Efficient calculation of test sizes for non-inferiority

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


The nuisance parameter presents a serious computational obstacle to the calculation of test sizes in non-inferiority tests. This obstacle is the principal reason why studies performing unconditional non-inferiority tests calculate test sizes for only a few cases, only by simulation or with gross approximations. Typically, when fine approximations are made to calculate test sizes for non-inferiority tests, the calculation is made with the exhaustive method, which demands considerable computational effort. Although Newton's method is generally more efficient than the exhaustive method, implementing the former requires that the first two derivatives of the power function have manageable closed forms. Unfortunately, for general critical regions, these derivatives have unmanageable representations. In this paper, we prove that when the critical regions are Barnard convex sets, the first two derivatives of the power function can take manageable closed forms, so Newton's method can be applied to calculate the test sizes. Because of the rapid convergence of Newton's method and the control that we have over the obtained precision, this method saves calculation time.

Original languageEnglish
Pages (from-to)4138-4145
Number of pages8
JournalComputational Statistics and Data Analysis
Issue number12
StatePublished - Dec 2012


  • Newton's method
  • Non-inferiority tests
  • Proportions
  • Test sizes
  • Unconditional tests


Dive into the research topics of 'Efficient calculation of test sizes for non-inferiority'. Together they form a unique fingerprint.

Cite this