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Stochastically Curtailed Tests Under Fractional Brownian Motion

Author

Listed:
  • Qiang Zhang
  • Dejian Lai
  • Barry R. Davis

Abstract

Stochastic curtailment has been considered for the interim monitoring of group sequential trials (Davis and Hardy, 1994). Statistical boundaries in Davis and Hardy (1994) were derived using theory of Brownian motion. In some clinical trials, the conditions of forming a Brownian motion may not be satisfied. In this paper, we extend the computations of Brownian motion based boundaries, expected stopping times, and type I and type II error rates to fractional Brownian motion (FBM). FBM includes Brownian motion as a special case. Designs under FBM are compared to those under Brownian motion and to those of O’Brien–Fleming type tests. One- and two-sided boundaries for efficacy and futility monitoring are also discussed. Results show that boundary values decrease and error rates deviate from design levels when the Hurst parameter increases from 0.1 to 0.9, these changes should be considered when designing a study under FBM.

Suggested Citation

  • Qiang Zhang & Dejian Lai & Barry R. Davis, 2015. "Stochastically Curtailed Tests Under Fractional Brownian Motion," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(5), pages 1053-1064, March.
    • Handle: RePEc:taf:lstaxx:v:44:y:2015:i:5:p:1053-1064
    DOI: 10.1080/03610926.2012.754469
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