Efficient block designs for comparing dual with single treatments. (English) Zbl 0940.62111
Summary: Experiments in blocks having two treatment factors are considered in which a particular treatment must be excluded. The work is motivated by medical trials of two drugs in which a double placebo cannot be administered on ethical grounds. The contrasts of interest compare the effects of having both treatment factor at non-zero labelled levels with the effects of having only one treatment factor at a non-zero labelled level. For \(n\times 2\) experiments, a class of designs containing highly efficient members is identified and a lower bound on the efficiencies of designs in this class is derived. Tables of efficient designs are provided.
MSC:
| 62P10 | Applications of statistics to biology and medical sciences; meta analysis |
| 62K10 | Statistical block designs |
| 62K15 | Factorial statistical designs |
Keywords:
\(A\)-optimality; dual versus single treatment contrasts; part-balance; tables; medical trials; lower boundReferences:
| [1] | Gerami, A., 1991. Block designs for comparing dual with single treatments. Ph.D. Thesis, Faculty of Mathematical Studies, University of Southampton, Southampton SO17 1BJ, UK.; Gerami, A., 1991. Block designs for comparing dual with single treatments. Ph.D. Thesis, Faculty of Mathematical Studies, University of Southampton, Southampton SO17 1BJ, UK. · Zbl 0752.62052 |
| [2] | Gerami, A.; Lewis, S. M., Comparing dual with single treatments in block designs, Biometrika, 79, 603-610 (1992) · Zbl 0752.62052 |
| [3] | Gupta, S. C., Multi-factor designs for test versus control comparisons, Utilitas Math., 47, 199-210 (1995) · Zbl 0827.62072 |
| [4] | Hedayat, A. S.; Majumdar, D., A-optimal incomplete block designs for control-test treatment comparisons, Technometrics, 26, 363-370 (1984) · Zbl 0549.62049 |
| [5] | Jones, B.; Eccleston, J. A., Exchange and interchange procedures to search for optimal designs, J. Roy Statist. Soc. B, 42, 238-243 (1980) · Zbl 0443.62064 |
| [6] | Kiefer, J., 1975. Construction and optimality of generalized Youden designs. In: Srivastava, J.N. (Ed.), A Survey of Statistical Designs and Linear Models, North-Holland, Amsterdam, pp. 333-353.; Kiefer, J., 1975. Construction and optimality of generalized Youden designs. In: Srivastava, J.N. (Ed.), A Survey of Statistical Designs and Linear Models, North-Holland, Amsterdam, pp. 333-353. · Zbl 0313.62057 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
