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Equivalence theorems for c and DA‐optimality for linear mixed effects models with applications to multitreatment group assignments in health care

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  • Xin Liu
  • Rong‐Xian Yue
  • Weng Kee Wong

Abstract

We construct c and DA‐optimal approximate designs for linear mixed models with group‐specific treatment for estimating parameters or contrasts in the population parameters. We establish equivalence theorems to confirm optimality of these designs under a linear mixed model and provide illustrative application to find D, DA and c‐optimal designs for polynomial and fractional polynomial models with multitreatment group assignments. For more complex models, we briefly review metaheuristics and their potential applications to find various optimal designs, including optimal designs for problems considered here and their extensions.

Suggested Citation

  • Xin Liu & Rong‐Xian Yue & Weng Kee Wong, 2022. "Equivalence theorems for c and DA‐optimality for linear mixed effects models with applications to multitreatment group assignments in health care," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(4), pages 1842-1859, December.
    • Handle: RePEc:bla:scjsta:v:49:y:2022:i:4:p:1842-1859
    DOI: 10.1111/sjos.12584
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    References listed on IDEAS

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