Test

## [1] "DualEndpointRW"

The relationships between dose and toxicity and between dose and PD biomarker will be modelled simultaneously.

A probit log normal model will describe the relationship between dose and toxicity: \[ \Phi^{-1}(Tox | d) = f(X = 1 | \theta, d) = \alpha + \beta \cdot log(d/d^*) \]where d* denotes a reference dose.

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

The reference dose will be 1.00.

The PD biomarker response w at dose d is modelled as \[ w(d) \sim N(f(d), \sigma_w^2) \]

where f(d) is a first order random walk such that

\[ f(d) = \beta_{W_i} - \beta_{W_{i - 1}}\sim N(0, 0.01 \times (d_i - d_{i - 1})) \]