## [1] "DualDesign"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
\[ f(d) = \beta_{W_i} - \beta_{W_{i - 1}}\sim N(0, 0.01 \times (d_i - d_{i - 1})) \]
No participants are yet evaluable.
The dose grid is 1, 3, 5, 10, 15, 20, 25, 40, 50, 80 and 100.
If either of the following rules are TRUE:
P(0.9 ≤ Biomarker ≤ 1) ≥ 0.5 (relative): If, at the next best dose, the posterior probability that the target biomarker is in the range (0.90, 1.00), relative to the maximum value of the target biomarker, is 50% or more.
≥ 40 patients dosed: If 40 or more participants have been treated.
| Min | Max | Increment |
|---|---|---|
| 0 | 20 | 1.00 |
| 20 | Inf | 0.33 |
Placebo will not be administered in the trial.
The dose recommended for the next cohort will be chosen in the following way. First, doses that are ineligible according to the increments rule will be discarded. Next, any dose for which the mean posterior probability of toxicity being in the overdose range - (0.35, 1] - is 0.25 or more will also be discarded. Finally, the dose amongst those remaining which has the highest chance that the mean posterior probability that the biomarker is in the target range for the biomarker, which is 0.9 to 1 (inclusive), of the maximum the biomarker value will be selected, provided that this probability exceeds 0.01. If no dose meets this threshold, then the highest eligible dose will be selected.
| Lower | Upper | Cohort size |
|---|---|---|
| 0 | 30 | 1 |
| 30 | Inf | 3 |
| Lower | Upper | Cohort size |
|---|---|---|
| 0 | 1 | 1 |
| 1 | Inf | 3 |
The starting dose is 3.