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Exact linear rank tests for two‐sample equivalence problems with continuous data

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  • Arnold Janssen
  • Stefan Wellek

Abstract

The present paper introduces a methodology for the semiparametric or non‐parametric two‐sample equivalence problem when the effects are specified by statistical functionals. The mean relative risk functional of two populations is given by the average of the time‐dependent risk. This functional is a meaningful non‐parametric quantity, which is invariant under strictly monotone transformations of the data. In the case of proportional hazard models, the functional determines just the proportional hazard risk factor. It is shown that an equivalence test of the type of the two‐sample Savage rank test is appropriate for this functional. Under proportional hazards, this test can be carried out as an exact level α test. It also works quite well under other semiparametric models. Similar results are presented for a Wilcoxon rank‐sum test for equivalence based on the Mann–Whitney functional given by the relative treatment effect.

Suggested Citation

  • Arnold Janssen & Stefan Wellek, 2010. "Exact linear rank tests for two‐sample equivalence problems with continuous data," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 64(4), pages 482-504, November.
    • Handle: RePEc:bla:stanee:v:64:y:2010:i:4:p:482-504
    DOI: 10.1111/j.1467-9574.2010.00466.x
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    References listed on IDEAS

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    1. Man-Lai Tang & Nian-Sheng Tang & Ivan Siu-Fung Chan & Ben Ping-Shing Chan, 2002. "Sample Size Determination for Establishing Equivalence/Noninferiority via Ratio of Two Proportions in Matched–Pair Design," Biometrics, The International Biometric Society, vol. 58(4), pages 957-963, December.
    2. Ivan S. F. Chan & Nian-Sheng Tang & Man-Lai Tang & Ping-Shing Chan, 2003. "Statistical Analysis of Noninferiority Trials with a Rate Ratio in Small-Sample Matched-Pair Designs," Biometrics, The International Biometric Society, vol. 59(4), pages 1170-1177, December.
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    Cited by:

    1. Arnold Janssen & Andreas Knoch, 2016. "Information bounds for nonparametric estimators of L-functionals and survival functionals under censored data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(2), pages 195-220, February.
    2. Rosa Arboretti & Fortunato Pesarin & Luigi Salmaso, 2021. "A unified approach to permutation testing for equivalence," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(3), pages 1033-1052, September.

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