Chemical graph theory and topological indices are key tools in the study of molecular structures and their properties. This research explores anticancer drugs using neighborhood degree-based topological indices and compares their efficacy through regression and machine learning models. The QSPR approach is applied to 15 anticancer drugs by constructing neighborhood-based molecular graphs, and calculating their respective topological indices. Regression models like quadratic, cubic, and random forest are employed to predict response metrics including like boiling point, refractivity, and surface area of the drugs. Comparative studies indicate that quadratic models provide better predictive performance then their cubic counterparts in most scenarios. Random forest models also demonstrate satisfactory accuracy with smaller error bounds. The present findings highlight the usefulness of topological indices in chemoinformatics and their application in predicting drug response.