Diagnosing Heteroskedasticity and Resolving Multicollinearity Paradoxes in Physicochemical Property Prediction

Lipophilicity (logP) prediction remains central to drug discovery, yet linear regression models for this task frequently violate statistical assumptions in ways that invalidate their reported performance metrics. We analyzed 426,850 bioactive molecules from a rigorously curated intersection of PubChem, ChEMBL, and eMolecules databases, revealing severe heteroskedasticity in linear models predicting computed logP values (XLOGP3): residual variance increases 4.2-fold in lipophilic regions (logP greater than 5) compared to balanced regions (logP 2 to 4). Classical remediation strategies (Weighted Least Squares and Box-Cox transformation) failed to resolve this violation (Breusch-Pagan p-value less than 0.0001 for all variants). Tree-based ensemble methods (Random Forest R-squared of 0.764, XGBoost R-squared of 0.765) proved inherently robust to heteroskedasticity while delivering superior predictive performance. SHAP analysis resolved a critical multicollinearity paradox: despite a weak bivariate correlation of 0.146, molecular weight emerged as the single most important predictor (mean absolute SHAP value of 0.573), with its effect suppressed in simple correlations by confounding with topological polar surface area (TPSA). These findings demonstrate that standard linear models face fundamental challenges for computed lipophilicity prediction and provide a principled framework for interpreting ensemble models in QSAR applications.

A Scalable Framework for logP Prediction: From Terabyte-Scale Data Integration to Interpretable Ensemble Modeling

This study presents a large-scale predictive modeling framework for logP prediction using 426850 bioactive compounds rigorously curated from the intersection of three authoritative chemical databases: PubChem, ChEMBL, and eMolecules. We developed a novel computational infrastructure to address the data integration challenge, reducing processing time from a projected over 100 days to 3.2 hours through byte-offset indexing architecture, a 740-fold improvement. Our comprehensive analysis revealed critical insights into the multivariate nature of lipophilicity: while molecular weight exhibited weak bivariate correlation with logP, SHAP analysis on ensemble models identified it as the single most important predictor globally. We systematically evaluated multiple modeling approaches, discovering that linear models suffered from inherent heteroskedasticity that classical remediation strategies, including weighted least squares and Box-Cox transformation, failed to address. Tree-based ensemble methods, including Random Forest and XGBoost, proved inherently robust to this violation, achieving an R-squared of 0.765 and RMSE of 0.731 logP units on the test set. Furthermore, a stratified modeling strategy, employing specialized models for drug-like molecules (91 percent of dataset) and extreme cases (nine percent), achieved optimal performance: an RMSE of 0.838 for the drug-like subset and an R-squared of 0.767 for extreme molecules, the highest of all evaluated approaches. These findings provide actionable guidance for molecular design, establish robust baselines for lipophilicity prediction using only 2D descriptors, and demonstrate that well-curated, descriptor-based ensemble models remain competitive with state-of-the-art graph neural network architectures.