Proper inference from Simon's two-stage designs

by Tatsuki Koyama, Heidi Chen and Will Gray

Introduction

There are many software available for constructing a Simon's design. These software usually give sample sizes and critical values for stages 1 and 2, therefore, hypothesis testing is simple to conduct. Analyzing the data beyond hypothesis testing, however, is not straightforward when a Simon's design is used. When the actual stage 2 sample size is different from the one originally planned, data analysis is more complicated. Many previously published clinical trials do not correctly account for such mid-course changes. We present a software that computes a preferable P value, a reasonable estimate and a confidence interval for the response rate. The method is based on "Proper inference from Simon's two-stage designs" by Koyama and Chen (under revision as of January 07).

Notation

Response Rate

• Response rate under the null hypothesis
• Response rate under the alternative hypothesis

Stage 1

• Planned sample size for stage 1.
• Critical value for stage 1. Note if there are or more ''successes'' in stage 1, the trial continues to stage 2.

Stage 2 (planned)

• Planned sample size for stage 2.
• Planned critical value at the end of stage 2. Note if there are or more ''successess'' in stage 1 and 2 combined, the null hyopthesis is rejected.

Stage 2 (actual)

• Actual sample size for stage 2.

Data

• Number of successes in stage 1.
• Number of successes in stage 2 (out of or ).

>> Inference from a Simon's Design