Chance factors in studies of quantitative structure-activity relationships

Abstract

Multiple regression analysis is a basic statistical tool used for QSAR studies in drug design. However, there is a risk or arriving at fortuitous correlations when too many variables are screened relative to the number of available observations. In this regard, a critical distinction must be made between the number of variables screened for possible correlation and the number which actually appear in the regression equation. Using a modified Fortran stepwise multiple-regression analysis program, simulated QSAR studies employing random numbers were run for many different combinations of screened variables and observations. Under certain conditions, a substantial incidence of correlations with high r2 values were found, although the overall degree of chance correlation noted was less than that reported in a previous study. Analysis of the results has provided a basis for making judgements concerning the level of risk of encountering chance correlations for a wide range of combinations of observations and screened variables in QSAR studies using multiple-regression analysis. For illustrative purposes, some examples involving published QSAR studies have been considered and the reported correlations shown to be less significant than originally presented through the influence of unrecognized chance factors.

A new computer program for QSAR‐analysis: ARTE‐QSAR

“…This is called the Topliss ratio. 16 As a rule-of-thumb, it is recommended that the Topliss ratio should have a value of at least 5. The structure of a QSAR model should always be inspected by validation techniques, able to detect over fitting due to variable multicollinearity, noise, sample specificity, and unjustified model complexity.…”

Identification of a molecular signature for leukemic promyelocytes and their normal counterparts: focus on DNA repair genes

“…As this structure might be associated with 'chance' correlations, 20 we inverted the respective roles of genes and normal/leukemic promyelocytes (statistical units and variables, respectively) and the resulting matrix was submitted to PCA. This method uses an unsupervised learning approach to investigate natural co-expression structures (components) of the entire genome.…”

Multivariate Analysis of Quantitative Chemical and Enzymic Characterization Data in Classification of Actinobacillus, Haemophilus and Pasteurella spp.

“…Cell sugars are therefore preferable to fatty acids as chemotaxonomic parameters for the Actinobacillus-Haemophilus-Pasteurella group. For a data-analytical problem such as that presented here, where discrimination between classes is of interest, but where the number of variables are approximately 2-3 times the number of samples in the major classes, the risk for chance correlations are obvious if one variable at a time is studied, or if methods based on multiple regression are used (Topliss & Edwards, 1979). One cannot, therefore, by directly screening one variable at a time, conclude that the D-glycero-D-mannoheptose variable is a 'true' indicator variable despite the fact that it perfectly distinguishes the A. actinomycetemcomitans and H .…”