Algorithm 2.

Adaptive PIPE with $ϵ$-tapering:

0. Set the dose for the first subject at the highest level $\left(K_A,K_B\right)$.

1. Enroll and treat a subject at a time.

2. Evaluate ${\hat{\mathit{\gamma }}}^{\text{GP}}$ using ${ϵ}_n$ based on data in the current $n$ subjects.

3. Define the sampling grid $\left({𝒮}_1\cup {𝒮}_0\right)$ in the same manner as in Algorithm 1.

4. Go to Step 1 with the dose randomly drawn from ${𝒮}_1\cup {𝒮}_0$, with two variations:

(a) Select all doses in ${𝒮}_1\cup {𝒮}_0$ with equal probability (Algorithm 2-EQ), or,

(b) Select a dose $(j,k)\in {𝒮}_1\cup {𝒮}_0$ with probability proportional to $p_{jk}$ (Algorithm 2-PP).