Illustration of the waterfall design for a 3 × 5 combination trial. The doses in the rectangle form a subtrial, and the asterisk denotes the candidate MTD. As shown in panel (a), the trial started by conducting the first subtrial with the starting dose A1B1. After the first subtrial identified A3B2 as the candidate MTD, we conducted the second subtrial with the starting dose A2B3 (see panel (b)). After the second subtrial identified A2B4 as the candidate MTD, we conducted the third subtrial with the starting dose A1B5 (see panel (c)). After all the subtrials were completed, we selected the MTD contour based on the data from all the subtrials, as shown in panel (d).