Applicability Domain of Polyparameter Linear Free Energy Relationship Models Evaluated by Leverage and Prediction Interval Calculation

Polyparameter linear free energy relationships (PP-LFERs) are accurate and robust models employed to predict equilibrium partition coefficients (K) of organic chemicals. The accuracy of predictions by a PP-LFER depends on the composition of the respective calibration data set. Generally, extrapolation outside the domain defined by the calibration data is likely to be less accurate than interpolation. In this study, the applicability domain (AD) of PP-LFERs was systematically evaluated by calculating the leverage (h) and prediction interval (PI). Repeated simulations with experimental data showed that the root mean squared error of predictions increased with h. However, the analysis also showed that PP-LFERs calibrated with a large number (e.g., 100) of training data were highly robust against extrapolation error. For such PP-LFERs, the common definition of extrapolation (h > 3 h_mean, where h_mean is the mean h of all training compounds) may be excessively strict. Alternatively, the PI is proposed as a metric to define the AD of PP-LFERs, as it provides a concrete estimate of the error range that agrees well with the observed errors, even for extreme extrapolations. Additionally, published PP-LFERs were evaluated in terms of their AD using the new concept of AD probes, which indicated the varying predictive performance of PP-LFERs in the existing literature for environmentally relevant compounds.