Equivalence theorems for multiple-design problems with application in mixed models

Bernstein, 2018 Bludowsky, 2015, Optimal designs for the carryover model with random interactions between subjects and treatments, Aust. N. Z. J. Stat., 57, 517, 10.1111/anzs.12136 Bose, 2015, Optimal design measures under asymmetric errors, with application to binary design points, J. Statist. Plann. Inference, 159, 28, 10.1016/j.jspi.2014.10.006 Boyd, 2004 Dumont, 2018, PFIM 4.0, an extended R program for design evaluation and optimization in nonlinear mixed-effect models, Comput. Methods Programs Biomed., 156, 217, 10.1016/j.cmpb.2018.01.008 Entholzner, 2005, A note on designs for estimating population parameters, Biom. Lett., 42, 25 Fedorov, 1997 Fedorov, 2005, The design of multicentre trials, Stat. Methods Med. Res., 14, 205, 10.1191/0962280205sm399oa Fedorov, 2013 Graßhoff, 2012, Optimal design for linear regression models in the presence of heteroscedasticity caused by random coefficients, J. Statist. Plann. Inference, 142, 1108, 10.1016/j.jspi.2011.11.025 Harman, 2019 Harman, 2018, Computing optimal experimental designs with respect to a compound Bayes risk criterion, Statist. Probab. Lett., 137, 135, 10.1016/j.spl.2018.01.017 Kiefer, 1974, General equivalence theory for optimum designs (approximate theory), Ann. Statist., 2, 849, 10.1214/aos/1176342810 Kunert, 2010, Optimal block designs comparing treatments with a control when the errors are correlated, J. Statist. Plann. Inference, 140, 2719, 10.1016/j.jspi.2010.03.037 Lemme, 2015, Efficient treatment allocation in two-way nested designs, Stat. Methods Med. Res., 24, 494, 10.1177/0962280213502145 Mentré, 1997, Optimal design in random-effects regression models, Biometrika, 84, 429, 10.1093/biomet/84.2.429 Pázman, 1986 Prus, 2015 Prus, 2020, Optimal designs in multiple group random coefficient regression models, TEST, 29, 233, 10.1007/s11749-019-00654-6 Prus, 2016, Optimal designs for the prediction of individual parameters in hierarchical models, J. R. Stat. Soc. Ser. B Stat. Methodol., 78, 175, 10.1111/rssb.12105 Pukelsheim, 1993 Schmelter, 2007, Considerations on group-wise identical designs for linear mixed models, J. Statist. Plann. Inference, 137, 4003, 10.1016/j.jspi.2007.04.017 Schmelter, 2007 Schwabe, 1996, Optimal design of experiments for multivariate response in two-factor linear models, 235 Schwabe, 2008, On optimal designs in random intercept models, Tatra Mt. Math. Publ., 39, 145 Seber, 2007 Whittle, 1973, Some general points in the theory of optimal experimental design, J. R. Stat. Soc. Ser. B Stat. Methodol., 35, 123 Wierich, 1989, An application of the Kiefer-Wolfowitz equivalence theorem to ANOVA models with additive regression, J. Statist. Plann. Inference, 21, 277, 10.1016/0378-3758(89)90046-3