Development of log P and log D models using a hierarchical linear regression approach

We present a hierarchical linear regression approach for the prediction of log P and log D, two key physicochemical properties in drug discovery. Molecular structures are described using radial substructure fragments of increasing complexity derived from Morgan count vectors, organized into three layers of features corresponding to radii of 0, 1, and 2. Starting with the simplest layer, a series of Bayesian ridge regression models are trained sequentially, where each successive model corrects the residuals of the previous one. The final prediction is obtained by summing the predictions of all three models. The final models employ approximately 1000 features in total and are trained on datasets of about 40,000 log P and 50,000 log D values compiled from public sources. Model performance was assessed by 5-fold cross-validation, yielding MAE of 0.35 and RMSE of 0.55 for log P, and MAE of 0.47 and RMSE of 0.69 for log D, which is competitive with results reported in the literature. External validation on two independent OpenADMET datasets confirmed that the model generalizes well to new data, while also demonstrating that retraining with even a small number of novel chemotypes can substantially improve performance on structurally distinct compound series. The hierarchical design, combined with the use of linear models, results in an interpretable and computationally lightweight approach suitable for deployment in browser-based applications via WebAssembly.