A Generative Cross-Modal Imputation Framework Using Variational Autoencoders for Breast Cancer Prognosis under Incomplete Multimodal Data

Abstract

Accurate prognosis of breast cancer supports decisions about adjuvant therapy, surveillance intensity, and patient counselling. Prognostic information is distributed across several data sources, including clinical attributes, messenger RNA (mRNA) expression, and copy number alteration (CNA) profiles, and combining these sources through multimodal deep learning can improve predictive performance. In practice, however, multimodal datasets are rarely complete. Genomic profiling may not be performed for every patient, samples may fail quality control, and records collected across institutions frequently differ in the data they contain. Conventional solutions either discard incomplete patients or apply simple imputation methods that ignore the relationships between modalities. This paper proposes "A Generative Cross-Modal Imputation Framework Using Variational Autoencoders for Breast Cancer Prognosis under Incomplete Multimodal Data". The framework trains a separate variational encoder for each modality and combines the observed modalities in a shared latent space using a product-of-experts formulation. Because the joint latent representation can be inferred from any subset of observed modalities, it can be decoded to reconstruct the missing modalities, providing biologically informed imputation instead of placeholder values. The completed latent representation is then used by a prognosis classifier to predict five-year survival status and recurrence risk, while Monte Carlo dropout is used to estimate prediction uncertainty, which is expected to increase when more modalities are missing. The framework can be evaluated using accuracy, precision, recall, F1-score, area under the receiver operating characteristic curve, calibration error, and imputation reconstruction error under controlled missing-data rates. The proposed approach aims to make full use of incomplete breast cancer cohorts, although its outputs require independent clinical validation before use in medical practice.