Alzaid, E. | Search bioRxiv

bioRxiv2026

Discovering Prognostic Risk Strata and Heterogeneous Progression Routes from Cross-Sectional Survival Data

Inferring how individual patients progress towards higher disease risk typically requires longitudinal observations, which are often unavailable. Population-level analyses of cross-sectional data can identify differences between risk groups but may obscure heterogeneous progression patterns across individual patients. In this work, we introduce GOTSurv, a framework for patient-specific progression modelling. Using cross-sectional survival data, it first learns to rank patients by survival risk and automatically stratify them into prognostic risk groups without requiring predefined risk cut-offs. It then uses unbalanced optimal transport to infer patient-specific changes in the magnitude and direction of features associated with transitions towards higher-risk strata. We evaluated GOTSurv across ten TCGA cancer cohorts using two modalities: gene expression (n=4,767) and whole-slide image representations (n=4,655), with external validation in two independent cohorts. Compared with established survival models, GOTSurv generally achieved stronger prognostic stratification without requiring predefined risk cut-offs, while retaining competitive survival-ranking accuracy. More importantly, GOTSurv enabled the discovery of individualised progression trajectories associated with increasing risk, revealing distinct progression patterns even among patients within the same risk stratum. Overall, GOTSurv provides a novel framework for inferring heterogeneous, patient-specific progression patterns from cross-sectional survival data, enabling the identification of distinct pathways associated with increasing disease risk and informing the development of personalised therapeutic strategies. The code for GOTSurv is available at https://github.com/EtharZaid/GOTSurv/.

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bioRxiv2026

GOTFlow: Learning Directed Population Transitions from Cross-Sectional Biomedical Data with Optimal Transport

MotivationMany biological and clinical processes are dynamic, yet most datasets are cross-sectional, capturing populations at discrete states rather than tracking individuals over time. This makes it difficult to quantify how populations change across developmental, physiological, or disease-associated conditions. Existing trajectory and transport-based methods often rely on fixed feature spaces, assumptions tailored to transcriptomic time-course data, or approximately linear progression, limiting their ability to model heterogeneous and unbalanced transitions across diverse biomedical modalities. Flexible methods are needed that can infer directed population-level change from cross-sectional data while retaining biological interpretability. ResultsWe present GOTFlow, a framework for learning directed population transitions from cross-sectional biomedical data using graph-constrained optimal transport in a learned latent space. GOTFlow integrates representation learning with unbalanced optimal transport to jointly estimate embeddings and transport couplings between biological states. This enables hypothesis-driven modelling of progression structures while accommodating non-linear geometry, branching relationships, and changes in population mass. From the inferred transport plans, GOTFlow derives interpretable summaries of dynamics, including drift vectors quantifying transitions, and feature-level transported changes that highlight molecular drivers of progression. In synthetic data, GOTFlow recovered known transitions with strong agreement between inferred and ground-truth drifts. Across three biological applications, endometrial remodelling, breast cancer risk progression, and prion disease, GOTFlow identified state-to-state transitions and biologically meaningful feature shifts reflecting impaired decidualisation, increasing cancer risk, and neurodegenerative progression. These results establish GOTFlow as a general and interpretable framework for analysing directed population dynamics from cross-sectional data. AvailabilityCode available at: https://github.com/wgrgwrght/GOTFlow

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