Table 1 Common choices for dose-toxicity models and resultant dose labels for the CRM
From: How to design a dose-finding study using the continual reassessment method
Model name | Model (F(β, d)) | General form of dose labels (di) | Choice of β* (prior mean or median) | Dose labels given β* (di) |
|---|---|---|---|---|
Power (empiric) | d exp( β) | \( {p}_i^{\frac{1}{\mathit{\exp}\left(\beta \right)}} \) | β = 0 | p i |
One-parameter logistic | \( \frac{\mathit{\exp}\left(3+\mathit{\exp}\ \left(\beta \right)\ d\right)}{1+\mathit{\exp}\left(3+\mathit{\exp}\ \left(\beta \right)\ d\right)} \) | \( \frac{\mathit{\ln}\left(\frac{p_i}{1-{p}_i}\right)-3}{\mathit{\exp}\left(\beta \right)} \) | β = 0 | \( \mathit{\ln}\left(\frac{p_i}{1-{p}_i}\right)-3 \) |
Two-parameter logistic | \( \frac{\mathit{\exp}\left({\beta}_1+\mathit{\exp}\ \left({\beta}_2\right)\ d\right)}{1+\mathit{\exp}\left({\beta}_1+\mathit{\exp}\ \left({\beta}_2\right)\ d\right)} \) | \( \frac{\mathit{\ln}\left(\frac{p_i}{1-{p}_i}\right)-{\beta}_1}{\mathit{\exp}\left({\beta}_2\right)} \) | β1 = 0, β2 = 0 | \( \mathit{\ln}\left(\frac{p_i}{1-{p}_i}\right) \) |