A Calculus for Design of Two-Stage Adaptive Procedures

Abstract

We propose calculus for designing two-stage adaptive procedures. We describe the design components that specify a two-stage adaptive design, define their interrelationships, and demonstrate how changes in one design component effect changes in the other components. Our technique allows us to control many aspects of a two-stage adaptive clinical trial, including the type I and type II error rates and the maximum total sample size. We also conduct an ANOVA-type study to understand the effects of different components of the design specification on the performance characteristics of the design. Stage I components—namely sample size, type I error rate, and type II error rate—are found to be the most influential.