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A Numerical Algorithm for Calculating Group Sequential Boundaries

  • Writer: Andrew Yan
    Andrew Yan
  • Jul 8, 2024
  • 1 min read

Updated: Feb 17

Calculating group sequential boundaries involves recursive evaluations of complex multivariate normal integrals. The Markov property of the standardized test statistics in a group sequential setting simplifies these calculations into successions of univariate integrals. Interestingly, Schoenfeld (2001) showed that the probability of crossing group sequential boundaries at each analysis can be calculated as a multiplication of a sequence of matrices, which can be used recursively to obtain the boundary values through numerical approximations. This post introduces this algorithm and provides an implementation using the SAS IML procedure.




The following document (gsd_apprx.docx) provides an implementation of this algorithm using the SAS IML procedure. Boundaries for one-sided tests under 𝜃 = 0 and those under the alternative hypotheses can be obtained in the same manner.



References

Schoenfeld, D. A. (2001). A simple Algorithm for Designing Group Sequential Clinical Trials. Biometrics 57, 972-974.

 
 
 

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