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Optimal repeated measurement designs for a model with partial interactions
Laboratoire de Mathématiques, UMR CNRS 6620, Université Blaise Pascal, 63 177 Aubière CEDEX, France pierre.druilhet{at}math.univ-bpclermont.fr
Laboratoire de Mathématiques Appliquées, UMR CNRS 5142, Université de Pau, BP 1155, 64013 PAU CEDEX, France walter.tinsson{at}univ-pau.fr
Received for publication 1 January 2007. Revision received 1 December 2008.
We consider crossover designs for a model with partial interactions. In this model, the carryover effect depends on whether the treatment is preceded by itself or not. When the aim of the experiment is to study the total effects corresponding to a single treatment, we obtain approximate optimal symmetric designs, within the competing class of circular designs, by generalizing the method introduced by Kushner (1997) and Kunert & Martin (2000). This generalization places the method proposed by Bailey & Druilhet (2004) into Kushner's context. The optimal designs obtained are not binary, as in Kunert & Martin (2000). We also propose efficient designs generated by only one sequence.
Key Words: Approximate design • Crossover design • Optimal design • Total effect • Universal optimality
References
-
Afsarinejad K., Hedayat A. S. Repeated measurements designs for a model with self and simple mixed carryover effects. J. Statist. Plan. Infer. (2002) 106:449–59.[CrossRef]
Azaïs J.-M. Design of experiments for studying intergenotypic competition. J. R. Statist. Soc. (1987) B 49:334–45.
Bailey R. A., Druilhet P. Optimality of neighbor-balanced designs for total effects. Ann. Statist. (2004) 32:1650–61.[CrossRef]
Bailey R. A., Kunert J. On optimal crossover designs when carryover effects are proportional to direct effects. Biometrika (2006) 93:613–25.
Druilhet P. Conditions for optimality in experimental designs. Lin. Algeb. Applic. (2004) 388:147–57.[CrossRef]
Druilhet P., Markiewicz A. Information matrices for non full rank subsystems. Metrika (2007) 65:171–82.[CrossRef][Web of Science]
Gaffke N. Further characterizations of design optimality and admissibility for partial parameter estimation in linear regression. Ann. Statist. (1987) 15:942–57.[CrossRef]
Kempton R. A., Ferris S. J., David O. Optimal change-over designs when carry-over effects are proportional to direct effects of treatments. Biometrika (2001) 88:391–9.
Kiefer J. Construction and optimality of generalized Youden designs. In: A Survey of Statistical Design and Linear Models—Srivastava J. N., ed. (1975) Amsterdam: North-Holland. 333–53.
Kunert J. Optimal design and refinement of the linear model with applications to repeated measurements designs. Ann. Statist. (1983) 11:247–57.[CrossRef]
Kunert J., Martin R. J. On the determination of optimal designs for an interference model. Ann. Statist. (2000) 28:1728–42.[CrossRef]
Kunert J., Stufken J. Optimal crossover designs in a model with self and mixed carryover effects. J. Am. Statist. Assoc. (2002) 97:898–906.[CrossRef][Web of Science]
Kushner H. B. Optimal repeated measurements designs: the linear optimality equations. Ann. Statist. (1997) 25:2328–44.[CrossRef]
Pukelsheim F. Optimal Design of Experiments (1993) New York: John Wiley.
Shah K. R., Bose M., Raghavarao D. Universal optimality of Patterson's crossover designs. Ann. Statist. (2005) 33:2854–72.[CrossRef]
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