Two-stage stepwise procedures for dose-finding in clinical trials with a biological endpoint

In clinical development of a new treatment, a phase I trial generally aims to determine the maximum dose that produces an acceptable level of toxicity, the so-called maximum tolerated dose (MTD). The traditional role of a phase II trial is a "proof of concept" by examining the potential efficacy of the new regimen. A common objective is often to identify doses that exhibit sufficient level of biological activity via the estimation of the minimum effective dose (MED) when compared to a placebo control. Stepwise test procedures for dose finding have been well studied in the context of non-human trials where sampling is done in one stage. Recently, increasing efforts have been made to seek trial designs which incorporate interim analysis to screen out ineffective doses at an early stage with the hope to reduce the sample size in general.; In this work we propose several two-stage designs which employ consecutively the standard one-stage stepwise test procedures. The decision rules of the proposed two-stage designs are calibrated to preserve the familywise type I error and to achieve comparable probability of correct selection with their one-stage competing procedures. The proposed methods are illustrated in re-designing two motivating clinical trials. Our findings indicate that the proposed designs reduce the required total sample size with a high probability except under the scenario when all doses tested are acceptable in terms of efficacy and toxicity. General guidelines on the choice of design parameters are given based on our findings.