Group sequential tests under fractional Brownian motion in monitoring clinical trials

Abstract

Clinical trials, Fractional Brownian motion, Group sequential design, Hurst coefficient,

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

“…Aggregation may lead to test statistic being long-memory property as described in Beran (1994, pp. 14-16) and as discussed in Lai (2010), that fractional Brownian motion is a convenient model for long memory stochastic processes. It may capture part of the correlated increment structure and lead to better statistical inferences.…”

“…Overall, for the two types of reasons above, we should account for the dependence of the test statistics across time. FBM has been considered for statistical monitoring and recruitment of clinical trials (Lai et al, 2000;Lai, 2004;Lai et al, 2001;Lai, 2010;Zhang andLai, 2010, 2011). Results from Zhang and Lai (2010) showed that when H increases the boundary value, expected sample sizes and stopping times will decrease and power increases.…”

Stochastically Curtailed Tests Under Fractional Brownian Motion

“…They showed that this method has desired properties even for short series with between 20 and 100 observations. Lai (2010) and Zhang and Lai (2010) one-sided group sequential designs and its operating characteristics for various alpha spending functions and analysis times. Results demonstrated that when H increases the boundary values, expected sample sizes/stopping times decrease and power increases for one-sided testing.…”