Gallstone disease is a complex, multifactorial condition with significant global health burdens. Identifying underlying risk factors and their interactions is crucial for early diagnosis, targeted prevention, and effective clinical management. Although logistic regression remains a standard tool for assessing associations between predictors and gallstone status, it often underperforms in high-dimensional settings and may fail to capture intricate relationships among variables. To address these limitations, we propose a hybrid machine learning framework that integrates robust variable selection with advanced interaction detection. Specifically, Adaptive LASSO is employed to identify a sparse and interpretable subset of influential features, followed by Bayesian Additive Regression Trees (BART) to model nonlinear effects and uncover key interactions. Selected interactions are further characterized by physiological knowledge through differential equation-informed interaction terms, grounding the model in biologically plausible mechanisms. The insights gained from these steps are then integrated into a final logistic regression model within a Bayesian framework, providing a balance between predictive accuracy and clinical interpretability. This proposed framework not only enhances prediction but also yields actionable insights, offering a valuable support tool for medical research and decision-making.

翻译：胆结石疾病是一种复杂的多因素疾病，对全球健康构成重大负担。识别潜在风险因素及其相互作用对于早期诊断、针对性预防和有效临床管理至关重要。尽管逻辑回归仍是评估预测因子与胆结石状态之间关联的标准工具，但在高维环境中其表现往往不佳，且可能无法捕捉变量间的复杂关系。为应对这些局限性，我们提出了一种混合机器学习框架，将稳健的变量选择与先进的交互作用检测相结合。具体而言，我们采用自适应LASSO来识别具有影响力特征的稀疏且可解释子集，随后利用贝叶斯加性回归树（BART）建模非线性效应并揭示关键交互作用。所选交互作用通过微分方程驱动的交互项结合生理学知识进一步表征，使模型建立在生物学合理的机制之上。这些步骤获得的洞见随后被整合到贝叶斯框架下的最终逻辑回归模型中，在预测准确性与临床可解释性之间取得平衡。该框架不仅提升了预测性能，还提供了可操作的见解，为医学研究和决策制定提供了有价值的支持工具。