Beware of <i>R</i>²: Simple, Unambiguous Assessment of the Prediction Accuracy of QSAR and QSPR Models

TLDR

Statistical metrics for external predictivity, such as R², have proliferated over the past decade and are employed across various regression contexts. The paper aims to clarify the proper use of R² as a model fit statistic in QSAR/QSPR, guide its application, and encourage reporting of RMSE while addressing user‑specific challenges. The authors analyze the Golbraikh and Tropsha model‑fit criteria using rigorous statistical methods. They identify shortcomings in the criteria and propose a clearer, simpler alternative for assessing model predictivity, illustrated with examples of correct and incorrect R² usage.

Abstract

The statistical metrics used to characterize the external predictivity of a model, i.e., how well it predicts the properties of an independent test set, have proliferated over the past decade. This paper clarifies some apparent confusion over the use of the coefficient of determination, R(2), as a measure of model fit and predictive power in QSAR and QSPR modeling. R(2) (or r(2)) has been used in various contexts in the literature in conjunction with training and test data for both ordinary linear regression and regression through the origin as well as with linear and nonlinear regression models. We analyze the widely adopted model fit criteria suggested by Golbraikh and Tropsha ( J. Mol. Graphics Modell. 2002 , 20 , 269 - 276 ) in a strict statistical manner. Shortcomings in these criteria are identified, and a clearer and simpler alternative method to characterize model predictivity is provided. The intent is not to repeat the well-documented arguments for model validation using test data but rather to guide the application of R(2) as a model fit statistic. Examples are used to illustrate both correct and incorrect uses of R(2). Reporting the root-mean-square error or equivalent measures of dispersion, which are typically of more practical importance than R(2), is also encouraged, and important challenges in addressing the needs of different categories of users such as computational chemists, experimental scientists, and regulatory decision support specialists are outlined.