Quantitative structure-activity relationship linear regression methods

Quantitative Structure - Activity Relationships (QSARs) are estimation methods developed and used to predict certain effects or properties of chemical substances, which are primarily based on the structure of the chemicals. The development of QSARs often relies on the application of statistical methods such as multiple linear regression (MLR) or partial least squares regression (PLS). However, since toxicity data often include uncertainties and measurements errors, when the aim is to point out the more toxic and thus hazardous chemicals and to set priorities, order models can be used as alternative to statistical methods such as multiple linear regression. 

Non-linear models may be fitted to data sets by the inclusion of functions of physicochemical parameters in a linear regression model—for example, an equation in n and as shown in Fig. 6.5—or by the use of non-linear fitting methods. The latter topic is outside the scope of this book but is well covered in many statistical texts (e.g. Draper and Smith 1981). Construction of linear regression models containing non-linear terms is most often prompted when the data is clearly not well fitted by a linear model, e.g. Fig. 6.4e, but where regularity in the data suggests that some other model will fit. A very common example in the field of quantitative structure-activity relationship (QSAR) involves non-linear relationships with hydrophobic descriptors such as log P or n. Non-linear dependency of biological properties on these parameters became apparent early in the... 

Sutter and co-workers reported a method for automated descriptor selection for quantitative structure-activity relationships using generalized simulated annealing (36,132). The cost function used to evaluate the effectiveness of the deseriptors was based on a neural network. The result is an automated descriptor selection algorithm that is an optimization inside of an optimization. Application of the method to QSAR shows that effective descriptor subsets are found, and they support models that are as good or better than those obtained using traditional linear regression methods. 

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