Linking ordinal log-linear models with Correspondence Analysis: an application to estimating drug-likeness in the drug discovery process

Ordinal log-linear models (OLLM's) are amid the most widely used and powerful techniques to model association among ordinal variables in categorical data analysis. The parameters of such models are traditionally estimated using iterative algorithms, such as the Newton-Raphson method and iterative proportional fitting. More recent advances involve a non-iterative estimation method that performs equally well for estimation of the linear-by-linear association in OLLMs for a two-way table. This paper establishes a link between the Beh-Davy non-iterative estimation method (BDNI) (Beh & Davy, 2003) and the well-known ordinal correspondence analysis (CA) technique for two dimensional tables. The BDNI estimator of association relies on orthogonal polynomials (OPs), an approach dating from Lancaster (1953) to Beh and Davy (2003). OPs provide insight into the origin and development of non-iterative estimation in OLLMs, as an alternative to popular iterative procedures. The main advantage of OPs is that the resultant parameters enable estimation of the linear, and also quadratic and higher order association structures amongst the ordered categories. Ordinal CA was first introduced by Beh (1997). We compare the linear-by-linear BDNI association procedure with the linear-by-linear association method depicted via graphical representation in ordinal CA. To demonstrate this link and theory we analyzed the relationships between predictors of drug-likeness used in drug discovery to filter out small molecule (drugs) that may fail clinical trials. In vitro absorption, distribution, metabolism and elimination (ADME) assays are now being conducted throughout the drug discovery process, from hit to lead optimization (Kerns & Li, 2008). The analytical community needs still to develop faster and better analytic methods to enhance the 'developability' of drug leads, and to formalize strategies for ADME assessment of candidates in the discovery and pre-clinical stages (Kassel 2004). Ass