Optimal designs for comparing population curves in hierarchical models

Abstract Summary: We construct μ p -optimal approximate designs for comparing population curves in hierarchical models with group-specific treatment. Equivalence theorems are given to confirm μ p -optimality of designs and the optimal allocation of sample size in each group. An illustrative application to find μ 1 and μ ∞ -optimal designs is presented for the random slope models with two-treatment group assignments.

[1]  Various optimality criteria for the prediction of individual response curves , 2018, Statistics & Probability Letters.

[2]  Steven E. Rigdon,et al.  Model-Oriented Design of Experiments , 1997, Technometrics.

[3]  F. Bretz,et al.  Simultaneous Confidence Bands for Nonlinear Regression Models with Application to Population Pharmacokinetic Analyses , 2011, Journal of biopharmaceutical statistics.

[4]  Seung-Ho Kang,et al.  Hierarchical Linear Models for Multiregional Clinical Trials , 2020, Statistics in Biopharmaceutical Research.

[5]  H. Dette,et al.  Optimal designs for comparing curves. , 2014, Annals of statistics.

[6]  T. Schmelter.  Considerations on group-wise identical designs for linear mixed models , 2007 .

[7]  J. Kiefer.  General Equivalence Theory for Optimum Designs (Approximate Theory) , 1974 .

[8]  R. Schwabe,et al.  Optimal designs for the prediction of individual parameters in hierarchical models , 2016 .

[9]  Holger Dette,et al.  Optimal designs for comparing regression models with correlated observations , 2016, Comput. Stat. Data Anal..

[10]  H. Dette,et al.  Equivalence of Regression Curves , 2018 .

[11]  H. Wynn,et al.  Assessing Nonsuperiority, Noninferiority, or Equivalence When Comparing Two Regression Models Over a Restricted Covariate Region , 2009, Biometrics.

[12]  Maryna Prus.  Optimal designs in multiple group random coefficient regression models , 2018, TEST.

[13]  R. Schwabe,et al.  Interpolation and Extrapolation in Random Coefficient Regression Models: Optimal Design for Prediction , 2016 .

[14]  T. Schmelter.  The Optimality of Single-group Designs for Certain Mixed Models , 2007 .

[15]  Optimal designs for minimax-criteria in random coefficient regression models , 2018, Statistical Papers.