Tree-Guided Rare Feature Selection and Logic Aggregation with Electronic Health Records Data
Jianmin Chen, Robert H. Aseltine, Fei Wang, Kun Chen
TL;DR
The paper tackles modeling with huge, sparse binary features in electronic health records by exploiting the hierarchical ICD code structure. It introduces TSLA, a convex, tree-guided framework that performs or-based feature aggregation via three steps: feature expansion to include meaningful interactions, a tree-based reparameterization that expresses aggregations through a γ-parameter on tree nodes, and a Child-$\ell_2$ regularization that enforces equi-sparsity along the tree. A smoothing proximal gradient algorithm solves the resulting optimization, backed by non-asymptotic theoretical guarantees under a $k$-ary tree, and the approach is validated through extensive simulations in both regression and classification, as well as a suicide-risk study using real KHIN EHR data. The results show TSLA improves prediction and yields interpretable aggregation patterns of ICD codes, revealing which higher-level categories and subcategories drive risk, and how much specificity is warranted for each category. The framework is general and scalable, with potential extensions to survival analysis, longitudinal EHR data, and more general logic operations on sparse binary features.
Abstract
Statistical learning with a large number of rare binary features is commonly encountered in analyzing electronic health records (EHR) data, especially in the modeling of disease onset with prior medical diagnoses and procedures. Dealing with the resulting highly sparse and large-scale binary feature matrix is notoriously challenging as conventional methods may suffer from a lack of power in testing and inconsistency in model fitting while machine learning methods may suffer from the inability of producing interpretable results or clinically-meaningful risk factors. To improve EHR-based modeling and utilize the natural hierarchical structure of disease classification, we propose a tree-guided feature selection and logic aggregation approach for large-scale regression with rare binary features, in which dimension reduction is achieved through not only a sparsity pursuit but also an aggregation promoter with the logic operator of ``or''. We convert the combinatorial problem into a convex linearly-constrained regularized estimation, which enables scalable computation with theoretical guarantees. In a suicide risk study with EHR data, our approach is able to select and aggregate prior mental health diagnoses as guided by the diagnosis hierarchy of the International Classification of Diseases. By balancing the rarity and specificity of the EHR diagnosis records, our strategy improves both prediction and model interpretation. We identify important higher-level categories and subcategories of mental health conditions and simultaneously determine the level of specificity needed for each of them in predicting suicide risk.