LogisticKadane — LogisticKadane-class • crmPack

LogisticKadane is the class for the logistic model in the parametrization of Kadane et al. (1980).

Usage

LogisticKadane(theta, xmin, xmax)

.DefaultLogisticKadane()

Arguments

theta: (proportion)
the target toxicity probability.
xmin: (number)
the minimum of the dose range.
xmax: (number)
the maximum of the dose range.

Details

Let rho0 = p(xmin) be the probability of a DLT at the minimum dose xmin, 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 $$[gamma * logit(rho0) - xmin * logit(theta)] / [gamma - xmin]$$ and slope $$[logit(theta) - logit(rho0)] / [gamma - xmin].$$

The priors are $$gamma ~ Unif(xmin, xmax).$$ and $$rho0 ~ Unif(0, theta).$$

Slots

theta: (proportion)
the target toxicity probability.
xmin: (number)
the minimum of the dose range.
xmax: (number)
the maximum of the dose range.

Note

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.

Typically, end-users will not use the .DefaultLogisticKadane() function.

Examples

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