In a phase II study, the minimal acceptable response rate is 0 = 0.25. We would like the width of the 95% CI of the true response rate using the normal approximation within 5% of this minimum acceptable rate.

We decided to use Gehan's two-stage design for this purpose. In the first stage, we will discard the new treatment if no patient out of n0 patients. Suppose the probability we can tolerate to discard the new treatment is 0 = 0.01 when in fact the actual response rate of this new treatment is greater than the minimum acceptable rate 0 = 0.25.

(a) Describe how you would set up this two-stage design; i.e., how many patients would you treat in the first stage? how many patients in the second stage?

(b) If the actual response rate is 0.25, what is the probability that the trial stops at the first stage?