Test

## [1] "LogisticLogNormalMixture"

A mixture of two logistic log normal models will describe the relationship between dose and toxicity: \[ p(Tox | d) = f(X = 1 | \theta, d) = 0.1 \times \frac{e^{\alpha_1 + \beta_1 \cdot log(d/d^*)}}{1 + e^{\alpha_1 + \beta_1 \cdot log(d/d^*)}} + (1 - 0.1) \times \frac{e^{\alpha_2 + \beta_2 \cdot log(d/d^*)}}{1 + e^{\alpha_2 + \beta_2 \cdot log(d/d^*)}} \]where d* denotes a reference dose.

The priors for both θ₁ and θ₂ are given by\[ \boldsymbol\theta = \begin{bmatrix}\alpha \\ \beta\end{bmatrix}\sim N \left(\begin{bmatrix}-0.85 \\ 1.00\end{bmatrix} , \begin{bmatrix} 1.00 & -0.50 \\ -0.50 & 1.00\end{bmatrix} \right) \]

The reference dose will be 50.00.