In this paper Free and Wilson analyse the variation in biological activity caused by substituents at various positions in a series of molecules.  They apply a simple least squares fitting to attribute a contribution that each substituent is making to the observed activity. This analysis of variance has become a fundamental tool for medicinal chemistry.  It is assumed that the SAR is additive although the possibility of additive and non-additive groups is discussed. The method should always be considered whenever the question is asked “have we made the best combination of substituents yet?” and as such should be used in almost every drug discovery project.  Recent developments building on the Free and Wilson approach have explored how many compounds must be included in the data set to ensure satisfactory values for the contributions of each group, for example:

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“A Mathematical Contribution to Structure-Activity Studies” by Free and Wilson. DOI:10.1021/jm00334a001