| Abstract: | In the group sequential (GS) approach with a fixed sample size design, the Type I error is controlled by the additivity of exit spending values. However, in a flexible sample size design where the sample size will be recalculated using the interim data, the overall Type I error rate can be inflated. Therefore, the predefined GS stopping boundaries have to be adjusted to maintain the Type I error level at each interim analysis and the at the overall level. The modified α spending function adjusted for sample size reestimation (SSR) is proposed to maintain the Type I error level. We use a unified approach and mathematically quantify the Type I error with and without sample size adjustment constraints. As a result, stopping boundaries can be obtained by inversely solving the exact Type I error functions. This unified approach, using Brownian motion theory, can be applied to normal, survival, and binary endpoints. Extensive simulations show the adjusted stopping boundaries can control the Type I error at each analysis and at the overall level. |
