The increasing use of machine learning in clinical decision support has been limited by the lack of transparency of many high-performing models. In clinical settings, predictions must be interpretable, auditable, and actionable. This study investigates Kolmogorov-Arnold Networks (KANs) as intrinsically interpretable alternatives to conventional black-box models for clinical classification of tabular health data, aiming to balance predictive performance with clinically meaningful transparency. We introduce two KAN-based models: the Logistic KAN, a flexible generalization of logistic regression, and the Kolmogorov-Arnold Additive Model (KAAM), an additive variant that yields transparent symbolic representations through feature-wise decomposability. Both models are evaluated on multiple public clinical datasets and compared with standard linear, tree-based, and neural baselines. Across all datasets, the proposed models achieve predictive performance comparable to or exceeding that of commonly used baselines while remaining fully interpretable. Logistic-KAN obtains the highest overall ranking across evaluation metrics, with a mean reciprocal rank of 0.76, indicating consistently strong performance across tasks. KAAM provides competitive accuracy while offering enhanced transparency through feature-wise decomposability, patient-level visualizations, and nearest-patient retrieval, enabling direct inspection of individual predictions. KAN-based models provide a practical and trustworthy alternative to black-box models for clinical classification, offering a strong balance between predictive performance and interpretability for clinical decision support. By enabling transparent, patient-level reasoning and clinically actionable insights, the proposed models represent a promising step toward trustworthy AI in healthcare (code: https://github.com/Patricia-A-Apellaniz/classification_with_kans).

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