Simultaneous Modeling of Disease Screening and Severity Prediction: A Multi-task and Sparse Regularization Approach

Identifying clinically relevant biomarkers and developing predictive models are central challenges in biomedical research. Biomarkers are commonly used for disease screening, and some provide information not only on the presence or absence of a disease but also on its severity. Such biomarkers can contribute to treatment prioritization and support clinical decision-making. To address both disease screening and severity prediction, this paper focuses on regression modeling for ordinal outcomes with a hierarchical structure. When the response variable is a combination of the presence of disease and severity, such as {healthy, mild, intermediate, severe}, a straightforward approach is to apply the conventional ordinal regression model. However, such models may lack the flexibility needed to capture heterogeneity in how predictors relate to response levels, particularly when the response levels have a heterogeneous association structure with predictors. Therefore, this paper proposes a model that treats screening and severity prediction as separate tasks, along with an estimation method based on structural sparse regularization. This method is designed to leverage a shared structure between the tasks. In numerical experiments, the proposed method demonstrated stable performance across many scenarios compared to existing ordinal regression methods.