## Optimal and efficient crossover designs for comparing test treatments with a control treatment.(English)Zbl 1068.62084

Summary: This paper deals exclusively with crossover designs for the purpose of comparing $$t$$ test treatments with a control treatment when the number of periods is no larger than $$t+1$$. Among other results it specifies sufficient conditions for a crossover design to be simultaneously A-optimal and MV-optimal in a very large and appealing class of crossover designs. It is expected that these optimal designs are highly efficient in the entire class of crossover designs. Some computationally useful tools are given and used to build assorted small optimal and efficient crossover designs. The model robustness of these newly discovered crossover designs is discussed.

### MSC:

 62K05 Optimal statistical designs 62K10 Statistical block designs 62P10 Applications of statistics to biology and medical sciences; meta analysis
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### References:

 [1] Afsarinejad, K. and Hedayat, A. S. (2002). Repeated measurements designs for a model with self and simple mixed carryover effects. J. Statist. Plann. Inference 106 449–459. · Zbl 1127.62392 [2] Carrière, K. C. and Reinsel, G. C. (1993). Optimal two-period repeated measurement designs with two or more treatments. Biometrika 80 924–929. · Zbl 0797.62061 [3] Cheng, C. S. and Wu, C.-F. (1980). Balanced repeated measurements designs. Ann. Statist. 8 1272–1283. JSTOR: · Zbl 0461.62064 [4] Hedayat, A. S. and Afsarinejad, K. (1975). Repeated measurements designs. I. In A Survey of Statistical Design and Linear Models (J. N. Srivastava, ed.) 229–242. North-Holland, Amsterdam. · Zbl 0304.62009 [5] Hedayat, A. S. and Afsarinejad, K. (1978). Repeated measurements designs. II. Ann. Statist. 6 619–628. JSTOR: · Zbl 0395.62056 [6] Hedayat, A. S., Jacroux, M. and Majumdar, D. (1988). Optimal designs for comparing test treatments with controls (with discussion). Statist. Sci. 3 462–491. JSTOR: · Zbl 0955.62616 [7] Hedayat, A. S. and Stufken, J. (2003). Optimal and efficient crossover designs under different assumptions about the carryover effects. J. Biopharmaceutical Statist. 13 519–528. · Zbl 1129.62429 [8] Hedayat, A. S. and Yang, M. (2003). Universal optimality of balanced uniform crossover designs. Ann. Statist. 31 978–983. · Zbl 1028.62060 [9] Hedayat, A. S. and Yang, M. (2004). Universal optimality for selected crossover designs. J. Amer. Statist. Assoc. 99 461–466. · Zbl 1117.62352 [10] Hedayat, A. S. and Zhao, W. (1990). Optimal two-period repeated measurements designs. Ann. Statist. 18 1805–1816. [Corrigendum 20 (1992) 619.] JSTOR: · Zbl 0714.62067 [11] Higham, J. (1998). Row-complete Latin squares of every composite order exist. J. Combin. Des. 6 63–77. · Zbl 0914.05010 [12] Kunert, J. (1983). Optimal design and refinement of the linear model with applications to repeated measurements designs. Ann. Statist. 11 247–257. JSTOR: · Zbl 0522.62054 [13] Kunert, J. (1984). Optimality of balanced uniform repeated measurements designs. Ann. Statist. 12 1006–1017. JSTOR: · Zbl 0544.62068 [14] Kunert, J. and Martin, R. J. (2000). On the determination of optimal designs for an interference model. Ann. Statist. 28 1728–1742. · Zbl 1103.62358 [15] Kunert, J. and Stufken, J. (2002). Optimal crossover designs in a model with self and mixed carryover effects. J. Amer. Statist. Assoc. 97 898–906. · Zbl 1048.62073 [16] Kushner, H. B. (1997). Optimal repeated measurements designs: The linear optimality equations. Ann. Statist. 25 2328–2344. · Zbl 0894.62088 [17] Kushner, H. B. (1998). Optimal and efficient repeated-measurements designs for uncorrelated observations. J. Amer. Statist. Assoc. 93 1176–1187. · Zbl 1064.62548 [18] Majumdar, D. (1988). Optimal repeated measurements designs for comparing test treatments with a control. Comm. Statist. Theory Methods 17 3687–3703. · Zbl 0696.62312 [19] Majumdar, D. and Notz, W. I. (1983). Optimal incomplete block designs for comparing treatments with a control. Ann. Statist. 11 258–266. JSTOR: · Zbl 0507.62070 [20] Matthews, J. N. S. (1994). Modeling and optimality in the design of crossover studies for medical application. J. Statist. Plann. Inference 42 89–108. · Zbl 0825.62649 [21] Stufken, J. (1991). Some families of optimal and efficient repeated measurements designs. J. Statist. Plann. Inference 27 75–83. · Zbl 0716.62069 [22] Stufken, J. (1996). Optimal crossover designs. In Design and Analysis of Experiments. Handbook of Statistics 13 (S. Ghosh and C. R. Rao, eds.) 63–90. North-Holland, Amsterdam. · Zbl 0911.62073
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