QSPR regression models

Liu and Zhong introduced a number of QSPR models based on molecular connectivity indices [151, 152], In a first iteration, the researchers developed polymer-dependent correlations descriptors were calculated for a set of solvents and models were developed per polymer type [151], Polymer classes under consideration were polystyrene, polyethylene, poly-1-butene, poly-l-pentene, poly(4-methyl-l-pentene), polydimethylsiloxane, and polyisobutylene. As the authors fail to provide any validation for their models, it is difficult to asses their predictive power. In a subsequent iteration and general expansion of this study, mixed and therefore more general models based on the calculated connectivity indices of both solvent and polymers were developed. While it is unclear from the paper which polymer representation was used for the calculation of the connectivity indices, the best regression model (eight parameter model) yields only acceptable predictive power (R = 0.77, = 0.77, s = 34.47 for the training set, R = 0.75... 

Furthermore, QSPR models for the prediction of free-energy based properties that are based on multilinear regression analysis are often referred to as LFER models, especially, in the wide field of quantitative structure-activity relationships (QSAR). 

Aqueous solubility is selected to demonstrate the E-state application in QSPR studies. Huuskonen et al. modeled the aqueous solubihty of 734 diverse organic compounds with multiple linear regression (MLR) and artificial neural network (ANN) approaches [27]. The set of structural descriptors comprised 31 E-state atomic indices, and three indicator variables for pyridine, ahphatic hydrocarbons and aromatic hydrocarbons, respectively. The dataset of734 chemicals was divided into a training set ( =675), a vahdation set (n=38) and a test set (n=21). A comparison of the MLR results (training, r =0.94, s=0.58 vahdation r =0.84, s=0.67 test, r =0.80, s=0.87) and the ANN results (training, r =0.96, s=0.51 vahdation r =0.85, s=0.62 tesL r =0.84, s=0.75) indicates a smah improvement for the neural network model with five hidden neurons. These QSPR models may be used for a fast and rehable computahon of the aqueous solubihty for diverse orgarhc compounds. 

Multiple linear regression (MLR) is a classic mathematical multivariate regression analysis technique [39] that has been applied to quantitative structure-property relationship (QSPR) modeling. However, when using MLR there are some aspects, with respect to statistical issues, that the researcher must be aware of ... 

Multivariate calibration has the aim to develop mathematical models (latent variables) for an optimal prediction of a property y from the variables xi,..., jcm. Most used method in chemometrics is partial least squares regression, PLS (Section 4.7). An important application is for instance the development of quantitative structure—property/activity relationships (QSPR/QSAR). 

QSPR models have been developed by six multivariate calibration methods as described in the previous sections. We focus on demonstration of the use of these methods but not on GC aspects. Since the number of variables is much larger than the number of observations, OLS and robust regression cannot be applied directly to the original data set. These methods could only be applied to selected variables or to linear combinations of the variables. 

Moody RP, MacPherson H (2003) Determination of dermal absorption QSAR/QSPRs by brute force regression multiparameter model development with Molsuite 2000. J Toxicol Env Healt A 66 1927-1942. 

As a possible alternative to in vitro metabolism studies, QSAR and molecular modelling may play an increasing role. Quantitative stracture-pharmacokinetic relationships (QSPR) have been studied for nearly three decades [42,45-52]. These are often based on classical QSAR approaches based on multiple linear regression. In its most simple form, the relationship between PK properties and lipophilicity has been discussed by various workers in the field [36, 49, 50]. 

A more common use of informatics for data analysis is the development of (quantitative) structure-property relationships (QSPR) for the prediction of materials properties and thus ultimately the design of polymers. Quantitative structure-property relationships are multivariate statistical correlations between the property of a polymer and a number of variables, which are either physical properties themselves or descriptors, which hold information about a polymer in a more abstract way. The simplest QSPR models are usually linear regression-type models but complex neural networks and numerous other machine-learning techniques have also been used. 

The multiple linear regression (MLR) method was historically the first and, until now, the most popular method used for building QSPR models. In MLR, a property is represented as a weighted linear combination of descriptor values F=ATX, where F is a column vector of property to be predicted, X is a matrix of descriptor values, and A is a column vector of adjustable coefficients calculated as A = (XTX) XTY. The latter equation can be applied only if the matrix XTX can be inverted, which requires linear independence of the descriptors ( multicollinearity problem ). If this is not the case, special techniques (e.g., singular value decomposition (SVD)26) should be applied. 

From another viewpoint, LFER methods tend to be model based. Model-based methods employ sets of descriptors that often (1) model classical chemical concepts, (2) are small in number, and (3) use simple regression analyses. For example, the Flammett equation involving the logarithm of the rate constant as a linear function of the substituent constant, a (mentioned earlier), is model based. Similarly, some QSAR and QSPR studies may be viewed in this manner, and so they are included as LFER subsets in this chapter. 

Quantitative structure property relationships (QSPRs) were thus developed using different statistical models multiple linear regressions on one hand, and neural networks on the other hand. The reliability of each of these models was determined from their predictive ability. 

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