Abstract
The two methods most often used to evaluate the robustness and predictivity of partial least squares (PLS) models are cross-validation and response randomization. Both methods may be overly optimistic for data sets that contain redundant observations, however. The kinds of perturbation analysis widely used for evaluating model stability in the context of ordinary least squares regression are only applicable when the descriptors are independent of each other and errors are independent and normally distributed; neither assumption holds for QSAR in general and for PLS in particular. Progressive scrambling is a novel, non-parametric approach to perturbing models in the response space in a way that does not disturb the underlying covariance structure of the data. Here, we introduce adjustments for two of the characteristic values produced by a progressive scrambling analysis -- the deprecated predictivity (\(Q_{\rm s}^{\ast^2}\)) and standard error of prediction (SDEP *s ) -- that correct for the effect of introduced perturbation. We also explore the statistical behavior of the adjusted values (\(Q_{\rm 0}^{\ast^2}\) and SDEP *0 ) and the sensitivity to perturbation (dq 2/dr yy ′ 2). It is shown that the three statistics are all robust for stable PLS models, in terms of the stochastic component of their determination and of their variation due to sampling effects involved in training set selection.
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References
G.W. Snedecor W.G. Cochran (1989) Statistical Methods EditionNumber10 Iowa State Press Ames, IA
H. Martens T. Næs (1989) Multivariate Calibration Wiley Chichester, UK
Wold, S., Johansson, E. and Cocchi, M., In Kubinyi, H. (Ed.), 3D QSAR in Drug Design: Theory, Methods and Applications, ESCOM, Leiden, The Netherlands, 1993, pp. 523–550.
J. Zupan J. Gasteiger (1999) Neural Networks in Chemistry and Drug Design EditionNumber2 Wiley-VCH Weinheim, Germany
Wold, S. and Eriksson, L., In van de Waterbeemd, H. (Ed.), Chemometric Methods in Molecular Design, VCH, Weinheim, Germany, 1995, pp. 309–318.
A. Tropsha P. Grammatica V.K. Gombar (2003) QSAR Comb. Sci., 22 69
A. Golbraikh A. Tropsha (2002) J. Mol. Graph. Model., 20 269
R.D. Clark (2003) J. Comput.-Aided Mol. Des., 17 265
D.M. Hawkins S.C. Basak D. Mills (2003) J. Chem. Inf. Comput. Sci., 43 579
K. Baumann M. von Korff H. Albert (2002) J. Chemom., 16 351
D.M. Hawkins (2004) J. Chem. Inf. Comput. Sci., 44 1
Heritage, T.W. and Lowis, D.R., In Parrill, A.L. and Reddy, M.R. (Eds.), Rational Drug Design: Novel Methodology and Practical Applications, ACS Symposium Series 719, American Chemical Society, Washington, DC, 1999, pp. 212–225.
Clark, R.D., Sprous, D.G. and Leonard, J.M., In Höltje, H.-D. and Sippl, W. (Eds.), Rational Approaches to Drug Design, Prous Science, Barcelona, Spain, 2001, pp. 475–485.
D.B. Kireev J.R. Chrétien D.S. Grierson C. Monneret (1997) J. Med. Chem., 40 4257
J.M. Luco F.H. Ferretti (1997) J. Chem. Inf. Comput. Sci., 37 392
HQSAR™ is distributed by Tripos, Inc., St. Louis, MO; www.tripos.com.
R.D. Cramer ParticleIII D.E. Patterson J.D. Bunce (1988) J. Am. Chem. Soc., 110 5959
Cramer III, R.D., DePriest, S.A., Patterson, D.E. and Hecht, P., In Kubinyi, H. (Ed.), 3D QSAR in Drug Design: Theory, Methods and Applications, ESCOM, Leiden, The Netherlands, 1993, pp. 443–485.
P. Chavatte S. Yous C. Marot N. Baurin D. Lesiur (2001) J. Med. Chem., 44 3223
H. Voet Particlevan der (1999) J. Chemom., 13 195
J.H. Kalivas J.B. Forrester H.A. Seipel (2004) J. Comput.-Aided Mol. Design 18 537
In fact, Equation 5 in Ref. 13 includes a typographical error, with sSDEP′ substituted for s.
M. Clark R.D. Cramer ParticleIII D.M. Jones D.E. Patterson P.E. Simeroth (1990) Tetrahedron Comput. Methodol., 3 47
Advanced CoMFA® and SYBYL® are distributed by Tripos, Inc., St. Louis, MO; www.tripos.com.
B.L. Bush R.B. Nachbar ParticleJr. (1993) J. Comput.-Aided Mol. Design, 7 587
Given that the most statistically powerful model will always be the one based on all available observations [Refs. 9–11].
M. Otto (1999) Chemometrics Wiley-VCH Weinheim, Germany
A full factorial design includes two observations for each first-order factor, each of which is a partial replicate of its complement in the descriptor space (see Ref. 27).
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Clark, R.D., Fox, P.C. Statistical variation in progressive scrambling. J Comput Aided Mol Des 18, 563–576 (2004). https://doi.org/10.1007/s10822-004-4077-z
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DOI: https://doi.org/10.1007/s10822-004-4077-z