A Combinatorial Approach to the Variable Selection in Multiple Linear Regression: Analysis of Selwood et al Data set -A Case Study.

A combinatorial protocol (CP) is introduced here to interface it with the multiple linear regression (MLR) for variable selection. The efficiency of CP-MLR is primarily based on the restriction of entry of correlated variables to the model development stage. It has been used for the analysis of Selwood et al data set [16], and the obtained models are compared with those reported from GFA [8] and MUSEUM [9] approaches. For this data set CP-MLR could identify three highly independent models (27, 28 and 31) with Q2 value in the range of 0.632-0.518. Also, these models are divergent and unique. Even though, the present study does not share any models with GFA [8], and MUSEUM [9] results, there are several descriptors common to all these studies, including the present one. Also a simulation is carried out on the same data set to explain the model formation in CP-MLR. The results demonstrate that the proposed method should be able to offer solutions to data sets with 50 to 60 descriptors in reasonable time frame. By carefully selecting the inter-parameter correlation cutoff values in CP-MLR one can identify divergent models and handle data sets larger than the present one without involving excessive computer time.

CP-MLR Directed QSAR Studies on the Antimycobacterial Activity of Functionalised Alkenols - Topological Descriptors in Modeling the Activity

The antimycobacterial activity of nitro/ acetamido alkenol derivatives and chloro/ amino alkenol derivatives has been analyzed through combinatorial protocol in multiple linear regression (CP-MLR) using different topological descriptors obtained from Dragon software. Among the topological descriptor classes considered in the study, the activity is correlated with simple topological descriptors (TOPO) and more complex 2D autocorrelation descriptors (2DAUTO). In model building the descriptors from other classes, that is, empirical, constitutional, molecular walk counts, modified Burden eigenvalues and Galvez topological charge indices have made secondary contribution in association with TOPO and / or 2DAUTO classes. The structure-activity correlations obtained with the TOPO descriptors suggest that less branched and saturated structural templates would be better for the activity. For both the series of compounds, in 2DAUTO the activity has been correlated to the descriptors having mass, volume and/ or polarizability as weighting component. In these two series of compounds, however, the regression coefficients of the descriptors have opposite arithmetic signs with respect to one another. Outwardly these two series of compounds appear very similar. But in terms of activity they belong to different segments of descriptor-activity profiles. This difference in the activity of these two series of compounds may be mainly due to the spacing difference between the C1 (also C6) substituents and rest of the functional groups in them.