FRESH PERSPECTIVES
Figure 7 - Sample Test Results – Classifi ed Placebo’s and Actives
Figure 9 - Spectra of new active products with their corresponding placebo
Figure 8 - Addition of new actives/placebos with similar formulations not separated
Figure 10 - Scores for PC 3 vs. PC 2 - PCA model for placebos only
For the problem at hand, we were not able to successfully achieve the requisite level of discrimination between actives and placebos with a single model once the two new products were introduced – even when the new products were made part of the calibration set. This can be interpreted as a result of the new products introducing new sources of variance preventing the achievement of class discrimination with a single hyperplane.
The
earlier attempt to do so was too ambitious, at least with the tools at hand. It was thus necessary to break down the problem into smaller parts to eventually reach the modeling objective.
Taking a step back and looking at the PCA results for just the placebos – all of the original products plus new products (designated as NP1
and NP2 ), the
directions defi ned by PCs 2 and 3 did a reasonable job of clustering this subset (Figure 10).
Preprocessing of the data has the potential to enhance separation by minimizing within-class variance and/or maximizing the distance between
64 American Pharmaceutical Review | Fresh Perspectives 2013
classes. The use of generalized least squares weighting (GLSW) collapses the three clusters for the original placebos into a single tight group, and spreads the NP1
and NP2 placebo groups much further apart (Figure 11)
[1]. The addition of GLSW to the preprocessing recipe was insuffi cient to completely separate all placebos from all actives with the addition of the new products. However, the discrimination enhancement aff orded by GLSW provides the impetus for creating the following modeling strategy, which was ultimately successful:
•
Identify classes – or even a single class – at each stage that can be readily separated from the others.
• Make conservative use of GLSW to down weight variables contributing to within-class variability.
• Once a model has been built that successfully discriminates one or more classes from the remaining samples, those classes no
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