Optimum Experiments with Sets of Treatment Combinations
Response surface designs are investigated in which points in the design region corresponds to single observations at each of s distinct settings of the explanatory variables. An extension of the “General Equivalence Theorem” for D-optimum designs is provided for experiments with such sets of treatment combinations. The motivation was an experiment in deep-brain therapy in which each patient receives a set of eight distinct treatment combinations and provides a response to each. The experimental region contains sixteen different sets of eight treatments.
I am grateful to Dr David Pedrosa of the Nuffield Department of Clinical Neurosciences, University of Oxford, for introducing me to the experimental design problem in deep-brain therapy that provided the motivation for this work.
I am also grateful to the referees whose comments strengthened and clarified the results of §3.
- 1.Atkinson, A.C.: Optimal model-based covariate-adaptive randomization designs. In: Sverdlov, O. (ed.) Modern Adaptive Randomized Clinical Trials: Statistical and Practical Aspects, pp. 131–154. Chapman and Hall/CRC Press, Boca Raton (2015)Google Scholar
- 2.Atkinson, A.C.: Optimum experiments for logistic models with sets of treatment combinations. In: Fackle-Fornius, E. (ed.) A Festschrift in Honor of Hans Nyquist on the Occasion of His 65th Birthday, pp. 44–58. Department of Statistics, Stockholm University, Stockholm (2015)Google Scholar
- 5.Atkinson, A.C., Woods, D.C.: Designs for generalized linear models. In: Dean, A., Morris, M., Stufken, J., Bingham, D. (eds.) Handbook of Design and Analysis of Experiments, pp. 471–514. Chapman and Hall/CRC Press, Boca Raton (2015)Google Scholar