Raport de cercetare - Lorentz JÄNTSCHI

[25]. In this
situation, three alternative linear regression methods may be considered, these are a) Ridge
Regression(RR), b) Principal Component Regression(PCR) and c) Partial Least Squares(PLS).
These three methods are also very useful even when the independent variables are highly
correlated. In the ridge regression method, descriptors are transformed into principal components
(PCs). All of the principal components are used in the regression, but they are first shrunk
differentially according to their eigenvalues and a ridging constant. In the principal components
regression, the descriptors are transformed into principal components after which a subset of the
PCs is used in an ordinary least square regression. Partial least squares also uses a set of linear
combinations of the descriptors but, in this approach, the dependent variable is also considered in
this step. Each of these methods makes use of the entire available pool of independent variables as
opposed to selecting a subset, which introduces bias and may result in the elimination of important
parameters from the study. Formal comparisons have consistently shown subsetting to be less
effective than alternative methods, such as these, that retain all of the independent variables and
use other approaches to deal with the rank deficiency [26]. Statistical theory suggests that RR is
the best of the three methods and this has been generally borne out in multiple comparative studies
[26–28]. As such, the RR models developed in the current study are analyzed in more detail than
the PCR and PLS models. The RR vector of regression coefficients, b, is given by b = (X T X+kI) -
1 X T Y, where X is the matrix of descriptors, Y is the vector of observed activities, I is an identity
matrix, and k is a nonnegative constant known as the “ridge” constant.
÷ Lucrare: Multivariate analysis of experimental and computational descriptors of molecular
lipophilicity
÷ Autori: Raimund Mannholda, Gabriele Crucianib, Karl Drossc, Roelof Rekkerd
÷ Sursa: Journal of Computer-Aided Molecular Design, Volume 12, Number 6, 1998, p. 573-
581(9).
÷ Rezumat:
Two experimental (log P, RMw) and 17 calculation descriptors for molecular lipophilicity
(fragmental, atom-based for based on molecular properties) were investigated by multivariate
analysis for a database of 159 compounds including both simple structures as well as more
complex drug molecules. Principal component analysis (PCA) of the entire database exhibits a
clustering of chemical groups; preciseness of clustering corresponds to chemical similarity. Thus,
diversity searching in databases might effectively be performed by PCA on the basis of
calculatedlog P. The comparative validity check of experimental and computational procedures by
regression analysis and PCA was performed with a chemically balanced, reduced data set (n D 55)
representing 11 chemical groups with 5 members each. Regression of experimental descriptors
(log Poct versus RMw) proves that chromatographic data, obtained under well-defined
experimental conditions, can be used as valid substitutes for log P. Regression of calculated versus
experimental lipophilicity data shows a superiority of fragmental over atom-based methods and
approaches based on molecular properties, as indicated by correlation coefficients, slopes and
intercepts. Inaddition, PCA revealed that fragmental methods (Rekker-type, KOWWIN, KLOGP)
sense the compound ranking in log P data to almost the same extent as experimental approaches.
For atom-based procedures and CLOGP, both the comparability of absolute values and the
sensing of the compound ranking in the database are slightly less. This trend is more pronounced
for the methods based on molecular properties, with the exception of BLOGP.
÷ Detalii de interes:
Validity check of calculation methods by regression analysis and PCA. Regression analysis of
calculated versus experimental data shows that in general fragmental methods are superior to
atom-based and 3D-related approaches. These results are in accord with our earlier analysis with a
smaller dataset [35]. A limited applicability is often attributed to fragmental methods due to
missing fragment values. This is true for CLOGP and Rekker-type methods, but not for
KOWWIN. Information obtained by PCA on the same dataset, in general parallels the regression
data, but unravels more precisely the comparability in absolute values and the reflection of
38