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)

Abstract

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 

Notation

A

Number of latent variables selected to build an LV model

bj

Inequality constraint assigned to the j-th element of ŷNEW

dt

Inequality constraint on the t-th element of xNEW

E

Residual matrix

e

Residual vector

g1,2,3

Weights for model inversion

lbx

Lower physical bound of the domain of xNEW

lby

Lower physical bound of the domain of ŷNEW

P

Loading matrix for the X space

p

Loading vector

Q

Loading matrix for the Y space

R2

Explained variance by an LV model

RX, RY

Rank of matrices X and Y

sa2

Variance of the a-th column of T

SPEi

Squared prediction error of the i-th sample

T

Score matrix for X

T2

Hotelling’s T 2

t

Score vector

tDES

Score vector of the solution of model inversion exercise

tREAL

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

ta

a-th element of t

ubx

Upper physical bound of the domain of xNEW

uby

Upper physical bound of the domain of ŷNEW

X

Matrix that includes historical samples

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

Reconstruction of X when A components are retained

xNEW

Solution of the optimization problem

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

Solution of the model inversion problem

Y

Matrix collecting the quality variables

yDES

Generic set of desired product properties

ŷNEW

Quality attributes corresponding to the solution xNEW

W

Weight matrix of the model for X

W*

Transformed weight matrix of the model for X

Notes

Acknowledgment

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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