Construction of Optimal and Efficient Designs of Experiments for Individualized Prediction in Hierarchical Models
Final Report Abstract
In this project, characterization and construction of optimal choices for experimental settings of explanatory variables were achieved to improve the statistical analysis in hierarchical model settings in the presence of individual random effects. These models include, in particular, random coefficient regression models in which each individual has its own response curve, but individuals may be considered as randomly selected representatives of a larger population. In particular, Prus (2019) gave analytical solutions for various popular criteria in random coefficient regression models, and provided results under minimax criteria for which optimal designs behave robust against misspecification of the covariance structure of the random effects. The resulting designs are, hence, efficient also in the case of a partially unknown covariance. For the case of cross-sectional observations, when only one observation may be available per individual due to physical or ethical constraints, optimal designs were obtained both for a model with a treatment and a control group model, and for an extended model with two treatment groups. Further results for sparse designs have been developed for multi-center (interlaboratory) models with applications to precision medicine. In an agricultural setup, Prus and Piepho provided results on optimization of allocation trials in crop variety testing based on the best linear unbiased prediction of genotype effects. An extension of the general equivalence theorem was propagated for situations where several designs have to be incorporated simultaneously into the design criterion. The results were applied to design optimization in multiple group random coefficient regression models with multivariate response for estimation of fixed effects, and for prediction of the random effects. Concerning computational aspects, an approach was developed for computing optimal approximate and exact designs for compound Bayes risk criteria which cover the prediction of individual effects in random coefficient regression models. Filová and Prus (2021) proposed a solution for computation of highly efficient exact designs for the multiple-design problems. The results obtained in the present project may be applied to medical research and agricultural studies, but are also applicable in engineering (material science) and pharmaceutical research (pharmacokinetics).
Publications
- (2018). Computing optimal experimental designs with respect to a compound Bayes risk criterion. Statistics and Probability Letters, 137, 135-141
Harman, R., Prus, M.
(See online at https://doi.org/10.1016/j.spl.2018.01.017) - (2019). Optimal designs for minimax-criteria in random coefficient regression models. Statistical Papers, 60, 465-478
Prus, M.
(See online at https://doi.org/10.1007/s00362-018-01072-w) - (2019). Various optimality criteria for the prediction of individual response curves. Statistics and Probability Letters, 146, 36-41
Prus, M.
(See online at https://doi.org/10.1016/j.spl.2018.10.022) - (2020). Optimal design in hierarchical random effect models for individual prediction with application in precision medicine. Journal of Statistical Theory and Practice, 14;24, 12 pages
Prus M., Benda N., Schwabe R.
(See online at https://doi.org/10.1007/s42519-020-00090-y) - (2020). Optimal designs in multiple group random coefficient regression models. TEST, 29, 233–254
Prus, M.
(See online at https://doi.org/10.1007/s11749-019-00654-6) - (2021) Equivalence theorems for multiple-design problems with application in mixed models. Journal of Statistical Planning and Inference, 217, 153-164
Prus, M.
(See online at https://doi.org/10.1016/j.jspi.2021.07.012) - (2021). Optimizing the allocation of trials to sub regions in multi-environment crop variety testing. Journal of Agricultural, Biological and Environmental Statistics , 26, 267-288
Prus, M. and Piepho, H.-P.
(See online at https://doi.org/10.1007/s13253-020-00426-y)
