Advertisement

TEST

pp 1–22 | Cite as

Optimal designs in multiple group random coefficient regression models

  • Maryna PrusEmail author
Original Paper

Abstract

The subject of this work is multiple group random coefficients regression models with several treatments and one control group. Such models are often used for studies with cluster randomized trials. We investigate A-, D- and E-optimal designs for estimation and prediction of fixed and random treatment effects, respectively, and illustrate the obtained results by numerical examples.

Keywords

Optimal design Treatment and control Random effects Cluster randomization Mixed models Estimation and prediction 

Mathematics Subject Classification

62K05 

Notes

References

  1. Bailey RA (2008) Design of comparative experiments. Cambridge University Press, CambridgeCrossRefzbMATHGoogle Scholar
  2. Bland JM (2004) Cluster randomised trials in the medical literature: two bibliometric surveys. BMC Med Res Methodol 4:21CrossRefGoogle Scholar
  3. Bludowsky A, Kunert J, Stufken J (2015) Optimal designs for the carryover model with random interactions between subjects and treatments. Aust. N Z J Stat 57:517–533MathSciNetCrossRefzbMATHGoogle Scholar
  4. Christensen R (2002) Plane answers to complex questions: the theory of linear models. Springer, New YorkCrossRefzbMATHGoogle Scholar
  5. Entholzner M, Benda N, Schmelter T, Schwabe R (2005) A note on designs for estimating population parameters. Biom Lett Listy Biometryczne 42:25–41Google Scholar
  6. Fedorov V, Jones B (2005) The design of multicentre trials. Stat Methods Med Res 14:205–248MathSciNetCrossRefzbMATHGoogle Scholar
  7. Gladitz J, Pilz J (1982) Construction of optimal designs in random coefficient regression models. Math Operationsforschung und Stat Ser Stat 13:371–385MathSciNetzbMATHGoogle Scholar
  8. Harman R, Prus M (2018) Computing optimal experimental designs with respect to a compound Bayes risk criterion. Stat Probab Lett 137:135–141MathSciNetCrossRefzbMATHGoogle Scholar
  9. Henderson CR (1975) Best linear unbiased estimation and prediction under a selection model. Biometrics 31:423–477CrossRefzbMATHGoogle Scholar
  10. Henderson CR (1984) Applications of linear models in animal breeding. University of Guelph, GuelphGoogle Scholar
  11. Henderson CR, Kempthorne O, Searle SR, von Krosigk CM (1959) The estimation of environmental and genetic trends from records subject to culling. Biometrics 15:192–218CrossRefzbMATHGoogle Scholar
  12. Kunert J, Martin RJ, Eccleston J (2010) Optimal block designs comparing treatments with a control when the errors are correlated. J Stat Plan Inference 140:2719–2738MathSciNetCrossRefzbMATHGoogle Scholar
  13. Lemme F, van Breukelen GJP, Berger MPF (2015) Efficient treatment allocation in two-way nested designs. Stat Methods Med Res 24:494–512MathSciNetCrossRefGoogle Scholar
  14. Majumdar D, Notz W (1983) Optimal incomplete block designs for comparing treatments with a control. Ann Stat 11:258–266MathSciNetCrossRefzbMATHGoogle Scholar
  15. Patton GC, Bond L, Carlin JB, Thomas L, Butler H, Glover S, Catalano R, Bowes G (2006) Promoting social inclusion in schools: a group-randomized trial of effects on student health risk behavior and well-being. Am J Public Health 96:1582–1587CrossRefGoogle Scholar
  16. Piepho HP, Möhring J (2005) Best linear unbiased prediction of cultivar effects for subdivided target regions. Crop Sci 45:1151–1159CrossRefGoogle Scholar
  17. Piepho HP, Möhring J (2010) Generation means analysis using mixed models. Crop Sci 50:1674–1680CrossRefGoogle Scholar
  18. Prus M (2015) Optimal designs for the prediction in hierarchical random coefficient regression models. Ph.D. thesis, Otto-von-Guericke University, MagdeburgGoogle Scholar
  19. Prus M, Schwabe R (2016) Optimal designs for the prediction of individual parameters in hierarchical models. J R Stat Soc: Ser B 78:175–191MathSciNetCrossRefGoogle Scholar
  20. Rasch D, Herrendörfer G (1986) Experimental design: sample size determination and block designs. Reidel, DordrechtzbMATHGoogle Scholar
  21. Schmelter T (2007) Experimental design for mixed models with application to population pharmacokinetic studies. Ph.D. thesis, Otto-von-Guericke University MagdeburgGoogle Scholar
  22. Schwabe R (1996) Optimum designs for multi-factor models. Springer, New YorkCrossRefzbMATHGoogle Scholar
  23. Wierich W (1986) The D- and A-optimality of product design measures for linear models with discrete and continuous factors of influence. Freie Universiät Berlin, HabilitationsschriftzbMATHGoogle Scholar

Copyright information

© Sociedad de Estadística e Investigación Operativa 2019

Authors and Affiliations

  1. 1.Institute for Mathematical StochasticsOtto von Guericke UniversityMagdeburgGermany

Personalised recommendations