Test

## [1] "LogisticKadane"

A logistic model using the parameterisation of Kadane (1980) will describe the relationship between dose and toxicity.

Let the minimum (x_min) and maximum (x_max) doses be 1.00 and 200.00.

Further, let θ denote the target toxicity rate and ρ₀ = p(DLT | D = x_min).

Let γ be the dose with target toxicity rate θ, so that p(DLT | D = γ) = θ = 0.33.

Using this parameterisation, standard logistic regression model has slope \[ \frac{\gamma \text{logit}(\rho_0) - x_{min} \text{logit}(\theta)}{\gamma - x_{min}} \] and intercept \[ \frac{\text{logit}(\theta) - logit(\rho_0)}{\gamma - x_{min}} \] The priors for Γ and Ρ₀ are \[ \Gamma \sim U( 1.00, 200.00) \] and, independently, \[ \mathrm{P}_0 \sim U(0, 0.33) \]

Note that x_min and x_max need not be equal to the smallest and largest values in the doseGrid slot of the corresponding Data object.