Predicting Drug Combination Doses for IC50 Using Complex Numbers and Matrix Factorization

Determining precise drug concentrations to inhibit cancer cell growth remains acritical yet resource-intensive challenge in oncology, especially when evaluatingdrug combinations that require testing numerous dose pairs. Although existingcomputational methods focus on predicting drug synergy or classifying interactions,they rarely address the inverse problem: estimating specific concentrationpairs needed to achieve a defined inhibitory effect. To the best of our knowledge,this study is the first to formally define and address the problem of predictingcombination drug dosages required to achieve a target inhibitory effect,specifically, the IC\textsubscript{50}, for a given cancer cell line. Here, we present ComplexMatrixComb, a novel matrix factorization framework that models drug pair–cellline interactions using complex numbers. By encoding the concentration of eachdrug as the real or imaginary component of a complex value, the model capturesthe dynamics of the joint dose-response and accurately predicts the concentrationsthat achieve half-maximum inhibition (IC\textsubscript{50}). Across three benchmarkdatasets, O’Neil, NCI-ALMANAC, and AZ-Dream, ComplexMatrixComb consistentlyoutperformed traditional machine learning models in both regressionand classification tasks. It also demonstrated robustness to drug order and generalizabilityin diverse experimental designs. When integrated into establishedinhibition prediction models such as ComboFM and ComboLTR, the concentrationspredicted by our framework resulted in inhibition levels closely matchingthose obtained with ground-truth doses. To validate its practical relevance, weexperimentally tested five high-confidence drug pair–cell line predictions using MTT assays, confirming that the predicted doses induced approximately50% growth inhibition. By directly addressing the challenge of dose estimation, ComplexMatrixComb reduces the reliance on exhaustive experimental screening andprovides a scalable, data-driven tool for drug combination design. Our frameworkhas the potential to accelerate preclinical research and contribute to moreeffective and personalized strategies in oncology.