LogisticKadane-class {crmPack}

Reparametrized logistic model

Description

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

Details

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

\frac{\gamma logit(\rho_{0}) - x_{min} logit(\theta)}{\gamma - x_{min}}

and slope

\frac{logit(theta) - logit(\rho_{0})}{\gamma - x_{min}}

The prior is a uniform distribution for \gamma between x_{min} and x_{max}, and for \rho_{0} as well a uniform distribution between 0 and \theta.

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.

Slots

theta

the target toxicity probability \theta

xmin

the minimum of the dose range x_{min}

xmax

the maximum of the dose range x_{max}

Examples

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