Conditional exact tests for dichotomous data in the comparison of two treatments with one control group

When we compare two treatments with one control group for dichotomous data whose response rates are expected to be small, Dunnett's test based on the large sample theory is unreliable. Hence, exact tests that are reliable in the cases of either small response rate or small samples need to be developed. In this article, we investigate the exact unconditional powers of the three exact tests (the two-step closed Fisher's exact test, the exact conditional Dunnett test, and the new conditional exact test proposed here). The exact unconditional power is computed based on complete enumeration. In many phase 3 clinical trials, two possible optimal doses from phase 2 clinical trials are expected to be more promising than the control. Therefore, the response rates of two possible optimal doses are greater than that of the control group. In such cases, we show that the new exact test is more powerful than the other two exact tests.