Proper inference from Simon's two-stage designs

Abstract

Simon's two-stage designs are very popular for phase II clinical trials. A literature review revealed that the inference procedures used with Simon's designs almost always ignore the actual sampling plan used. Reported P-values, point estimates and confidence intervals for the response rate are not usually adjusted for the design's adaptiveness. In addition, we found that the actual sample size for the second stage is often different from that planned. We present here a method for inferences using both the planned and the actual sample sizes. The conventional and the preferred inference procedures usually yield similar P-values and confidence intervals for the response rate. The conventional inference, however, may contradict the result of the corresponding hypothesis testing.

Figure 1

Extension of the observed conditional P value to other x1 values based on π*. The solid line is the conditional type I error rate, and the dotted line is the conditional power under the alternative. The conditional P value is indicated by a solid circle. The bold line is the conditional power function that goes through this point.