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A mapping-based universal Kriging model for order-of-addition experiments in drug combination studies

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  • Xiao, Qian
  • Xu, Hongquan

Abstract

In modern pharmaceutical studies, treatments may include several drugs added sequentially, and the drugs’ order-of-addition can have significant impacts on their efficacy. In practice, experiments enumerating all possible drug sequences are often not affordable, and appropriate statistical models which can accurately predict all cases using only a small number of experimental trials are required. A novel mapping-based universal Kriging (MUK) model and its simplified variant are proposed for analyzing such order-of-addition experiments with blocking. They can provide accurate predictions and have robust performances under various experimental designs. The MUK model can also incorporate available domain knowledge to enhance its interpretation. The superiority of the proposed methods is illustrated via a real five-drug experiment on lymphoma and two simulation examples.

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  • Xiao, Qian & Xu, Hongquan, 2021. "A mapping-based universal Kriging model for order-of-addition experiments in drug combination studies," Computational Statistics & Data Analysis, Elsevier, vol. 157(C).
    • Handle: RePEc:eee:csdana:v:157:y:2021:i:c:s0167947320302462
    DOI: 10.1016/j.csda.2020.107155
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    1. Kleijnen, Jack P.C., 2009. "Kriging metamodeling in simulation: A review," European Journal of Operational Research, Elsevier, vol. 192(3), pages 707-716, February.
    2. Berger J.O. & De Oliveira V. & Sanso B., 2001. "Objective Bayesian Analysis of Spatially Correlated Data," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1361-1374, December.
    3. Allahverdi, Ali & Gupta, Jatinder N. D. & Aldowaisan, Tariq, 1999. "A review of scheduling research involving setup considerations," Omega, Elsevier, vol. 27(2), pages 219-239, April.
    4. Riccardo Scarpa & Danny Campbell & W. George Hutchinson, 2007. "Benefit Estimates for Landscape Improvements: Sequential Bayesian Design and Respondents’ Rationality in a Choice Experiment," Land Economics, University of Wisconsin Press, vol. 83(4), pages 617-634.
    5. Roustant, Olivier & Ginsbourger, David & Deville, Yves, 2012. "DiceKriging, DiceOptim: Two R Packages for the Analysis of Computer Experiments by Kriging-Based Metamodeling and Optimization," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 51(i01).
    6. David Ginsbourger & Delphine Dupuy & Anca Badea & Laurent Carraro & Olivier Roustant, 2009. "A note on the choice and the estimation of Kriging models for the analysis of deterministic computer experiments," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 25(2), pages 115-131, March.
    7. Hamilton Emmons, 1969. "One-Machine Sequencing to Minimize Certain Functions of Job Tardiness," Operations Research, INFORMS, vol. 17(4), pages 701-715, August.
    8. Mebane Jr., Walter R. & Sekhon, Jasjeet S., 2011. "Genetic Optimization Using Derivatives: The rgenoud Package for R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 42(i11).
    9. Akira Shinohara & Tomoko Ogawa, 1998. "Stimulation by Rad52 of yeast Rad51- mediated recombination," Nature, Nature, vol. 391(6665), pages 404-407, January.
    10. Boik, Robert J. & Robinson-Cox, James F., 1998. "Derivatives of the Incomplete Beta Function," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 3(i01).
    11. Chen, Ray-Bing & Hsu, Yen-Wen & Hung, Ying & Wang, Weichung, 2014. "Discrete particle swarm optimization for constructing uniform design on irregular regions," Computational Statistics & Data Analysis, Elsevier, vol. 72(C), pages 282-297.
    12. Gramacy, Robert B., 2007. "tgp: An R Package for Bayesian Nonstationary, Semiparametric Nonlinear Regression and Design by Treed Gaussian Process Models," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 19(i09).
    13. W. Townsend, 1978. "The Single Machine Problem with Quadratic Penalty Function of Completion Times: A Branch-and-Bound Solution," Management Science, INFORMS, vol. 24(5), pages 530-534, January.
    14. Yong-Dao Zhou & Hongquan Xu, 2014. "Space-Filling Fractional Factorial Designs," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(507), pages 1134-1144, September.
    15. T.C. Cheng & Guoqing Wang, 2000. "Single Machine Scheduling with Learning Effect Considerations," Annals of Operations Research, Springer, vol. 98(1), pages 273-290, December.
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    1. Shengli Zhao & Zehui Dong & Yuna Zhao, 2022. "Order-of-Addition Orthogonal Arrays with High Strength," Mathematics, MDPI, vol. 10(7), pages 1-17, April.
    2. Zhao, Yuna & Lin, Dennis K.J. & Liu, Min-Qian, 2022. "Optimal designs for order-of-addition experiments," Computational Statistics & Data Analysis, Elsevier, vol. 165(C).

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