Data-Driven Optimal Treatment Combination Regimes for Multiple Stressors Controlling for Multiple Adverse Effects

Combination drug treatment plays a central role in addressing complex diseases by enhancing the therapeutic benefit while mitigating adverse effects. However, determining optimal dose levels remains challenging due to additive drug effects, competing safety constraints, and the scarcity of reliable data in clinical and experimental settings. This paper develops a data-driven robust optimization framework for combination dose selection under uncertainty. The proposed approach integrates posterior sampling via Markov Chain Monte Carlo with convex hull-based and mean-based filtration methods to generate, evaluate, and refine candidate optimal solutions. By embedding uncertainty quantification into the optimization process, the framework systematically balances therapeutic efficacy against the risk of adverse effects, yielding risk-averse yet effective dose strategies. Numerical experiments using exponential dose–response models and the ED50 criterion demonstrate that convex hull-based methods consistently produce feasible solutions, while mean-based approaches are prone to infeasibility except in limited cases. Among hull methods, balance-oriented filtration (BOF) achieves the best balance between performance and conservativeness, closely approximating the benchmark solution under moderate levels of uncertainty for models with additive drug effects. These findings highlight the advantages of robust optimization for dose selection in settings where data are limited, variability is high, and risk management is essential.