Diabetes Risk Prediction under Severe Class Imbalance: Comparing Firth Logistic Regression and SMOTEN-Based Logistic Regression

Diabetes mellitus is a major noncommunicable disease, and reliable early-detection prediction can support Sustainable Development Goal (SDG) Target 3.4. This study compares standard logistic regression, Firth's Penalized Logistic Regression, and SMOTEN-based logistic regression for diabetes risk prediction under severe class imbalance using Wave 5 of the Indonesia Family Life Survey (IFLS5). The analysis included 115 respondents, comprising 8 diabetes cases (6.96%), with all predictors represented as categorical variables. Model performance was evaluated using 50 repeated stratified 75/25 train-test splits, with SMOTEN applied only to training data to prevent leakage. Standard logistic regression failed to converge across all partitions. Firth's Penalized Logistic Regression identified waist circumference as significantly associated with diabetes status (odds ratio = 10.69, 95% CI: 1.5673.14) and achieved mean accuracy of 89.17%, sensitivity of 8.00%, specificity of 95.19%, and AUC of 0.692. SMOTEN-based logistic regression achieved accuracy of 86.90%, sensitivity of 12.00%, specificity of 92.44%, and AUC of 0.632. Brier scores were 0.089 and 0.098, respectively, compared with 0.064 for the prevalence benchmark, indicating poorer overall probabilistic prediction performance. These findings illustrate the challenges of rare-event prediction under severe class imbalance and highlight the need for larger samples and further validation before clinical application.