Equivalence with Respect to a Control: Stepwise Tests

Bofinger, Eve; Bofinger, Mark

doi:10.1111/j.2517-6161.1995.tb02058.x

Cited by 10 publications

(8 citation statements)

References 20 publications

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“…Hence we conclude that E is bioequivalent to R (using limits of 80-125%). Similar results can be obtained with step-down or step-up procedures as in Bofinger & Bofinger (1995) using δ = log 1.25 = − log 0.80.…”

Section: Application Asupporting

confidence: 80%

“…Hence, to investigate bioavailability, we have analysed log transformed data from which we find X 0 = 0.7612,X 1 = 0.8346 andX 2 = 0.7968, andσ 2 1/2 n −1/2 = 0.032763 with ν = 20. Proceeding as in Bofinger & Bofinger (1995) we have, using a single step procedure, joint 90% confidence intervals of ((0.0734 − 1.724 × 0.032763) − , (0.0734 + 1.724 × 0.032763) + ) = (0, 0.130) for µ 1 − µ 0 , and of (−0.021, 0.092) for µ 2 − µ 0 . These intervals correspond to relative bioavailability intervals of (10 0 , 10 0.130 )100% = (100%, 135%) and (95%, 124%), respectively.…”

Section: Application Amentioning

confidence: 99%

“…Chow & Liu, 1992 for an introduction). Giani & Strassburger (1994), Bofinger & Bofinger (1995) and others proposed methods for assessing the equivalence of several treatments with a control. When the brand-name drug is too expensive for most of the population, which is often the situation in many developing countries, then, even if none of the experimental drugs is bioequivalent, it may still be advisable to choose one of them as an available alternative.…”

Section: Introductionmentioning

confidence: 99%

“…Finally, Section 4 contains two examples applying the new inference procedure; one of them involves choosing a drug (which is marketed in India) for the treatment of tuberculosis. To illustrate the case in which the aim is to identify bioequivalent drugs, rather than to select the closest, we also apply the procedure of Bofinger & Bofinger (1995) to find joint confidence intervals for µ i − µ 0 (i = 1, . .…”

Section: Introductionmentioning

confidence: 99%

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Theory & Methods: Selecting Closest to Control

Bofinger¹,

Liu

2001

Aus NZ J of Statistics

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Consider the usual one-way fixed effect analysis of variance model where the populations i (i = 0, 1, . . . , k) have independent normal distributions with unknown means and common unknown variance. Let 0 be a control population with which the other (treatment) populations are to be compared. The basic problem is to select the treatment that is closest to the control mean. This situation occurs when one of the i must be chosen, regardless of how many are equivalent to the control in the sense of having means sufficiently close. This paper follows the approach of Hsu (1996) and is based on a set of simultaneous confidence intervals. It provides a table of critical values which allows direct implementation of the new inference procedure. The applications given are of the balanced cross-over design type with negligible carry-over effects, for which the results of this paper may be used. One of the applications refers to the selection of a drug, which may not be bioequivalent to a reference formulation but is the closest of those drugs that are readily available to the group of patients considered.

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Section: Application Asupporting

confidence: 80%

Section: Application Amentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Theory & Methods: Selecting Closest to Control

Bofinger¹,

Liu

2001

Aus NZ J of Statistics

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“…Much less attention has been given to the equivalence-testing case (e.g. Berger, 1982;Bofinger and Bofinger, 1995;Berger and Hsu, 1996;Wang et al, 1999;Quan et al, 2001;Romano, 2005). In addition, most of this work is theoretical and not yet adaptable to cases where practical analysis is required.…”

Section: Possible Approaches For Multiple Comparisonsmentioning

confidence: 99%

Statistical considerations for the safety evaluation of GMOs

2010

EFS2

105

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This opinion proposes: 1) updated statistical guidelines and possible approaches for the analysis of compositional, agronomic and phenotypic data from field trials carried out for the risk assessment of GM plants and derived foods/feeds; 2) minimum requirements that should be met in the experimental design of field trials, such as the inclusion of commercial varieties, in order to ensure sufficient statistical power and reliable estimation of natural variability. A graphical representation is proposed to allow the comparison of the GMO, its conventional counterpart and the commercial varieties with respect to many variables, taking into account natural variability. It is recommended to quantify natural variability from data on non‐GM commercial varieties treated in the same way and in the same experiments as the GM and the conventional counterpart test materials. Only when such estimates are unavailable may they be estimated from databases or literature. Estimated natural variability should be used to specify equivalence limits to test the difference between the GMO and the commercial varieties. Adjustments to these equivalence limits allow a simple graphical representation so that a single pair of confidence limits may be used to display statistically significant differences and to visually assess equivalence. The possible types of outcome of this graphical representation are described and a proposal is made when further evaluation should be performed. In addition to providing specific recommendations for the interpretation of compositional analysis, this opinion highlights some statistical issues of a more challenging nature, such as the simultaneous assessment of many characteristics (i.e. multivariate analysis), which will require further research. The principles proposed in this opinion may be used, in certain cases, for the evaluation of GMOs other than plants.

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On familywise type I error control for multiplicity in equivalence trials with three or more treatments

Röhmel

2011

Biometrical J

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For the all pairwise comparisons for equivalence of k (k≥2) treatments Lauzon and Caffo proposed simply to divide the type I error level α by k-1 to achieve a Bonferroni-based familywise error control when declaring pairs of two treatments equivalent. This rule is shown to be too liberal for k≥4. It works for k=3 yet for reasons not considered by Lauzon and Caffo. Based on the two one-sided testing procedures and using the closure test principle we develop valid alternatives based on Bonferroni's inequality. The set H of intersection hypotheses reveals a rich structure, leading to the possibility to present H as a directed acyclic graph (DAG). This in turn allows using some graph theoretical theorems and eases proving properties of the resulting multiple testing problems.

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Equivalence with Respect to a Control: Stepwise Tests

Cited by 10 publications

References 20 publications

Theory & Methods: Selecting Closest to Control

Theory & Methods: Selecting Closest to Control

Statistical considerations for the safety evaluation of GMOs

On familywise type I error control for multiplicity in equivalence trials with three or more treatments

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