Shapley Regression for Rare Disease Diagnosis Support: a case study on APDS

TL;DR

This paper introduces Shapley regression, a transparent, game-theoretic model that improves rare disease diagnosis by capturing complex symptom interactions, validated on biomedical datasets and real-world APDS patient data.

Contribution

The paper presents a novel Shapley regression model that balances interpretability and predictive power for rare disease detection, addressing limitations of traditional scoring and deep learning methods.

Findings

2-additive model with l2 regularization balances accuracy and robustness

Shapley regression accurately distinguishes APDS cases from controls

Validated phenotypes and symptom interactions with clinical expert confirmation

Abstract

Activated PI3K8 Syndrome (APDS) is a rare genetic immune disorder caused by variants in PIK3CD or PIK3R1, with highly heterogeneous symptoms that often delay diagnosis. Early recognition is hampered by overlapping clinical presentations and limited clinician awareness, motivating systematic, data-driven approaches to detect APDS-associated phenotypic patterns in routine electronic health records. Traditional linear scoring systems cannot capture complex symptom interactions, while deep learning models, though expressive, often lack interpretability. To bridge this gap, we propose Shapley regression, a novel game-theoretic model replacing the linear predictor with a k-additive cooperative game, explicitly modeling co-occurrence of symptoms while maintaining the transparency and convexity of logistic regression. We carry out an empirical study of our lightweight method on eight public biomedical datasets, showing that a 2-additive model with $l_{2}$ regularization achieves an optimal trade-off between predictive power and noise robustness. We also apply it to a real-world cohort of 222 patients, on which Shapley regression accurately distinguished APDS cases from matched controls, confirming and validating phenotypes known to be associated with APDS, and facilitating the exploration of pairwise interactions between symptoms, validated by clinical experts.