Monitoring Ongoing Clinical Trials Under Fractional Brownian Motion with Drift
Peng Zhang* and Tai Xie and Yong Lin and Weichung Joe Shih and K. K. Gordon Lan
Over the past decades, there has been lots of methods developed for monitoring clinical trials and adaptive design under Brownian motion structure. Those approached were built under Brownian motion (Bm) structure, which assumes the independent and identical distribution. However, in real clinical trials, sponsor or Data monitoring committee usually could not make the decision based on the one-point statistics but would like to see if any trend exists, in terms of dependence or mean change. In this paper, we proposed the procedure for inference of Hurst exponent for dependence under fBm with linear drift. Moreover, the formula of conditional power and SSR under fBm with linear drift are given. Further, adjusted critical boundary calculation is given if an extreme Hurst exponent is observed to protect type I error rate. Finally, a model of fractional Brownian motion with piece-wise linear drift is developed.