MMAD-Risk: Multivariate Mixed Survival Analysis for the Prediction of Age-Dependent Disease Risks from Plasma Proteomes

Abstract

Motivation Multivariate survival analysis with hundreds of correlated outcomes is computationally challenging. Established approaches either ignore correlations between response variables, rely on black-box deep learning or are limited to small-scale outcomes. Results We introduce MMAD-Risk, a novel multivariate mixed accelerated failure time (AFT) model that enables scalable analysis of high-dimensional survival analysis data. We train MMAD-Risk using amortized variational inference where we design the variational distribution such that it factorizes across diseases, allowing us to decompose multivariate disease risk prediction into a series of tractable, one-dimensional problems. This allows us to calculate the ELBO analytically, enabling fast computation. The model employs a low-rank decomposition of the effect size matrix B = VW⊤ to capture shared disease mechanisms and latent random effects Vzn to model comorbidity. MMAD-Risk is trained on the UK Biobank Pharma Proteomics cohort (N ≈ 55000, P ≈ 3000 proteins, D = 271 diseases). Using the full 3,000-protein dataset, MMAD-Risk achieved a mean concordance index (c-index) of 0.744 for diagnoses occurring ⩾ 10 years after blood sample collection, outperforming a Cox proportional hazards model (mean c-index = 0.709). Greedy backward selection identified a 10-protein panel that preserved > 99% of the full-model performance. On this reduced panel MMAD-Risk still outperformed Cox regression (0.738 vs. 0.679). Availability and implementation https://github.com/soedinglab/MMAD-Risk.git Contact soeding@mpinat.mpg.de Supplementary information Supplementary data are available at Bioinformatics online.