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Efficient calculation of test sizes for non-inferiority

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  • Almendra-Arao, Félix

Abstract

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.

Suggested Citation

  • Almendra-Arao, Félix, 2012. "Efficient calculation of test sizes for non-inferiority," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 4138-4145.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:12:p:4138-4145
    DOI: 10.1016/j.csda.2011.11.008
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    References listed on IDEAS

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    1. Munk, A. & Skipka, G. & Stratmann, B., 2005. "Testing general hypotheses under binomial sampling: the two sample case--asymptotic theory and exact procedures," Computational Statistics & Data Analysis, Elsevier, vol. 49(3), pages 723-739, June.
    2. Skipka, G. & Munk, A. & Freitag, G., 2004. "Unconditional exact tests for the difference of binomial probabilities--contrasted and compared," Computational Statistics & Data Analysis, Elsevier, vol. 47(4), pages 757-773, November.
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