MOSIC: Model-Agnostic Optimal Subgroup Identification with Multi-Constraint for Improved Reliability

Identifying subgroups that benefit from specific treatments using observational data is a critical challenge in personalized medicine. Most existing approaches solely focus on identifying a subgroup with an improved treatment effect. However, practical considerations, such as ensuring a minimum subgroup size for representativeness or achieving sufficient confounder balance for reliability, are also important for making findings clinically meaningful and actionable. While some studies address these constraints individually, none offer a unified approach to handle them simultaneously. To bridge this gap, we propose a model-agnostic framework for optimal subgroup identification under multiple constraints. We reformulate this combinatorial problem as an unconstrained min-max optimization problem with novel modifications and solve it by a gradient descent ascent algorithm. We further prove its convergence to a feasible and locally optimal solution. Our method is stable and highly flexible, supporting various models and techniques for estimating and optimizing treatment effectiveness with observational data. Extensive experiments on both synthetic and real-world datasets demonstrate its effectiveness in identifying subgroups that satisfy multiple constraints, achieving higher treatment effects and better confounder balancing results across different group sizes.