Partial least squares models cross-validation

Ekins et al. (163) used the rat ortholog 2B6 to generate a pharmacophore model and compared these findings with a partial least squares (PLS) model using MS-WHIM descriptors. The model was constructed using 16 B-lymphoblastoids and yielded a good cross-validated r2 of 0.607. The analysis included molecular surface properties (size) together with positive elec-... 

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]. 

PCM modeling aims to find an empirical relation (a PCM equation or model) that describes the interaction activities of the biopolymer-molecule pairs as accurate as possible. To this end, various linear and nonlinear correlation methods can be used. Nonlinear methods have hitherto been used to only a limited extent. The method of prime choice has been partial least-squares projection to latent structures (PLS), which has been found to work very satisfactorily in PCM. PCA is also an important data-preprocessing tool in PCM modeling. Modeling includes statistical model-validation techniques such as cross validation, external prediction, and variable-selection and signal-correction methods to obtain statistically valid models. (For general overviews of modeling methods see [10]). 

Intermediate Least Squares regression (ILS) is an extension of the Partial Least Squares (PLS) algorithm where the optimal variable subset model is calculated as intermediate to PLS and stepwise regression, by two parameters whose values are estimated by cross-validation [Frank, 1987]. The first parameter is the number of optimal latent variables and the second is the number of elements in the weight vector w set to zero. This last parameter (ALIM) controls the number of selected variables by acting on the weight vector of each mth latent variable as the following ... 

Partial least squares (PLS) is similar to MLR in that it also assumes a linear relationship between a vector x and a target property y. However, it avoids the problems of collinear descriptors by calculating the principal components for the molecular descriptors and target property separately. The scores for the molecular descriptors are used as the feature vector x and are also used to predict the scores for the target property, which can in turn be used to predict y. An important consideration in PLS is the appropriate number of principal components to be used for the QSAR model. This is usually determined by using cross-validation methods like fivefold cross validation and leave-one-out. PLS has been applied to the prediction of carcinogenicity [19], fathead minnow toxicity [20], Tetrahymena pyriformis toxicity [21], mammalian toxicity [22], and Daphnia magna toxicity [23],... 

The last step in a CoMFA study is a partial least squares (PLS) analysis (chapter 5.3) to determine the minimal set of grid points which is necessary to explain the biological activities of the compounds. Most often good to excellent results are obtained. However, the predictive value of the model must be checked by cross-validation if necessary, the model is refined and the analysis is repeated until a model of high predictive ability is obtained. 

Several applications can be found in literature regarding the use of NIR for the paediction of the main physical and rheological parameters of pasta and bread. De Temmerman et al. in 2007 proposed near-infrared (NIR) reflectance spectroscopy for in-line determination of moisture concentrations in semolina pasta immediately after the extrusion process. Several pasta samples with different moisture concentrations were extruded while the reflectance spectra between 308 and 1704 ran were measured. An adequate prediction model was developed based on the Partial Least Squares (PLS) method using leave-one-out cross-validation. Good results were obtained with R2 = 0,956 and very low level of RMSECV. This creates opportunities for measuring the moisture content with a low-cost sensor. 

This method was in fact carried out around two decades ago [30, 31]. However, it was applied only in the fermentation of pure microbial cultures. In a recent report by Acros-Hernandez and coworkers [32], infrared spectroscopy was applied to quantify the PHA produced in microbial mixed cultures. Around 122 spectra from a wide range of production systems were collected and used for calibrating the partial least squares (PLS) model, which relates the spectra with the PHA content (0.03-0.58 w/w) and 3-hydroxyvalerate monomer (0-63 mol%). The calibration models were evaluated by the correlation between the predicted and measured PHA content (R ), root mean square error of calibration, root mean square error of cross validation and root mean square error of prediction (RMSEP). The results revealed that the robust PLS model, when coupled with the Fourier-Transform infrared spectrum, was found to be applicable to predict the PHA content in microbial mixed cultures, with a low RMSEP of 0.023 w/w. This is considered to be a reliable method and robust enough for use in the PHA biosynthesis process using mixed microbial cultures, which is far more complex. 

Spectrophotometric monitoring with the aid of chemometrics has also been applied to more complex mixtures. To solve the mixtures of corticosteroid de-xamethasone sodium phosphate and vitamins Bg and Bi2, the method involves multivariate calibration with the aid of partial least-squares regression. The model is evaluated by cross-validation on a number of synthetic mixtures. The compensation method and orthogonal function and difference spectrophotometry are applied to the direct determination of omeprazole, lansoprazole, and pantoprazole in grastroresistant formulations. Inverse least squares and PCA techniques are proposed for the spectrophotometric analyses of metamizol, acetaminophen, and caffeine, without prior separation. Ternary and quaternary mixtures have also been solved using iterative algorithms. 

Instead promoter strength was predicted quantitatively based on a PLS-R(Partial Least Squares Regression) model named PSP (Promoter Strength Predictive) using nucleotide sequences of 49 promoters from an E. coli SPL. 42 of the promoters were used as training set in a leave-one-out cross-validated model determining the... 

In summary, the support vector machine (SVM) and partial least square (PLS) methods were used to develop quantitative structure activity relationship (QSAR) models to predict the inhibitory activity of nonpeptide HIV-1 protease inhibitors. Cenetic algorithm (CA) was employed to select variables that lead to the best-fitted models. A comparison between the obtained results using SVM with those of PLS revealed that the SVM model is much better than that of PLS. The root mean square errors of the training set and the test set for SVM model were calculated to be 0.2027, 0.2751, and the coefficients of determination (R2) are 0.9800, 0.9355 respectively. Furthermore, the obtained statistical parameter of leave-one-out cross-validation test (Q ) on SVM model was 0.9672, which proves the reliability of this model. Omar Deeb is thankful for Al-Quds University for financial support. 

We have applied kNN (Zheng and Tropsha 2000) and simulated annealing - partial least squares (SA-PLS) (Cho et al. 1998) QSAR approaches to a dataset of 48 chemically diverse functionalized amino acids (FAAs) with anticonvulsant activity that were synthesized previously, and successful QSAR models of FAA anticonvulsants have been developed (Shen et al. 2002). Both methods utilized multiple descriptors such as molecular connectivity indices or atom-pair descriptors, which are derived from two-dimensional molecular topology. QSAR models with high internal accuracy were generated, with leave-one-out cross-validated (q ) values rang-... 

Westad F, Afseth NK, Bro R. Finding relevant spectral regions between spectroscopic techniques by use of cross-model validation and partial least squares regression. Anal Chim Acta 2007 595 323-7. 

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