Review Articles

D-optimal population designs in linear mixed effects models for multiple longitudinal data

Hongyan Jiang ,

a Department of Mathematics and Physics, Huaiyin Institute of Technology, Huaian, People's Republic of China

Rongxian Yue

b Department of Mathematics, Shanghai Normal University, Shanghai People's Republic of China

Pages 88-94 | Received 25 Jun. 2020, Accepted 29 Jan. 2021, Published online: 12 Feb. 2021,
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The main purpose of this paper is to investigate D-optimal population designs in multi-response linear mixed models for longitudinal data. Observations of each response variable within subjects are assumed to have a first-order autoregressive structure, possibly with observation error. The equivalence theorems are provided to characterise the D-optimal population designs for the estimation of fixed effects in the model. The semi-Bayesian D-optimal design which is robust against the serial correlation coefficient is also considered. Simulation studies show that the correlation between multi-response variables has tiny effects on the optimal design, while the experimental costs are important factors in the optimal designs.


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