Beware of Unreliable Q²! A Comparative Study of Regression Metrics for Predictivity Assessment of QSAR Models

Validation is an essential step of QSAR modeling, and it can be performed by both internal validation techniques (e.g., cross-validation, bootstrap) or by an external set of test objects, that is, objects not used for model development and/or optimization. The evaluation of model predictive ability is then completed by comparing experimental and predicted values of test molecules. When dealing with quantitative QSAR models, validation results are generally expressed in terms of Q² metrics. In this work, four fundamental mathematical principles, which should be respected by any Q² metric, are introduced. Then, the behavior of five different metrics (Q_F1², Q_F2², Q_F3², Q_CCC², and Q_Rm²) is compared and critically discussed. The conclusions highlight that only the Q_F3² metric satisfies all the stated conditions, while the remaining metrics show different theoretical flaws.