Bayesian Analysis of Drift Fractional Brownian Motion for Monitoring Clinical Trials

Leixin Xia, The University of Texas School of Public Health


Clinical trials are commonly used for evaluating the safety and benefits of drugs, medical devices and the therapies. They provide information for patients, physicians and pharmaceutical companies to develop and evaluate treatments and devices. Classical Brownian motion techniques have been used for sequential monitoring of clinical trials (Lan K. K., 1988; Lan K. K., 1993). If some of the assumptions that generate Brownian motion are only partially met, then we need a more general class of stochastic processes. Previous studies consider the conditional power only under null hypothesis for standard fractional Brownian motion. It noteworthy that Z-value in interim analysis may exhibit linear trend (Lan K. K., 1988), and how to calculate the conditional power under alternative hypothesis remains unknown for fractional Brownian motion, because there was no straightforward way to estimate the drift parameter. In this dissertation, we propose a Bayesian estimation method for drift fractional Brownian motion, our Bayesian framework can estimate all three unknown parameters, we simulated a wide range of fBm data, e.g., H = 0.5 (that is, classical Bm) vs. 0.5 0.5 and also matches better with the empirical results.

Subject Area

Statistics|Statistical physics|Applied Mathematics|Biomedical engineering

Recommended Citation

Xia, Leixin, "Bayesian Analysis of Drift Fractional Brownian Motion for Monitoring Clinical Trials" (2021). Texas Medical Center Dissertations (via ProQuest). AAI29060204.