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Efficient designs for one-sided comparisons of two or three treatments with a control in a one-way layout

Efficient designs for one-sided comparisons of two or three treatments with a control in a one-way layout
Efficient designs for one-sided comparisons of two or three treatments with a control in a one-way layout
The problem of providing lower confidence bounds for the mean improvements of p ? 2 test treatments over a control treatment is considered. The expected average and expected maximum allowances are two criteria for comparing different systems of confidence intervals or bounds. In this paper, lower bounds are derived for the expected average allowance and the expected maximum allowance of Dunnett's simultaneous lower confidence bounds for the p mean improvements. These lower bounds hold for any p ? 2 and any allocation of sample sizes. For p = 2 test treatments, sample allocations are given for which the bounds are achievable. For p = 3 test treatments, a tighter set of bounds is derived which enables easy determination of the sample allocation required to achieve highly efficient designs. A table of the bounds for the expected average and expected maximum allowances and the sample allocation that achieves these bounds is given for p = 2, 3. The theoretical results can easily be adapted to cover upper confidence bounds.
control treatment, dunnett's critical values, expected average allowance, expected maximum allowance, multiple comparisons, one-way layout, optimal design
0006-3444
127-135
Bortnick, Steven M.
18e6fb74-7bcc-446d-a8fa-de90519d7dc8
Dean, Angela M.
9c90540a-cdf4-44ce-9d34-6b7b495a1ea3
Santner, Thomas J.
25c0e9d6-daa2-4757-bee2-a714805eb67c
Bortnick, Steven M.
18e6fb74-7bcc-446d-a8fa-de90519d7dc8
Dean, Angela M.
9c90540a-cdf4-44ce-9d34-6b7b495a1ea3
Santner, Thomas J.
25c0e9d6-daa2-4757-bee2-a714805eb67c

Bortnick, Steven M., Dean, Angela M. and Santner, Thomas J. (2006) Efficient designs for one-sided comparisons of two or three treatments with a control in a one-way layout. Biometrika, 93 (1), 127-135. (doi:10.1093/biomet/93.1.127).

Record type: Article

Abstract

The problem of providing lower confidence bounds for the mean improvements of p ? 2 test treatments over a control treatment is considered. The expected average and expected maximum allowances are two criteria for comparing different systems of confidence intervals or bounds. In this paper, lower bounds are derived for the expected average allowance and the expected maximum allowance of Dunnett's simultaneous lower confidence bounds for the p mean improvements. These lower bounds hold for any p ? 2 and any allocation of sample sizes. For p = 2 test treatments, sample allocations are given for which the bounds are achievable. For p = 3 test treatments, a tighter set of bounds is derived which enables easy determination of the sample allocation required to achieve highly efficient designs. A table of the bounds for the expected average and expected maximum allowances and the sample allocation that achieves these bounds is given for p = 2, 3. The theoretical results can easily be adapted to cover upper confidence bounds.

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Published date: March 2006
Keywords: control treatment, dunnett's critical values, expected average allowance, expected maximum allowance, multiple comparisons, one-way layout, optimal design
Organisations: Statistics

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Local EPrints ID: 353914
URI: http://eprints.soton.ac.uk/id/eprint/353914
ISSN: 0006-3444
PURE UUID: 49ff5376-6d7d-4bea-96c8-77bdc4fa488c

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Date deposited: 25 Jun 2013 09:26
Last modified: 19 Jul 2019 21:33

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Contributors

Author: Steven M. Bortnick
Author: Angela M. Dean
Author: Thomas J. Santner

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