Test

## [1] "LogisticLogNormalGrouped"

A logistic log normal model will describe the relationship between dose and toxicity: \[ p(Tox | d) = f(X = 1 | \theta, d) = \frac{e^{(\alpha + I_c \times \delta_0) + (\beta + I_c \times \delta_1) \cdot log(d/d^*)}}{1 + e^{(\alpha + I_c \times \delta_0) + (\beta + I_c \times \delta_1) \cdot log(d/d^*)}} \]where d* denotes a reference dose and I_c is a binary indicator which is 1 for the combo arm and 0 for the mono arm.

The prior for θ is given by\[ \boldsymbol\theta = \begin{bmatrix}\alpha \\ \beta \\ log(\delta_0) \\ log(\delta_1)\end{bmatrix}\sim N \left(\begin{bmatrix} 0.00 \\ 0.00 \\ 0.00 \\ 0.00\end{bmatrix} , \begin{bmatrix} 1.00 & 0.00 & 0.00 & 0.00 \\ 0.00 & 1.00 & 0.00 & 0.00 \\ 0.00 & 0.00 & 1.00 & 0.00 \\ 0.00 & 0.00 & 0.00 & 1.00\end{bmatrix} \right) \]

The reference dose will be 1.00.