QSAR's based on partial order ranking

The development of Quantitative Structure Activity Relationships (QSAR's) often relies heavily on the application of statistical methods such as multi-linear regression (MLR) or principal component analysis/partial least square (PCA/PLS). Partial order ranking (POR), which from a mathematical point of view is based on elementary methods of Discrete Mathematics, appears as an attractive and operationally simple and more general alternative since the method does not require specific functional relationships between the single descriptors or the end-points. The POR method allows ranking of a series of compounds, based on selected descriptors characterizing their structural and/or electronic nature (model diagram). The ranking of the compounds based on their end-points (experimental ranking) can then be compared to the model diagram. If the model diagram resembles the experimental ranking of the end-points under investigation, other compounds, not being experimentally investigated, can be assigned a rank in the model and hereby obtain an identity based on the known compounds. The present study elucidates the applicability of POR as a simple tool for QSAR modeling. Based on illustrative examples the POR approach to QSAR modeling will be presented with special focus on the precision and the uncertainties of the method, which will be discussed in terms of the number of descriptors and compounds involved. The advantageous interplay between POR and PCA, the latter being applied in order to reduce a possible large number of descriptors into a limited number of latent descriptors will be discussed.