crmPack (version 1.0.6)

LogisticKadane-class: Reparametrized logistic model

Description

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

Slots

theta

the target toxicity probability \(\theta\)

xmin

the minimum of the dose range \(x_{min}\)

xmax

the maximum of the dose range \(x_{max}\)

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.

Examples

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