Design Space; Design of Experiments; Multi-criteria Decision Methods; Multivariate Linear Model; Bayesian Statistics; Uncertainty; Analytical Method Development; Robust Optimization
Abstract :
[en] The International Conference for Harmonization (ICH) has released regulatory guidelines for Pharmaceutical Development. In the document ICH Q8, The Design Space of a process is presented as the set of factor settings providing satisfactory results. However, ICH Q8 does not propose any practical methodology to define, derive and compute Design Space. In parallel, in the last decades, it has been observed that the diversity and the quality of analytical methods have evolved exponentially allowing substantial gains in selectivity and sensitivity. However, there is still a lack for a rationale towards the development of robust separation methods in a systematic way.
Applying ICH Q8 to analytical methods provides a methodology for predicting a region of the space of factors in which results will be reliable. Combining design of experiments and Bayesian standard multivariate regression, an identified form of the predictive distribution of a new response vector has been identified and used, under non-informative as well as informative prior distributions of the parameters. From the responses and their predictive distribution, various critical quality attributes can be easily derived.
This Bayesian framework was then extended to the multi-criteria setting to estimate the predictive probability that several critical quality attributes will be jointly achieved in the future use of an analytical method.
An example based on a high-performance liquid chromatography (HPLC) method is given. For this example, a constrained sampling scheme was applied to ensure the modeled responses have desirable properties.
Disciplines :
Physical, chemical, mathematical & earth Sciences: Multidisciplinary, general & others
Author, co-author :
Lebrun, Pierre ; Université de Liège - ULiège > Département de pharmacie > Chimie analytique
Boulanger, Bruno ; Université de Liège - ULiège > Département de pharmacie > Analyse des médicaments
Debrus, Benjamin ; Université de Liège - ULiège > Département de pharmacie > Chimie analytique
Lambert, Philippe ; Université de Liège - ULiège > Institut des sciences humaines et sociales > Méthodes quantitatives en sciences sociales
Hubert, Philippe ; Université de Liège - ULiège > Département de pharmacie > Chimie analytique
Language :
English
Title :
A Bayesian Design Space for analytical methods based on multivariate models and predictions
Box, G. E. P., Tiao, G. C. (1973). Bayesian Inference in Statistical Analysis. New York, NY: Wiley Classic Library
Dawid, A. P. (1981). Some Matrix-variate distribution theory: Notational considerations and a Bayesian application. Biometrika 68(1):264-274
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
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
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
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
Derringer, G. C., Suich, R. (1980). Simultaneous optimization of several response variables. Journal of Quality Technology 12(4):214-219
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)
Geisser, S. (1965). Bayesian estimation in multivariate analysis. Annals of Mathematical Statistics 36(1):150-159
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
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.
Gupta, A. K., Nagar, D. K. (1999). Matrix Variate Distributions. Boca Raton, FL: Chapman and Hall/CRC
Guttman, I. (1970). Statistical Tolerance Regions: Classical and Bayesian. Griffin?s statistical monographs and courses. London: Griffin
Hamada, M., Johnson, V., Moore, L. M. (2004). Bayesian prediction intervals and their relationship to tolerance intervals. Technometrics 46(4):452-459
Harrington, E. C. (1965). The desirability function. Industrial. Quality Control 21:494-498
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
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)
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
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)
Peterson, J. J. (2004). A posterior predictive approach to multiple response surface optimization. Journal Quality Technology 36:139-153
Peterson, J. J. (2008). A Bayesian approach to the ICH Q8 definition of Design Space. Journal Biopharmaceutical Statistics 18:959-975
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
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
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
Press, S. J. (1972). Applied Multivariate Analysis: Using Bayesian and Frequentist Methods of Inference. New York, NY: Holt, Rinehart and Winston
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
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
Schoenmakers, P. (1988). Optimization of chromatographic selectivity: A guide to method development. Analytica Chimica Acta 208:357-358
Snyder, L. R., Kirkland, J. J., Glajch, J. L. (1997). Practical HPLC Method Development, 2nd ed. New York, NY: Wiley-Interscience
Steuer, D. (2000). An Improved optimisation procedure for desirability indices. Technical report 27/00, SFB 475. Dortmund, Germany: Dortmund University
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
Tee-Won, L. (2001). Independent Component Analysis, Theory and Applications. Dordrecht, The Netherlands: Kluwer Academic
Timm, N. H. (2002). Applied Multivariate Analysis. New York, NY: Springer-Verlag
Vanbel, P. F. (1999). Development of flexible and efficient strategies for optimizing chromatographic conditions. Journal of Pharmaceutical Biomedical Analysis 21:603-610 (Pubitemid 29512226)
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