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Optimal allocation for comparing \(k\) test treatments to positive and negative control with unequal weighting under A-optimality and MV-optimality. (English) Zbl 1105.62075
Summary: Experiments in real life often involve comparisons of test treatments to more than one control. However, the controls may not always be of equal importance. We introduce a weighted MV optimality criterion and present a detailed study using both weighted A and MV optimality criteria for the problem of optimally comparing a set of test treatments to two controls (positive and a negative) that are of unequal importance to the experimenter.

MSC:
62K05 Optimal statistical designs
62J15 Paired and multiple comparisons; multiple testing
62P10 Applications of statistics to biology and medical sciences; meta analysis
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[1] Bauer P, Rohmel J, Maurer W, Hothorn L (1998) Testing strategies in multi-dose experiments including active control. Stat Med 17:2133–2146
[2] D’Agostino RB, Hareen TC (1991) Multiple Comparisons in over-the-counter drug clinical trials with both positive and placebo controls. Stat Med 10:1–6
[3] Dunnett CW (1955) A multiple comparison procedure for comparing several treatments with a control. J Am Stat Assoc 50:1096–1121 · Zbl 0066.12603
[4] Dunnett CW, Tamhane AC (1992) Comparisons between a new drug and Active and Placebo controls in an efficacy clinical trial. Stat Med 11:1057–1063
[5] Gupta VK, Ramana DVV, Prasad R (2002) Weighted A-optimal block designs for comparing treatments with controls with unequal precision. J Stat Plan Inf 106:159–175 · Zbl 1127.62387
[6] Hedayat AS, Jacroux M, Majumdar D (1998) Optimal designs for comparing test treatments with controls (with discussion). Stat Sci 3:462–491 · Zbl 0955.62616
[7] Hothrorn LA, Hayashi M, Seidel D (2000) Dose-response relationships in mutagenicity assays including an appropriate positive control group: a multiple testing approach. Environ Ecol Stat 7:27–42
[8] Jacroux M (1990) Some optimal designs for comparing a set of test treatment with a set of controls. Ann Inst Stat Math 42:173–185 · Zbl 0703.62074
[9] Jacroux M (1993) On the construction of trend resistant design fior comparing a set of test treatments with a set of controls. J Amer Stat Assoc 88:1398–1403 · Zbl 0792.62063
[10] Jaggi S, Gupta VK, Parsad R (1996) A_ efficient block designs for comparing two disjoint sets of treatments. Commun Stat Theory Methods 25(5):967–983 · Zbl 0875.62388
[11] Masters N, Mcguire MA, Beerman KA, Dasgupta N, McGuire MK (2002) Maternal supplementation with conjugated linoleic acid decreses milk fat in humans. Lipids 37(2):133–138
[12] Majumdar D (1986) Optimal designs for comparing between two sets of treatments. J Stat Plan Inf 14:359–372 · Zbl 0603.62082
[13] Majumdar D (1996). Optimal and efficient treatment-control designs. In: Ghosh S, Rao CR (eds). Handbook of Statistics, Vol 13. Elsevier, Amsterdam, pp 1007–1053 · Zbl 0911.62072
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