Two-Stage Designs for Phase II Clinical Trials

[[abstract]]Two-stage designs play an important role in the study of new drugs especially toxicity is the endpoint of interest. Given $(p_0,p_1,\alpha,\beta)$, there exists a set $$S=\{(r_1,n_1,r_2,n_2)|r_1 \leq n_1,r_2 \leq n_2,n_1\in\mathds{N},(r_1,r_2,n_2) \in \mathds{N} \cup \{ 0\}\}$$ including all the probable two-stage designs which are satisfied with the two probabilities of error $(\alpha,\beta)$. Every two-stage designs lead to give an expected sample size EN$(p)$, a probability of early termination PET$(p)$, and a total sample size $n=n_1+n_2$. A suggested design can be searched from $S$ once a criterion is given based on EN$(p)$, PET$(p)$, $n$. Optimal and \lq\lq minimax\rq\rq two-stage designs have been discussed in the literature (Simon, 1989). The optimal designs are based on EN$(p_0)$, and the minimax can be considered for $n$ and EN$(p_0)$ where $p_0$ is a given success probability. We find different designs under distinct criteria and these designs give us dissimilar advantage. Several designs under distinct criteria are tabulated for our interested parameters