Repeated Confidence Intervals Under Fractional Brownian Motion in Long-Term Clinical Trials

Abstract

Repeated confidence interval (RCI) is an important tool for design and monitoring of group sequential trials according to which we do not need to stop the trial with planned statistical stopping rules. In this article, we derive RCIs when data from each stage of the trial are not independent thus it is no longer a Brownian motion (BM) process. Under this assumption, a larger class of stochastic processes fractional Brownian motion (FBM) is considered. Comparisons of RCI width and sample size requirement are made to those under Brownian motion for different analysis times, Type I error rates and number of interim analysis. Power family spending functions including Pocock, O'Brien-Fleming design types are considered for these simulations. Interim data from BHAT and oncology trials is used to illustrate how to derive RCIs under FBM for efficacy and futility monitoring.

Keywords:

• Brownian motion
• Fractional Brownian motion
• Group sequential trial
• Interim analysis
• Repeated confidence intervals

Mathematics Subject Classification:

• 60J65
• 60G22
• 62L10

Acknowledgment

Project supported by RTOG grant U10 CA21661 and CCOP grant U10 CA37422 from the NCI.

Notes

*The ratios are CI width at t = 1 to unadjusted CI and sample sizes to that of a fixed design.