This paper was motivated by the challenge of early AD diagnosis, particularly in scenarios when clinicians encounter varied availability of patient imaging data, such as MRI and PET scans, often constrained by cost or accessibility issues. We propose an incomplete multimodal learning framework that produces tailored models for patients with only MRI and patients with both MRI and PET. This approach improves the accuracy and effectiveness of early AD diagnosis, especially when imaging resources are limited, via bi-directional knowledge transfer. We introduced a teacher model that prioritizes extracting common information between different modalities, significantly enhancing the student model's learning process. This paper includes theoretical analysis, simulation study, and realworld case study to illustrate the method's promising potential in early AD detection. However, practitioners should be mindful of the complexities involved in model tuning. Future work will focus on improving model interpretability and expanding its application. This includes developing methods to discover the key brain regions for predictions, enhancing clinical trust, and extending the framework to incorporate a broader range of imaging modalities, demographic information, and clinical data. These advancements aim to provide a more comprehensive view of patient health and improve diagnostic accuracy across various neurodegenerative diseases.
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