Biomedical language models (LMs) encode textual semantics but do not explicitly preserve medical code hierarchies. We present Hyperbolic Clinical Ontology Embeddings (HCOE) for hierarchy-aware clinical concept representation. HCOE maps frozen BioBERT embeddings into a Poincare ball, combining parent-side and child-side ontology-guided contrastive learning with coarse-to-fine ontology-path aggregation. It uses International Classification of Diseases (ICD) codes organized by Clinical Classifications Software (CCS) and Anatomical Therapeutic Chemical (ATC) medication hierarchies. Evaluations show that HCOE performs best on ICD/ATC clinical relation prediction and CCS-to-PheCode hierarchy transfer. On the MIMIC-IV dataset, HCOE also achieves the best performance on mortality prediction, readmission prediction, medication recommendation, and rare drug prediction.

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