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Wald tests for variance-adjusted equivalence assessment with normal endpoints.

Yue-Ming Chen1, Yu-Ting Weng2, Xiaoyu Dong2

  • 1a Department of Biostatistics , The University of Texas School of Public Health , Houston , Texas , USA.

Journal of Biopharmaceutical Statistics
|December 2, 2016
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This study explores variance-adjusted equivalence tests. The constrained maximum likelihood (CML) method offers improved statistical power for equivalence hypothesis testing, especially in smaller sample sizes.

Keywords:
Constrained maximum likelihood estimateWald testsequivalence tests

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Area of Science:

  • Statistics
  • Biostatistics
  • Hypothesis Testing

Background:

  • Equivalence tests compare mean differences using variance-adjusted margins.
  • Standard tests may lack appropriate distributions under the null hypothesis, especially with high variability.
  • Existing methods require careful consideration of measurement variability.

Purpose of the Study:

  • Investigate asymptotic tests for the equivalence hypothesis.
  • Evaluate the performance of different variance estimation methods in Wald tests.
  • Identify a robust method for equivalence testing with varying sample sizes and variability.

Main Methods:

  • Applied the Wald test statistic with three variance estimators: maximum likelihood estimate (MLE), uniformly minimum variance unbiased estimate (UMVUE), and constrained maximum likelihood estimate (CMLE).
  • Evaluated test performance using simulations, focusing on type I error rate control and statistical power.
  • Compared asymptotic normalized tests against Wald tests with different variance estimates.

Main Results:

  • Asymptotic normalized tests were generally conservative.
  • Wald tests using MLE and UMVUE showed inflated significance levels with unequal group sizes.
  • The Wald test employing the CMLE demonstrated superior power compared to MLE and UMVUE, particularly for medium and small sample sizes.

Conclusions:

  • The constrained maximum likelihood estimate (CMLE) provides a more powerful approach for equivalence hypothesis testing than MLE and UMVUE.
  • The CMLE-based Wald test offers improved performance, especially in scenarios with unequal group sizes and smaller sample sizes.
  • This research contributes to more reliable statistical inference in equivalence testing.