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Asymptotic properties of the two one-sided t-tests – new insights and the Schuirmann-constant

Author

Listed:
  • Palmes Christian

    (Boehringer Ingelheim Pharma GmbH & Co. KG, Birkendorfer Str. 65, 88397 Biberach, Germany)

  • Bluhmki Tobias

    (Ulm University, Helmholtzstr. 20, 89081 Ulm, Germany)

  • Funke Benedikt

    (FH Aachen, University of Applied Sciences, Eupener Str. 70, 52066 Aachen, Germany)

  • Bluhmki Erich

    (Boehringer Ingelheim Pharma GmbH & Co. KG, Birkendorfer Str. 65, 88397 Biberach, Germany)

Abstract

The two one-sided t-tests (TOST) method is the most popular statistical equivalence test with many areas of application, i.e., in the pharmaceutical industry. Proper sample size calculation is needed in order to show equivalence with a certain power. Here, the crucial problem of choosing a suitable mean-difference in TOST sample size calculations is addressed. As an alternative concept, it is assumed that the mean-difference follows an a-priori distribution. Special interest is given to the uniform and some centered triangle a-priori distributions. Using a newly developed asymptotical theory a helpful analogy principle is found: every a-priori distribution corresponds to a point mean-difference, which we call its Schuirmann-constant. This constant does not depend on the standard deviation and aims to support the investigator in finding a well-considered mean-difference for proper sample size calculations in complex data situations. In addition to the proposed concept, we demonstrate that well-known sample size approximation formulas in the literature are in fact biased and state their unbiased corrections as well. Moreover, an R package is provided for a right away application of our newly developed concepts.

Suggested Citation

  • Palmes Christian & Bluhmki Tobias & Funke Benedikt & Bluhmki Erich, 2022. "Asymptotic properties of the two one-sided t-tests – new insights and the Schuirmann-constant," The International Journal of Biostatistics, De Gruyter, vol. 18(1), pages 19-38, May.
    • Handle: RePEc:bpj:ijbist:v:18:y:2022:i:1:p:19-38:n:18
    DOI: 10.1515/ijb-2020-0057
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