## [1] "DesignCombo"A logistic log normal model will describe the relationship between dose combinations and toxicity. The two single-agent dose-toxicity surfaces are modelled separately and then combined with an interaction term that captures any additional combination effect.
The first single-agent model is:
A logistic log normal model will describe the relationship between dose and toxicity: \[ p(Tox | d) = f(X = 1 | \theta, d) = \frac{e^{\alpha + \beta \cdot log(d/d_{ref})}}{1 + e^{\alpha + \beta \cdot log(d/d_{ref})}} \]where dref denotes a reference dose.
The prior for θ is given by\[ \boldsymbol\theta = \begin{bmatrix}\alpha \\ log(\beta)\end{bmatrix}\sim N \left(\begin{bmatrix}-0.85 \\ 1.00\end{bmatrix} , \begin{bmatrix} 1.00 & -0.50 \\ -0.50 & 1.00\end{bmatrix} \right) \]
The reference dose will be 10.00.
The second single-agent model is:
A logistic log normal model will describe the relationship between dose and toxicity: \[ p(Tox | d) = f(X = 1 | \theta, d) = \frac{e^{\alpha + \beta \cdot log(d/d_{ref})}}{1 + e^{\alpha + \beta \cdot log(d/d_{ref})}} \]where dref denotes a reference dose.
The prior for θ is given by\[ \boldsymbol\theta = \begin{bmatrix}\alpha \\ log(\beta)\end{bmatrix}\sim N \left(\begin{bmatrix}-0.70 \\ 0.80\end{bmatrix} , \begin{bmatrix} 1.10 & -0.30 \\ -0.30 & 0.90\end{bmatrix} \right) \]
The reference dose will be 20.00.
The prior for the interaction term \(\eta\) is \(N( 0.00, 1.00^2)\).
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 of toxicity is in the target toxicity range of 0.2 to 0.35 (inclusive) will be selected.
≥ 20 patients dosed: If 20 or more participants have been treated.
The minimum of the increments defined in the following rules:
At most one drug may be escalated in any given cohort. If drug 1 is escalated above its last administered dose, then drug 2 must remain at or below its last administered dose, and vice versa.
The maximum admissible doses are defined independently for each drug by the following rules:
Drug 1
| Min | Max | Increment |
|---|---|---|
| 0 | Inf | 1 |
Drug 2
| Min | Max | Increment |
|---|---|---|
| 0 | Inf | 1 |
A constant size of 3 participants.
No participants are yet evaluable.
The dose grid for drug1 is 10, 20 and 30.
The dose grid for drug2 is 20, 40 and 60.
No backfill cohorts at all will be opened.
The starting dose combination is drug1 = 10 and drug2 = 20.