Multivariate statistical models Partial least square analysis

Quantitative structure-activity/pharmacokinetic relationships (QSAR/ QSPKR) for a series of synthesized DHPs and pyridines as Pgp (type I (100) II (101)) inhibitors was generated by 3D molecular modelling using SYBYL and KowWin programs. A multivariate statistical technique, partial least square (PLS) regression, was applied to derive a QSAR model for Pgp inhibition and QSPKR models. Cross-validation using the leave-one-out method was performed to evaluate the predictive performance of models. For Pgp reversal, the model obtained by PLS could account for most of the variation in Pgp inhibition (R2 = 0.76) with fair predictive performance (Q2 = 0.62). Nine structurally related 1,4-DHPs drugs were used for QSPKR analysis. The models could explain the majority of the variation in clearance (R2 = 0.90), and cross-validation confirmed the prediction ability (Q2 = 0.69) [ 129]. 

A total of 185 emission lines for both major and trace elements were attributed from each LIBS broadband spectrum. Then background-corrected, summed, and normalized intensities were calculated for 18 selected emission lines and 153 emission line ratios were generated. Finally, the summed intensities and ratios were used as input variables to multivariate statistical chemometric models. A total of 3100 spectra were used to generate Partial Least Squares Discriminant Analysis (PLS-DA) models and test sets. 

In the past few years, PLS, a multiblock, multivariate regression model solved by partial least squares found its application in various fields of chemistry (1-7). This method can be viewed as an extension and generalization of other commonly used multivariate statistical techniques, like regression solved by least squares and principal component analysis. PLS has several advantages over the ordinary least squares solution therefore, it becomes more and more popular in solving regression models in chemical problems. 

When compounds are selected according to SMD, this necessitates the adequate description of their structures by means of quantitative variables, "structure descriptors". This description can then be used after the compound selection, synthesis, and biological testing to formulate quantitative models between structural variation and activity variation, so called Quantitative Structure Activity Relationships (QSARs). For extensive reviews, see references 3 and 4. With multiple structure descriptors and multiple biological activity variables (responses), these models are necessarily multivariate (M-QSAR) in their nature, making the Partial Least Squares Projections to Latent Structures (PLS) approach suitable for the data analysis. PLS is a statistical method, which relates a multivariate descriptor data set (X) to a multivariate response data set Y. PLS is well described elsewhere and will not be described any further here [42, 43]. 

The basic principle of experimental design is to vary all factors concomitantly according to a randomised and balanced design, and to evaluate the results by multivariate analysis techniques, such as multiple linear regression or partial least squares. It is essential to check by diagnostic methods that the applied statistical model appropriately describes the experimental data. Unacceptably poor fit indicates experimental errors or that another model should be applied. If a more complicated model is needed, it is often necessary to add further experimental runs to correctly resolve such a model. 

Two fundamentally different statistical approaches to biomarker selection are possible. With the first, experimental data can be used to construct multivariate statistical models of increasing complexity and predictive power - well-known examples are Partial Least Square Discriminant Analysis (PLS-DA) (Barker Rayens, 2003 Kemsley, 1996 Szymanska et al., 2011) or Principal Component Linear Discriminant Analysis (PC-LDA) (Smit et al., 2007 Werf et al., 2006). Inspection of the model coefficients then should point to those variables that are important for class discrimination. As an alternative, univariate statistical tests can be... 

The improvement in computer technology associated with spectroscopy has led to the expansion of quantitative infrared spectroscopy. The application of statistical methods to the analysis of experimental data is known as chemometrics [5-9]. A detailed description of this subject is beyond the scope of this present text, although several multivariate data analytical methods which are used for the analysis of FTIR spectroscopic data will be outlined here, without detailing the mathematics associated with these methods. The most conunonly used analytical methods in infrared spectroscopy are classical least-squares (CLS), inverse least-squares (ILS), partial least-squares (PLS), and principal component regression (PCR). CLS (also known as K-matrix methods) and PLS (also known as P-matrix methods) are least-squares methods involving matrix operations. These methods can be limited when very complex mixtures are investigated and factor analysis methods, such as PLS and PCR, can be more useful. The factor analysis methods use functions to model the variance in a data set. 

Linear or nonlinear multiple regression analysis is used as a statistical tool to derive quantitative models, to check the significance of these models and of each individual term in the regression equation. Other statistical methods, such as discriminant analysis, principal component analysis (PCA), or partial least squares (PLS) analysis (see Partial Least Squares Projections to Latent Structures (PLS) in Chemistry) are alternatives to regression analysis (see Che mo me tries Multivariate View on Chemical Problems)Newer approaches compare the similarity of molecules with respect to different physicochemical or other properties with their biological activities. 

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