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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 \( \mathit{\ln}\left(\frac{p_i}{1-{p}_i}\right) \)
  1. Notation: pi = skeleton probability of DLT at ith dose level; di = dose label for for ith dose level