Test

## [1] "LogisticNormalMixture"

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

The prior for θ is given by \[ \theta = \begin{bmatrix} \alpha \\ log(\beta) \end{bmatrix} \sim w \cdot N \left(\begin{bmatrix}-0.85 \\ 1.00\end{bmatrix} , \begin{bmatrix} 1.00 & -0.50 \\ -0.50 & 1.00\end{bmatrix} \right) + (1 - w) \cdot N \left(\begin{bmatrix} 1.00 \\ 1.50\end{bmatrix} , \begin{bmatrix} 1.20 & -0.45 \\ -0.45 & 0.60\end{bmatrix} \right) \]

and the prior for w is given by

\[ w \sim Beta( 1.00, 1.00) \]

The reference dose will be 50.00.