Symmetrical Confidence Intervals for Bioequivalence Trials

Westlake, Wilfred J.

doi:10.2307/2529259

Cited by 326 publications

(189 citation statements)

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“…The multiplicative model, which looks at the ratio of means, will not be considered further in this paper. The commonly used procedure in biostatistics for this problem is to use the "two one-sided tests" procedure, or TOST (Westlake, 1976(Westlake, , 1979Schuirmann, 1981Schuirmann, , 1987. With the TOST, the researcher will consider two groups equivalent if he can show that they differ by less than some constant τ , the equivalence bound, in both directions.…”

Section: Methodsmentioning

confidence: 99%

“…Lehmann (1959) anticipated the need for interval testing in his classic volume on the theory of hypothesis testing. Many of the currently employed methods of equivalence testing were developed in the 1970's and 1980's to address biostatistical and pharmaceutical problems (Westlake, 1976(Westlake, , 1979Schuirmann, 1981Schuirmann, , 1987Anderson & Hauck, 1983;Patel & Gupta, 1984). Rogers, Howard, and Vessey (1993) introduced the use of equivalence testing methods to the social sciences.…”

Section: Introductionmentioning

confidence: 99%

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A Comparison Of Equivalence Testing In Combination With Hypothesis Testing And Effect Sizes

Mecklin

2003

J. Mod. App. Stat. Meth.

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Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Comparison Of Equivalence Testing In Combination With Hypothesis Testing And Effect Sizes

Mecklin

2003

J. Mod. App. Stat. Meth.

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“…To avoid those problems, we adopt a different decision rule, somewhat analogous to frequentist equivalence testing (e.g., Rogers, Howard, & Vessey, 1993;Westlake, 1976Westlake, , 1981. The procedure requires establishing a region of practical equivalence (ROPE) around the null value that expresses a range of parameter values that are equivalent to the null value for current practical purposes.…”

Section: Bayesian Estimation and Highest Density Intervalmentioning

confidence: 99%

The Bayesian New Statistics: Hypothesis testing, estimation, meta-analysis, and power analysis from a Bayesian perspective

2017

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In the practice of data analysis, there is a conceptual distinction between hypothesis testing, on the one hand, and estimation with quantified uncertainty on the other. Among frequentists in psychology, a shift of emphasis from hypothesis testing to estimation has been dubbed "the New Statistics" (Cumming, 2014). A second conceptual distinction is between frequentist methods and Bayesian methods. Our main goal in this article is to explain how Bayesian methods achieve the goals of the New Statistics better than frequentist methods. The article reviews frequentist and Bayesian approaches to hypothesis testing and to estimation with confidence or credible intervals. The article also describes Bayesian approaches to meta-analysis, randomized controlled trials, and power analysis.Keywords Null hypothesis significance testing · Bayesian inference · Bayes factor · Confidence interval · Credible interval · Highest density interval · Region of practical equivalence · Meta-analysis · Power analysis · Effect size · Randomized controlled trial · Equivalence testingThe New Statistics emphasizes a shift of emphasis away from null hypothesis significance testing (NHST) to "estimation based on effect sizes, confidence intervals, and metaanalysis" (Cumming, 2014, p. 7). There are many reasons John K. Kruschke johnkruschke@gmail.com 1 Indiana University, Bloomington, USA to eschew NHST, with its seductive lapse to black-and-white thinking about the presence or absence of effects. There are also many reasons to promote instead a cumulative science that incrementally improves estimates of magnitudes and uncertainty. These reasons were recently highlighted in a prominent statement from the American Statistical Association (ASA; Wasserstein & Lazar, 2016) that will be summarized later in this article. Recent decades have also seen repeated calls to shift emphasis away from frequentist methods to Bayesian analysis (e.g., Lindley, 1975).In this article, we review both of these recommended shifts of emphasis in the practice of data analysis, and we promote their convergence in Bayesian methods for estimation. The goals of the New Statistics are better achieved by Bayesian methods than by frequentist methods. In that sense, we recommend a Bayesian New Statistics. Within the domain of Bayesian methods, we have a more nuanced emphasis. Bayesian methods provide a coherent framework for hypothesis testing, so when null hypothesis testing is the crux of the research then Bayesian null hypothesis testing should be carefully used. But we also believe that typical analyses should not routinely stop with hypothesis testing alone. In that sense, we recommend a New Bayesian Statistics, that is, Bayesian analyses that also consider estimates of magnitudes and uncertainty, along with meta-analyses.This article begins with an extensive description of frequentist and Bayesian approaches to null hypothesis testing and estimation with confidence or credible intervals. Subsequently, the article explains Bayesian approaches to metaanalysis, rando...

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“…Although interest has usually centered around the testing problem in (5.1), there is also considerable interest (and benefit) in constructing confidence intervals for p 2 -p 1 • Given a 1-a confidence interval C(x) for p 2 -p 1 , an a-level test of (5.1) can be conducted by rejecting H 0 whenever C{x) C (-6, 6), as proposed by Westlake (1972Westlake ( , 1976. (Notice that this use of confidence sets as tests is reversed from the usual use.…”

Section: Connectiods With Bioequivalencementioning

confidence: 99%

Optimal Confidence Sets, Bioequivalence, and the Limaçon of Pascal

Brown

Casella

Hwang

1995

Journal of the American Statistical Association

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We begin with a decision-theoretic investigation into confidence sets that minimize expected volume at a given parameter value. Such sets are constructed by inverting a family of uniformly most powerful tests, hence also enjoy the optimality property of being uniformly most accurate. In addition, these sets possess Bayesian optimal volume properties, and represent the first case (to our knowledge) of a frequentist 1-a confidence set that possesses a Bayesian optimality property.The hypothesis testing problem that generates these sets is similar to that encountered in bioequivalence testing. Our sets are optimal for testing bioequivalence in certain settings, and in the case of the normal distribution, the optimal sets are curves known as the lim~on of Pascal. We illustrate the use of these curves with an example.

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Symmetrical Confidence Intervals for Bioequivalence Trials

Cited by 326 publications

References 5 publications

A Comparison Of Equivalence Testing In Combination With Hypothesis Testing And Effect Sizes

A Comparison Of Equivalence Testing In Combination With Hypothesis Testing And Effect Sizes

The Bayesian New Statistics: Hypothesis testing, estimation, meta-analysis, and power analysis from a Bayesian perspective

Optimal Confidence Sets, Bioequivalence, and the Limaçon of Pascal

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