Advanced Process Decision Making Using Multivariate Latent Variable Methods

  • Matteo Ottavian
  • Emanuele Tomba
  • Massimiliano Barolo
Part of the Methods in Pharmacology and Toxicology book series (MIPT)


This chapter is intended to show how latent variable modeling techniques can be used to support several pharmaceutical development and manufacturing activities by exploitation of historical databases deriving from experiments, ongoing manufacturing processes or historical products already developed. Basic theoretical concepts about latent variable modeling and latent variable model inversion are first introduced. Then, some applications are reviewed to show how the pharmaceutical industry can benefit from these modeling techniques to support decision-making activities in process development, formulation design, process scale-up, product transfer, process control, and raw materials acceptability assessment.

Key words

Latent variable models Product design Process understanding Quality by design Design space Process analytical technologies Principal component analysis Partial least-squares regression 



Number of latent variables selected to build an LV model


Inequality constraint assigned to the j-th element of ŷNEW


Inequality constraint on the t-th element of xNEW


Residual matrix


Residual vector


Weights for model inversion


Lower physical bound of the domain of xNEW


Lower physical bound of the domain of ŷNEW


Loading matrix for the X space


Loading vector


Loading matrix for the Y space


Explained variance by an LV model


Rank of matrices X and Y


Variance of the a-th column of T


Squared prediction error of the i-th sample


Score matrix for X


Hotelling’s T 2


Score vector


Score vector of the solution of model inversion exercise


Score vector of the real input variable projections onto the score space


a-th element of t


Upper physical bound of the domain of xNEW


Upper physical bound of the domain of ŷNEW


Matrix that includes historical samples

\( \widehat{\mathbf{X}} \)

Reconstruction of X when A components are retained


Solution of the optimization problem

\( {\widehat{\mathbf{x}}}^{\mathrm{NEW}} \)

Solution of the model inversion problem


Matrix collecting the quality variables


Generic set of desired product properties


Quality attributes corresponding to the solution xNEW


Weight matrix of the model for X


Transformed weight matrix of the model for X



M.O. and M.B. gratefully acknowledge “Fondazione Ing. Aldo Gini” and “Fondazione CARIPARO” (Project # PARO104725–2010) for the financial support.


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Matteo Ottavian
    • 1
  • Emanuele Tomba
    • 2
  • Massimiliano Barolo
    • 3
  1. 1.Manufacturing Science & TechnologySandoz Industrial Products S.p.A.RoveretoItaly
  2. 2.Technical Development Drug ProductGSK VaccinesSienaItaly
  3. 3.CAPE-Lab — Computer-Aided Process Engineering Laboratory, Department of Industrial EngineeringUniversity of PadovaPadovaItaly

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