Two-Stage Dose Finding For Cytostatic Agents Under Umbrella Order

Establishing the dose–response relationship is one of the most importantactivities in developing a new drug. A clinical development program for a new drugcan be broadly divided into three phases. Some statists divide it into four phases. Theyregard post-marketing studies as the fourth phase. The primary mission of phase Ⅰisto identify the MTD, which is the maximum tolerated dose. The goal of phase Ⅱis todetermine the most efficient dose. What we do in phaseⅢ is so-call “ComparativeExperiments”. Dose-finding of all kinds of methods play important roles in phaseⅡ.A good method in dose-finding can save a lot of money, energy, and time. In thispaper what we consider is to structure a method of finding the most efficient dose inthe umbrella sharp constraints.