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Repeated confidence intervals and prediction intervals using stochastic curtailment under fractional Brownian motion

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  • Qiang Zhang
  • Dejian Lai
  • Barry R. Davis

Abstract

Repeated confidence intervals (RCIs) and prediction intervals (PIs) can be used for the design and monitoring of group sequential trials. Stochastically curtailed tests (SCTs) under fractional Brownian motion (FBM) have been studied for the interim analysis of clinical trials (Zhang et al., 2015). In this article, we derive RCIs and PIs based on SCTs under FBM for one-sided derived tests (Jennison and Turnbull, 2000). Comparisons of RCI width and sample size requirement are made to those under Brownian motion (BM) and to those of Pocock and O'Brien-Fleming design types for various type I, type II error rates, and number of interim analyses. Interim data from Beta-Blocker Heart Attack Trial are used to illustrate how to design and monitor clinical trials using these RCIs and PIs under FBM. Results show that these one-sided derived tests based on SCTs have narrower final confidence intervals and require smaller sample sizes than those using classical group sequential designs. The Hurst parameter has more impact on the RCI width than on the sample size requirements for the proposed designs.

Suggested Citation

  • Qiang Zhang & Dejian Lai & Barry R. Davis, 2016. "Repeated confidence intervals and prediction intervals using stochastic curtailment under fractional Brownian motion," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(14), pages 4295-4306, July.
    • Handle: RePEc:taf:lstaxx:v:45:y:2016:i:14:p:4295-4306
    DOI: 10.1080/03610926.2014.919400
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