Non‐Linear Dose–Response Relationship for Metformin in Japanese Patients With Type 2 Diabetes: Analysis of Irregular Longitudinal Data by Interpretable Machine Learning Models

The dose-response relationship between metformin and change in hemoglobin A1c (HbA1c) shows a maximum at 1500-2000 mg/day in patients with type 2 diabetes (T2D) in the U.S. In Japan, there is little evidence on the HbA1c-lowering effect of high-dose metformin because the maintenance and maximum doses of metformin were raised in 2010. The aim of this study was to investigate whether there is saturation of the dose-response relationship for metformin in Japanese T2D patients. Longitudinal clinical information of T2D patients was extracted from electronic medical records. Supervised machine learning models with random effect were constructed to predict change in HbA1c: generalized linear mixed-effects models (GLMM) with/without a feature selection and combining tree-boosting with Gaussian process and mixed-effects models (GPBoost). GPBoost was interpreted by SHapley Additive exPlanations (SHAP) and partial dependence. GPBoost had better predictive performance than GLMM with/without feature selection: root mean square error was 0.602 (95%CI 0.523-0.684), 0.698 (0.629-0.774) and 0.678 (0.609-0.753), respectively. Interpretation of GPBoost by SHAP and partial dependence suggested that the relationship between the daily dose of metformin and change in HbA1c is non-linear rather than linear, and the HbA1c-lowering effect of metformin reaches a maximum at 1500 mg/day. Interpretation of GPBoost, a non-linear supervised machine-learning algorithm, suggests that there is saturation of the dose-response relationship of metformin in Japanese patients with T2D. This finding may be useful for decision-making in pharmacotherapy for T2D.