Multiple parameter method, Hansch

The basic principles on which the Hansch multiple parameter method for structure-activity correlation depends are described. These are compared with the basic features of the Free-Wilson method for assigning additivity constants to structural features of related compounds. An example is given for which the two methods of analysis have led to similar structure-activity relationships. Factors which determine the particular method to use in a new situation are discussed. The Free-Wilson method is presented in considerable operational detail with special emphasis on the detection and avoidance of situations which lead to singularity problems in solution of the matrix. Favorable analyses, which result in additivity constants that can be correlated with known physical constants, may lead to predictions for new compounds not covered in the original matrix. 

Tihe two methods of structure-activity correlation which have received the most application in the past decade are the Hansch multiple parameter method, or the so-called extrathermodynamic approach, and the Free-Wilson, or additive model. The basic differences and similarities of these methods are discussed in this presentation. 

On the basis of the origin of molecular descriptors used in calculations, QSAR methods can be divided into three groups. One group is based on a relatively small number (usually many times smaller than the number of compounds in a data set) of physicochemical properties and parameters describing,for example, hydrophobic, steric, and electrostatic effects. Usually, these descriptors are used as independent variables in multiple regression approaches (18) Jn the literature, these methods are typically referred to as Hansch analysis (8).These types of descriptors and corresponding linear optimization methods used in traditional QSAR analyses are discussed extensively in the chapter by Celassie (7) and therefore is not reviewed here. 

Statistical methods. Certainly one of the most important considerations in QSAR is the statistical analysis of the correlation of the observed biological activity with structural parameters - either the extrathermodynamic (Hansch) or the indicator variables (Free-Wilson). The coefficients of the structural parameters that establish the correlation with the biological activity can be obtained by a regression analysis. Since the models are constructed in terms of multiple additive contributions the method of solution is also called multiple linear regression analysis. This method is based on three requirements (223) i) the independent variables (structural parameters) are fixed variates and the dependent variable (biological activity) is randomly produced, ii) the dependent variable is normally and independently distributed for any set of independent variables, and iii) the variance of the dependent variable must be the same for any set of independent variables. 

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