A non-iterative approach to ordinal log-linear models: investigation of log D in drug discovery

We investigate drug-likeness by considering the relationships between surrogate measures of drug-likeness (solubility, permeability) and structural properties (lipophilicity (log P), molecular weight (MW)). We study the pair-wise association between categorised variants of the traditional parameters of Lipinskis rule of five (Ro5), namely MW and log P, and an additional parameter, polar surface area (PSA), introduced by Veber et al., (2002) across strata, where strata are defined by a molecule's druggable versus non-druggable (Ro5 compliant vs violation) status. Zafar, et al. (2013) earlier showed that logP's association with MW changed sign from significantly negative to positive for nondruggable vs druggable strata, becoming lower (positive) for nondruggable vs druggable. These findings support recent criticisms about using log P (Bhal et al., 2007). This study explores further the pairwise relationships of log P in comparison with log D, a distribution coefficient, and shows that log D does not swap sign nor magnitude in its relationship with MW; thereby it is a better lipophicility measure. We use the Beh-Davy non-iterative (BDNI) direct estimation approach (Beh and Davy, 2004; Zafar et al., 2015) to estimate the linear-by-linear association of the pairwise relationships, within the framework of well-known ordinal log-linear models (OLLMs). We also provide correspondence analysis (CA) plots for comparing the pairwise associations of logP and log D with MW.