The inherent multimodality and heterogeneous temporal structures of medical data pose significant challenges for modeling. We propose MedM2T, a time-aware multimodal framework designed to address these complexities. MedM2T integrates: (i) Sparse Time Series Encoder to flexibly handle irregular and sparse time series, (ii) Hierarchical Time-Aware Fusion to capture both micro- and macro-temporal patterns from multiple dense time series, such as ECGs, and (iii) Bi-Modal Attention to extract cross-modal interactions, which can be extended to any number of modalities. To mitigate granularity gaps between modalities, MedM2T uses modality-specific pre-trained encoders and aligns resulting features within a shared encoder. We evaluated MedM2T on MIMIC-IV and MIMIC-IV-ECG datasets for three tasks that encompass chronic and acute disease dynamics: 90-day cardiovascular disease (CVD) prediction, in-hospital mortality prediction, and ICU length-of-stay (LOS) regression. MedM2T outperformed state-of-the-art multimodal learning frameworks and existing time series models, achieving an AUROC of 0.947 and an AUPRC of 0.706 for CVD prediction; an AUROC of 0.901 and an AUPRC of 0.558 for mortality prediction; and Mean Absolute Error (MAE) of 2.31 for LOS regression. These results highlight the robustness and broad applicability of MedM2T, positioning it as a promising tool in clinical prediction. We provide the implementation of MedM2T at https://github.com/DHLab-TSENG/MedM2T.

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