Monitoring ongoing clinical trials under fractional Brownian motion with drift

Over the past decades, there has been lots of methods developed for monitoring clinical trials and adaptive design under Brownian motion structure. Early efficacy, futility stopping could be conducted by looking at the treatment effect or Z-value at the interim. Conditional power could predict the trial success in the end and sample size re-estimation could be conducted to achieve desired power while a low conditional power is observed. 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. While fractional Brownian motion (fBm) model take dependence into consideration, we could both assume non-linear drift into the model to handle mean change. In this dissertation, we proposed the procedure for inference of Hurst exponent for dependence under fBm with linear drift. Numerical results have been given to detect the property under finite sample size. Moreover, the formula of conditional power and SSR under fBm with linear drift are given. We provide examples to illustrate how to apply the methods on the real study and compare the results between different model structures. 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. Estimation, test of change-point is discussed as well as conditional power calculation under fBm with non-linear drift.Ph.D.Includes bibliographical reference