Sequential monitoring clinical trial by conditional power under drift fractional Brownian motion

Abstract

In this article, using conditional power, we extended the widely used classical Brownian motion (Bm) technique for monitoring clinical trial data to a larger class of stochastic processes fractional Brownian motion (fBm) with drift, and compare these results. We applied a Bayesian method to estimate parameters. The simulation study is presented as an example to illustrate scenarios under classical and fractional Brownian motion. We demonstrated the drift fractional Brownian motion in sequential monitoring of clinical trials and provided a formula for calculating conditional power under an alternative hypothesis for interim analysis. We investigated cases commonly used in clinical trials, with the Hurst parameter H = 0.5 and H > 0.5, respectively. Our simulation study suggests that the conditional power under the fBm assumption is generally higher than that under the Bm assumption when H > 0.5 and also matches better with our empirical results.