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Abstract
Validation is a crucial aspect of quantitative structure–activity relationship (QSAR) modeling. The present paper shows that traditionally used validation parameters (leave-one-out Q2 for internal validation and predictive R2 for external validation) may be supplemented with two novel parameters rm2 and Rp2 for a stricter test of validation. The parameter rm2(overall) penalizes a model for large differences between observed and predicted values of the compounds of the whole set (considering both training and test sets) while the parameter Rp2 penalizes model R2 for large differences between determination coefficient of nonrandom model and square of mean correlation coefficient of random models in case of a randomization test. Two other variants of rm2 parameter, rm2(LOO) and rm2(test), penalize a model more strictly than Q2 and R2pred respectively. Three different data sets of moderate to large size have been used to develop multiple models in order to indicate the suitability of the novel parameters in QSAR studies. The results show that in many cases the developed models could satisfy the requirements of conventional parameters (Q2 and R2pred) but fail to achieve the required values for the novel parameters rm2 and Rp2. Moreover, these parameters also help in identifying the best models from among a set of comparable models. Thus, a test for these two parameters is suggested to be a more stringent requirement than the traditional validation parameters to decide acceptability of a predictive QSAR model, especially when a regulatory decision is involved.
Highlights
Quantitative structure-activity relationships (QSARs) are statistically derived models that can be used to predict the physicochemical and biological properties of molecules from the knowledge of chemical structure
For the three data sets (I, II and III), QSAR models were separately developed from genetic function approximation (GFA) technique [39] with 5,000 crossovers using Cerius2 version 4.10 software [40]
The CCR5 binding affinity data (IC50) of 119 piperidine derivatives [33,34,35,36] were converted to logarithmic scale [pIC50 = -logIC50] and used for the QSAR study
Summary
Quantitative structure-activity relationships (QSARs) are statistically derived models that can be used to predict the physicochemical and biological (including toxicological) properties of molecules from the knowledge of chemical structure. The description of QSAR models has been a topic for scientific research for more than 40 years and a topic within the regulatory framework for more than 20 years [1]. In the field of QSAR, the main objective is to investigate these relationships by building mathematical models that explain the relationship in a statistical way with ultimate goal of prediction and/or mechanistic interpretation. One of the major applications of QSAR models is to predict the biological activity of untested compounds from their molecular structures [5]
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