Test

## [1] "LogisticKadaneBetaGamma"

A logistic model using the parameterisation of Kadane (1980) will describe the relationship between dose and toxicity, using a Beta distribution as the prior for ρ₀ and a Gamma distribution as the prior for γ.

Let the minimum (x_min) and maximum (x_max) doses be 0.00 and 7.00.

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 = 0.3.

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 \[ \Gamma \sim U( 0.56, 0.12) \] and, independently, \[ \mathrm{P}_0 \sim Beta(1, 19) \]

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.