Optimal cross-over designs for nonlinear mixed models using a first-order expansion

• Published in: Journal of statistical planning and inference Vol. 139; no. 2; pp. 203 - 212
• Main Authors: Wang, Jixian, Jones, Byron
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier B.V 01.02.2009; Elsevier
• Subjects: Combinatorics; Combinatorics. Ordered structures; Cross-over design; Designs and configurations; Exact sciences and technology; Experimental design; First-order expansion; General topics; Mathematics; Multivariate linear mixed models; Nonlinear mixed effect models; Optimal design; Probability and statistics; Probability theory and stochastic processes; Sciences and techniques of general use; Special processes (renewal theory, markov renewal processes, semi-markov processes, statistical mechanics type models, applications); Statistics; Multivariate linear mixed models; Nonlinear mixed effect models; Cross-over design; First-order expansion; Optimal design; Covariance analysis; Uniform design; Statistical decision; Multivariate analysis; Variance analysis; Linear model; Variance; Statistical method; Statistical regression; Optimal allocation; Experimental design; Balanced design; Mixed model; Non linear model; Optimal design(statistics); Mathematical expansion; Expansion
• ISSN: 0378-3758; 1873-1171
• DOI: 10.1016/j.jspi.2008.02.012

We consider the construction of optimal cross-over designs for nonlinear mixed effect models based on the first-order expansion. We show that for AB/BA designs a balanced subject allocation is optimal when the parameters depend on treatments only. For multiple period, multiple sequence designs, uniform designs are optimal among dual balanced designs under the same conditions. As a by-product, the same results hold for multivariate linear mixed models with variances depending on treatments.