Test

## [1] "LogisticLogNormalOrdinal"

Let p_k(d) be the probability that the response of a patient treated at dose d is in category k or higher, k=0, …, K; d=1, …, D.

Then \[ p_k(d) = f(X \ge k \; | \; \theta, d) = \begin{cases} 1 & k = 0 \\ \frac{e^{\alpha_k + \beta \cdot log(d/d^*)}}{1 + e^{\alpha_k + \beta \cdot log(d/d^*)}} & k=1, ..., K\end{cases} \]

where d* denotes a reference dose.

The αs are constrained such that α₁ > α₂ > … > α_K.

The prior for θ is given by\[ \boldsymbol\theta = \begin{bmatrix}\alpha_1 \\ \alpha_2 \\ \beta\end{bmatrix}\sim N \left(\begin{bmatrix}-3.00 \\ -4.00 \\ 1.00\end{bmatrix} , \begin{bmatrix} 3.00 & 0.00 & 0.00 \\ 0.00 & 4.00 & 0.00 \\ 0.00 & 0.00 & 1.00\end{bmatrix} \right) \]

The reference dose will be 50.00.