Step Down Procedures for Comparison With a Control

Bofinger, Eve

doi:10.1111/j.1467-842x.1987.tb00751.x

Cited by 26 publications

(11 citation statements)

References 6 publications

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“…In case of r 6 ¼ k þ 1 they coincide with the bounds derived by Bofinger (1987) and Stefansson et al (1988). 44 H. Finner and K. Strassburger:…”

Section: One Sided Multiple Comparisons With a Controlsupporting

confidence: 68%

“…They can be worse than, better than, or identical to the corresponding single step CI's (Dunnett, 1955) or stepdown CI's (Bofinger, 1987;Stefansson et al, 1988). Moreover, step-up confidence bounds are not monotone in the sense that in general y i > y j does not imply L i ðy; wÞ !…”

Section: One Sided Multiple Comparisons With a Controlmentioning

confidence: 92%

“…(a) on p. 116), an exercise for fanatics. However, meanwhile there are some examples of step-down related confidence bounds the first of which were given by Bofinger (1987) and Stefansson et al (1988), who derived step-down confidence bounds by partitioning the parameter space.…”

Section: Introductionmentioning

confidence: 98%

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Step‐up Related Simultaneous Confidence Intervals for MCC and MCB

Finner

Straßburger

2007

Biometrical J

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The derivation of compatible confidence bounds related to stepwise decision procedures is a serious issue. Especially the derivation of step-up related bounds is rather complex. In this article we consider (one-sided) multiple comparisons with a control (MCC) and multiple comparisons with the best (MCB) with the aim of establishing delta-equivalence to the best and derive step-up related confidence bounds by applying the projection method proposed in Finner and Strassburger (2006). Some examples illustrate the resulting procedures.

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“…In case of r 6 ¼ k þ 1 they coincide with the bounds derived by Bofinger (1987) and Stefansson et al (1988). 44 H. Finner and K. Strassburger:…”

Section: One Sided Multiple Comparisons With a Controlsupporting

confidence: 68%

Section: One Sided Multiple Comparisons With a Controlmentioning

confidence: 92%

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Step‐up Related Simultaneous Confidence Intervals for MCC and MCB

Finner

Straßburger

2007

Biometrical J

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“…In fact, it has long been thought that stepwise procedures do not naturally yield confidence sets through inversion (Lehmann, 1986) until Bonfinger (1987) and Stefansson et al (1988) who derive confidence bounds following a step-down test by partitioning principle. Subsequently, Hsu and Berger (1999) propose a dose-response method to find stepwise confidence bounds without multiplicity adjustment.…”

Section: Introductionmentioning

confidence: 99%

A note on confidence bounds after fixed-sequence multiple tests

Cheng

Cheung

2012

Journal of Statistical Planning and Inference

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We are concerned with the problem of estimating the treatment effects at the effective doses in a dose-finding study. Under monotone dose-response, the effective doses can be identified through the estimation of the minimum effective dose, for which there is an extensive set of statistical tools. In particular, when a fixed-sequence multiple testing procedure is used to estimate the minimum effective dose, Hsu and Berger (1999) show that the confidence lower bounds for the treatment effects can be constructed without the need to adjust for multiplicity. Their method, called the dose-response method, is simple to use, but does not account for the magnitude of the observed treatment effects. As a result, the dose-response method will estimate the treatment effects at effective doses with confidence bounds invariably identical to the hypothesized value. In this paper, we propose an error-splitting method as a variant of the dose-response method to construct confidence bounds at the identified effective doses after a fixed-sequence multiple testing procedure. Our proposed method has the virtue of simplicity as in the dose-response method, preserves the nominal coverage probability, and provides sharper bounds than the dose-response method in most cases.

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“…Closed subset selection procedures, often also termed sequentially rejective procedures, were first suggested by Naik (1975) and later by Brostrom (1981) and Bofinger (1987) within the framework of the subset selection approach involving a con- trol. All procedures use a step-down algorithm, whereas the procedure recently proposed by Dunnett and Tamhane (1 992) in the context of simultaneously testing against a control is of step-up type.…”

Section: Introductionmentioning

confidence: 99%

Testing and Selecting for Equivalence with Respect to a Control

Giani

Straßburger

1994

Journal of the American Statistical Association

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The problem of equivalence assessment of several treatments with a control is considered. The first approach uses a hypothesis testing formulation in which the alternative states global equivalence. With respect to a family of distributions with location parameter, a test based on a two-sided many-one statistic is proposed. Least favorable parameter configuration results are presented as being necessary to evaluate critical values and to determine sample sizes implied by certain power requirements when planning experiments. The second approach concerns a stepwise selection procedure. The goal is to select a subset of treatments containing all those actually equivalent to the control in the absence of global equivalence. The normal case is dealt with in detail for randomized block designs as well as for one-way layouts. Concerning the test problem, optimal allocations of total sample sizes are determined to guarantee specified power requirements for the one-way layout.KEY WORDS: Closed subset selection procedure: Least favorable configuration: Multiple hypotheses testing: One-way layout;Randomized block design: Sample size determination.

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Step Down Procedures for Comparison With a Control

Cited by 26 publications

References 6 publications

Step‐up Related Simultaneous Confidence Intervals for MCC and MCB

Step‐up Related Simultaneous Confidence Intervals for MCC and MCB

A note on confidence bounds after fixed-sequence multiple tests

Testing and Selecting for Equivalence with Respect to a Control

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