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

Abstract

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.

Keywords:

• D-optimal designs
• longitudinal data
• multi-response linear mixed model
• equivalence theorem

MSC 2010:

• 62K05

Acknowledgments

This work was partly supported by the National Natural Science Foundation of China (Nos. 11971318, 11871143) and Shanghai Rising-Star Program (No. 20QA1407500).

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was partly supported by the National Natural Science Foundation of China (Nos. 11971318, 11871143) and Shanghai Rising-Star Program (No. 20QA1407500).

Notes on contributors

Hongyan Jiang

Hongyan Jiang is a Ph.D. in Statistics, Shanghai Normal University, 2019, Associate Professor in Huaiyin Institute of Technology, Jiangsu, 2019–Present.

Rongxian Yue

Rongxian Yue is a Ph.D. in Statistics, Hong Kong Baptist University, 1997. Postdoctoral Research Fellow in Statistics, East China Normal University, 1997–1999. Associate Professor (1999–2001) and Professor (2001–Present), Shanghai Normal University.