ComplexMatrixComb: predicting anticancer drug combination dosages for target growth inhibition via complex-number matrix factorization

Abstract Determining precise drug concentration combinations required to inhibit cancer cell growth remains a critical yet resource-intensive challenge in oncology, particularly in combination therapies where exhaustive experimental screening of dose pairs is impractical. While most existing computational approaches focus on predicting drug synergy or classifying interaction types given predefined doses, they rarely address the inverse problem of estimating the specific drug concentration pairs needed to achieve a predefined inhibitory effect. In this study, we formally define and address the problem of drug combination dose estimation for a target level of growth inhibition, with a particular focus on achieving approximately 50% inhibition, a widely used and clinically relevant benchmark. We introduce ComplexMatrixComb, a novel complex-valued matrix factorization framework that models drug pair-cell line interactions by encoding the concentration of each drug as the real or imaginary component of a complex number. This representation enables the model to capture joint dose-response dynamics and predict drug concentration pairs that achieve the desired inhibitory effect within partially observed interaction spaces. We evaluated ComplexMatrixComb across three benchmark datasets (O’Neil, NCI-ALMANAC, and AZ-DREAM), where it consistently outperformed traditional machine learning models in both regression and classification tasks. The framework demonstrated robustness across heterogeneous experimental settings, stability under drug-order perturbations, and strong agreement between predicted and observed inhibition levels when evaluated alongside established inhibition prediction models such as ComboFM, ComboLTR and PanThera. To assess practical relevance, we experimentally validated five high-confidence drug pair-cell line predictions using MTT assays on previously untested combinations. The results confirmed that the model-predicted dose combinations induced inhibition levels close to the targeted 50% growth reduction. By directly addressing the challenge of drug combination dose estimation, ComplexMatrixComb reduces reliance on exhaustive experimental screening and provides a scalable, data-driven tool for preclinical drug combination design, with potential applications in precision oncology.