{max}, and for ρ_{0} as well a uniform distribution between 0 and θ.

The slots of this class, required for creating the model, are the target toxicity, as well as the minimum and maximum of the dose range. Note that these can be different from the minimum and maximum of the dose grid in the data later on.



the target toxicity probability θ


the minimum of the dose range x_{min}


the maximum of the dose range x_{max}


model <- LogisticKadane(theta = 0.33,
                        xmin = 1,
                        xmax = 200)

crmPack documentation built on Sept. 3, 2022, 1:05 a.m.