Multivariate statistical models Discriminant analysis

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... 

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. 

There are many other statistical models which can be used for the evaluation of DICE studies. Inclusion of not only a group factor, but also a time factor in the experiment methods of the analysis of variance (ANOVA) can be applied to find expression changes within the temporal course of the protein expression or to find interactions between the group and time factor. Several multivariate statistical methods are of use, too. Spots with similar expression profiles can be grouped by cluster analysis or, on the other hand, new spots can be assigned to existing groups by the methods of discriminant analysis. 

It is commonly the case that a wide variety of properties can be included in a QSAR analysis and a decision must be made on whether to include all possibilities or limit the number of descriptors. This decision depends on the size of the data set and the correlation matrix between the properties. Farge sets of property data contain a lot of redundancy of information. For example, molecular weight, surface area and molar refraction are always highly correlated, therefore a decision to nse only molecular weight could be made. Some multivariate statistical analysis methods are tolerant of data sets which contain more properties than compounds, for example, PFS, while others are not, for example, linear discriminant analysis (FDA). Ideally, a set of uncorrelated properties is desirable as this is most likely to give a robust, interpretable model. 

PCA is a least square method and therefore its results depend on data scaling. The initial variance of a column variable partly determines its importance in the model. In order to avoid the problem of over- or under-representation of variables, column variables are scaled to unit variance before analysis. The column average is then subtracted from each variable, which, from a statistical point of view, corresponds to moving the multivariate system to the center of the data, which becomes the starting point of the mathematical analysis. The same auto-scaUng and centering procedures are applied in PLS discriminant analysis. 

Then the next step consists on application of multivariate statistical methods to find key features involving molecules, descriptors and anticancer activity. The methods include principal component analysis (PCA), hiererchical cluster analysis (HCA), K-nearest neighbor method (KNN), soft independent modeling of class analogy method (SIMCA) and stepwise discriminant analysis (SDA). The analyses were performed on a data matrix with dimension 25 lines (molecules) x 1700 columns (descriptors), not shown for convenience. For a further study of the methodology apphed there are standard books available such as (Varmuza FUzmoser, 2009) and (Manly, 2004). 

Models for homologous series of substances using simple regression methods. Quantitative substructure-based models derived from multivariate statistics (e.g. discriminant analysis), which may be applicable to a variety of chemical classes. 

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. 

---