A bayesian design space for analytical methods based on multivariate models and predictions

Journal of Biopharmaceutical Statistics

Volumn 23, Issue 6, 2013, Pages 1330-1351

  Lebrun, Pierre ^a   Boulanger, Bruno ^b   Debrus, Benjamin ^a   Lambert, Philippe ^a   Hubert, Philippe ^a  

^a UNIVERSITY OF LIÈGE   (Belgium)

^b Arlenda SA   (Belgium)

Author keywords

Analytical method development; Bayesian statistics; Design of experiments; Design space; Multicriteria decision methods; Multivariate linear models; Robust optimization; Uncertainty

Indexed keywords

ANALYTIC METHOD; ARTICLE; BAYES THEOREM; COMPUTER PROGRAM; EXPERIMENT; HIGH PERFORMANCE LIQUID CHROMATOGRAPHY; METHODOLOGY; PREDICTION; PRIORITY JOURNAL; PROBABILITY; STATISTICAL MODEL;

BAYES THEOREM; CHROMATOGRAPHY, HIGH PRESSURE LIQUID; DATA INTERPRETATION, STATISTICAL; LINEAR MODELS; MODELS, STATISTICAL; MULTIVARIATE ANALYSIS; REPRODUCIBILITY OF RESULTS; RESEARCH DESIGN; TECHNOLOGY, PHARMACEUTICAL; UNCERTAINTY;

EID: 84886808395     PISSN: 10543406     EISSN: 15205711     Source Type: Journal    
DOI: 10.1080/10543406.2013.834922     Document Type: Article

References (35)

1. Box, G. E. P., Tiao, G. C. (1973). Bayesian Inference in Statistical Analysis. New York, NY: Wiley Classic Library
2. Dawid, A. P. (1981). Some Matrix-variate distribution theory: Notational considerations and a Bayesian application. Biometrika 68(1):264-274
3. Debrus, B., Lebrun, P., Ceccato, A., Caliaro, G., Govaerts, B., Olsen, B. A., Rozet, E., Boulanger, B., Hubert, P. (2009). A new statistical method for the automated detection of peaks in UV-DAD chromatograms of a sample mixture. Talanta 79:77-85
4. Debrus, B., Lebrun, P., Ceccato, A., Caliaro, G., Rozet, E., Nistor, I., Oprean, R. Ruperez, F. J., Barbas, C., Boulanger, B., Hubert, P. (2011a). Application of new methodologies based on 31 design of experiments, independent component analysis and design space for robust optimization in liquid chromatography. Analytica Chimica Acta 691(12):33-42
5. Debrus, B., Lebrun, P., Mbinze Kindenge, J., Lecomte, F., Ceccato, A., Caliaro, G., Mavar Tayey Mbay, J., Boulanger, B., Marini, R. D., Rozet, E., Hubert, P. (2011b). Innovative high-performance liquid chromatography method development for the screening of 19 antimalarial drugs based on a generic approach, using design of experiments, independent component analysis and design space. Journal of Chromotography A 1218(31):5205-5215. Available at: http://hdl.handle.net/2268/93241
6. Del Castillo, E., Colosimo, B. M., Alshraideh, H. (2012). Bayesian modeling and optimization of functional responses affected by noise factors. Journal of Quality Technology 44(2):117-135
7. Derringer, G. C., Suich, R. (1980). Simultaneous optimization of several response variables. Journal of Quality Technology 12(4):214-219
8. Dewé, W., Marini, R. D., Chiap, P., Hubert, P., Crommen, J., Boulanger, B. (2004). Development of response models for optimizing HPLC methods. Chemometrics and Intelligent Laboratory Systems 74:263-268 (Pubitemid 39488379)
9. Geisser, S. (1965). Bayesian estimation in multivariate analysis. Annals of Mathematical Statistics 36(1):150-159
10. Genz, A., Bretz, F., Miwa, T., Mi, X., Leisch, F., Scheipl, F., Hothorn, T. (2011). mvtnorm: Multivariate Normal and t Distributions. Available at: http://CRAN.Rproject.org/package=mvtnorm
11. Geweke, J. (1991). Efficient simulation from the multivariate normal and Student-t distributions subject to linear constraints and the evaluation of constraint probabilities. Computing Science and Statistics: 23rd Symposium on the Interface, Seattle, WA; April.
12. Gupta, A. K., Nagar, D. K. (1999). Matrix Variate Distributions. Boca Raton, FL: Chapman and Hall/CRC
13. Guttman, I. (1970). Statistical Tolerance Regions: Classical and Bayesian. Griffin?s statistical monographs and courses. London: Griffin
14. Hamada, M., Johnson, V., Moore, L. M. (2004). Bayesian prediction intervals and their relationship to tolerance intervals. Technometrics 46(4):452-459
15. Harrington, E. C. (1965). The desirability function. Industrial. Quality Control 21:494-498
16. Le Bailly de Tilleghem, C., Govaerts, B. (2005). Distribution of desirability index in multicriteria optimization using desirability functions based on the cumulative distribution function of the standard normal. Technical report 0531, Louvain-la-Neuve: Université Catholique de Louvain
17. Lebrun, P., Govaerts, B., Debrus, B., Ceccato, A., Caliaro, G., Hubert, P., Boulanger, B. (2008). Development of a new predictive modelling technique to find with confidence equivalence zone and design space of chromatographic analytical methods. Chemometrics and Intelligent Laboratory Systems 91:4-16 (Pubitemid 351288949)
18. Martin, A. D., Quinn, K. M., Hee Park, J. (2011). MCMCpack: Markov chain Monte Carlo in R. Journal of Statistical Software 42(9):22. Available at: http://www.jstatsoft.org/v42/i09
19. Miró-Quesada, G., del Castillo, E., Peterson, J. J. (2004). A Bayesian approach for multiple response surface optimization in the presence of noise variable. Journal of Applied Statistics 13(3):251-270 (Pubitemid 38516977)
20. Peterson, J. J. (2004). A posterior predictive approach to multiple response surface optimization. Journal Quality Technology 36:139-153
21. Peterson, J. J. (2008). A Bayesian approach to the ICH Q8 definition of Design Space. Journal Biopharmaceutical Statistics 18:959-975
22. Peterson, J. J., Lief, K. (2010). The ICH Q8 definition of design space: A comparison of the overlapping means and the Bayesian predictive approaches. Statistics in Biopharmaceutical Research 2:249-259
23. Peterson, J. J., Yahyah, M. (2009). A Bayesian design space approach to robustness and system suitability for pharmaceutical assays and other processes. Statistics in Biopharmaceutical Research 1(4):441-449
24. Peterson, J. J., Miró-Quesada, G., del Castillo, E. (2009). A Bayesian reliability approach to multiple response optimization with seemingly unrelated regression models. Journal of Quality Technology Quantitative Management 6:353-369
25. Press, S. J. (1972). Applied Multivariate Analysis: Using Bayesian and Frequentist Methods of Inference. New York, NY: Holt, Rinehart and Winston
26. R Development Core Team. (2011). R: A Language and Environment for Statistical Computing. Vienna, Austria: R Foundation for Statistical Computing Available at: http://www.R-project.org
27. Royston, J. P. (1995). Remark AS R94: A remark on algorithm AS 181: TheW-Test for normality. Journal of Royoal Statistics Society C (Applied Statistics) 44(4):547-551
28. Schoenmakers, P. (1988). Optimization of chromatographic selectivity: A guide to method development. Analytica Chimica Acta 208:357-358
29. Snyder, L. R., Kirkland, J. J., Glajch, J. L. (1997). Practical HPLC Method Development, 2nd ed. New York, NY: Wiley-Interscience
30. Steuer, D. (2000). An Improved optimisation procedure for desirability indices. Technical report 27/00, SFB 475. Dortmund, Germany: Dortmund University
31. Stockdale, G. W., Cheng, A. (2009). Finding design space and a reliable operating region using a multivariate Bayesian approach with experimental design. Journal of Quality Technology Quantitative Management 4:391-408
32. Tee-Won, L. (2001). Independent Component Analysis, Theory and Applications. Dordrecht, The Netherlands: Kluwer Academic
33. Timm, N. H. (2002). Applied Multivariate Analysis. New York, NY: Springer-Verlag
34. Vanbel, P. F. (1999). Development of flexible and efficient strategies for optimizing chromatographic conditions. Journal of Pharmaceutical Biomedical Analysis 21:603-610 (Pubitemid 29512226)
35. Wang, G., Ding, Q., Hou, Z. (2008). Independent component analysis and its applications in signal processing for analytical chemistry. Trends in Analytical Chemistry 37(4):368-376