Confidence regions for the location of response surface optima: the R package OptimaRegion

References

• Box, G., and N. Draper. 1987. Empirical model building and response surfaces. New York, NY: John Wiley & Sons.
   Google Scholar
• Box, G. E. P., and J. S. Hunter. 1954. A confidence region for the solution of a set of simultaneous equations with an application to experimental design. Biometrika 41 (1-2):190–99. doi:10.1093/biomet/41.1-2.190.
   Web of Science ®Google Scholar
• Brooks, R., J. Hunt, M. W. Blows, M. J. Smith, L. F. Bussiere, and M. D. Jennions. 2005. Experimental evidence for multivariate stabilizing sexual selection. Evolution 59 (4):871–80. doi:10.1554/04-662.
   PubMed Web of Science ®Google Scholar
• Cahya, S., E. del Castillo, and J. J. Peterson. 2004. Computation of confidence regions for optimal factor levels in constrained response surface problems. Journal of Computational and Graphical Statistics 13 (2):499–518. doi:10.1198/1061860043443.
   Web of Science ®Google Scholar
• Carter, W. H., G. L. Wampler, D. M. Stablein, and E. D. Campbell. 1982. Drug activity and therapeutic synergy in cancer treatment. Cancer Research 42 (8):2963–71.
   PubMed Web of Science ®Google Scholar
• Casella, G., and R. Berger. 2002. Statistical inference. Pacific Grove, CA: Duxbury Press.
   Google Scholar
• Del Castillo, E. 1997. Stopping rules for steepest ascent in experimental optimization. Communications in Statistics Part B: Simulation and Computation 26 (4):1599–615.
   Web of Science ®Google Scholar
• Del Castillo, E. 2007. Process optimization: A statistical approach. Vol. 105. New York, NY: Springer.
   Google Scholar
• Del Castillo, E., and S. Cahya. 2001. A tool for computing confidence regions on the stationary point of a response surface. The American Statistician 55 (4):358–65. doi:10.1198/000313001753272349.
   Web of Science ®Google Scholar
• Ermakov, S., and D. Semenchikov. 2019. Genetic global optimization algorithms. Communications in Statistics - Simulation and Computation. Advance online publication. doi:10.1080/03610918.2019.1672739.
   Google Scholar
• FDA. 2012. Guidance document: Q11 development and manufacture of drug substances. https://www.fda.gov/regulatory-information/search-fda-guidance-documents/\\q11-development-and-manufacture-drug-substances.
   Google Scholar
• Henrion, D., and J.-B. Lasserre. 2003. Gloptipoly: Global optimization over polynomials with matlab and sedumi. ACM Transactions on Mathematical Software 29 (2):165–94. doi:10.1145/779359.779363.
   Web of Science ®Google Scholar
• Lasserre, J. B. 2001. Global optimization with polynomials and the problem of moments. SIAM Journal on Optimization 11 (3):796–817. doi:10.1137/S1052623400366802.
   Web of Science ®Google Scholar
• Miró-Quesada, G., and E. Del Castillo. 2004. An enhanced recursive stopping rule for steepest ascent searches in response surface methodology. Communications in Statistics - Simulation and Computation 33 (1):201–28. doi:10.1081/SAC-120028441.
   Web of Science ®Google Scholar
• Myers, R., D. Montgomery, and C. Anderson-Cook. 2009. Response surface methodology. 3rd. ed. New York, NY: Wiley.
   Google Scholar
• Nychka, D., R. Furrer, J. Paige, and S. Sain. 2017. fields: Tools for Spatial Data (R package version 9.8-3). https://github.com/NCAR/Fields.
   Google Scholar
• Nychka, D. W. 2000. Spatial-process estimates as smoothers. Smoothing and Regression: Approaches, Computation, and Application 329:393.
   Google Scholar
• Peterson, J. 2008. A Bayesian approach to the ICH Q8 definition of design space. Journal of Biopharmaceutical Statistics 18 (5):959–75. doi:10.1080/10543400802278197.
   PubMed Web of Science ®Google Scholar
• Peterson, J. J., S. Cahya, and E. del Castillo. 2002. A general approach to confidence regions for optimal factor levels of response surfaces. Biometrics 58 (2):422–31. doi:10.1111/j.0006-341x.2002.00422.x.
   PubMed Web of Science ®Google Scholar
• Peterson, J. J., and S. J. Novick. 2007. Nonlinear blending: A useful general concept for the assessment of combination drug synergy. Journal of Receptor and Signal Transduction Research 27 (2-3):125–46. doi:10.1080/10799890701417576.
   PubMed Web of Science ®Google Scholar
• Rao, C. R. 1973. Linear statistical inference and its applications. New York, NY: Wiley.
   Google Scholar
• Rapkin, J., K. Jensen, C. R. Archer, C. M. House, S. K. Sakaluk, E. Del Castillo, and J. Hunt. 2018. The geometry of nutrient space-based life-history trade-offs: Sex-specific effects of macronutrient intake on the trade-off between encapsulation ability and reproductive effort in decorated crickets. The American Naturalist 191 (4):452–74. doi:10.1086/696147.
   PubMed Web of Science ®Google Scholar
• Tukey, J. 1975. Mathematics and the picturing of data. Proceedings of the International Congress of Mathematicians 2:523–31.
   Google Scholar
• Wahba, G. 1990. Spline models for observational data, Vol. 59. Montpelier, VT: SIAM.
   Google Scholar
• Wan, F., W. Liu, F. Bretz, and Y. Han. 2016. Confidence sets for optimal factor levels of a response surface. Biometrics 72 (4):1285–93. doi:10.1111/biom.12500.
   PubMed Web of Science ®Google Scholar
• Wei, B., and S. Lee. 2012. Second-order accuracy of depth-based bootstrap confidence regions. Journal of Multivariate Analysis 105 (1):112–23. doi:10.1016/j.jmva.2011.08.016.
   Web of Science ®Google Scholar
• Woutersen, T., and J. Ham. 2018. Confidence sets for continuous and discontinuous functions of parameters. Technical report. University of Arizona, Tucson, AZ.
   Google Scholar
• Zhu, Z., and Y. Ye. 2016. R interface to DSDP semidefinite programming library. https://www.mcs.anl.gov/hs/software/DSDP.
   Google Scholar