Abstract
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. In this paper we introduce weighted MV optimality criterion and present a detailed study using both weighted A and MV optimality criteria, of 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.
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References
Bauer P, Rohmel J, Maurer W, Hothorn L (1998) Testing strategies in multi-dose experiments including active control. Stat Med 17:2133–2146
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
Dunnett CW (1955) A multiple comparison procedure for comparing several treatments with a control. J Am Stat Assoc 50:1096–1121
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
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
Hedayat AS, Jacroux M, Majumdar D (1998) Optimal designs for comparing test treatments with controls (with discussion). Stat Sci 3:462–491
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
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
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
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
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
Majumdar D (1986) Optimal designs for comparing between two sets of treatments. J Stat Plan Inf 14:359–372
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
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Dasgupta, N., SahaRay, R. Optimal Allocation for Comparing k Test Treatments to Positive and Negative Control with Unequal Weighting Under A-optimality and MV-optimality. Metrika 65, 83–92 (2007). https://doi.org/10.1007/s00184-006-0061-z
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DOI: https://doi.org/10.1007/s00184-006-0061-z