ROAMM-EHR & SCMTF: EHR Phenotyping

• The paper introduces SCMTF, a supervised coupled matrix-tensor factorization method that integrates multi-modal EHR and PRO data for computational phenotyping in ulcerative colitis.
• The methodology jointly factorizes static demographics with temporal lab and PRO data while handling up to 90% missing entries via masked reconstruction and imputation.
• The approach achieved high predictive performance (AUC 0.853 at 8 months) and offered clinical interpretability by identifying distinct latent phenotypes.

ROAMM-EHR is not directly referenced or defined as a stand-alone term in the arXiv source, but its relevant context, methodologies, and technical workflows are exemplified by the Supervised Coupled Matrix-Tensor Factorization (SCMTF) approach for computational phenotyping of patient-reported outcomes (PROs) within electronic health record (EHR) systems, as applied to ulcerative colitis (UC) data (Minoccheri et al., 24 Jun 2025). The following sections detail the foundation, mathematical formalism, missing data handling, optimization, and the interpretability and significance of SCMTF-based approaches in EHR-driven clinical phenotyping.

1. Foundational Principles: Multi-Modal and Heterogeneous Data in EHR

SCMTF addresses computational phenotyping by distinguishing latent patient phenotypes through joint factorization of multi-modal, heterogeneous, and highly incomplete EHR-derived data. This paradigm incorporates both time-varying and static patient variables. Traditionally, patient-reported outcomes (PROs)—subjective, noisy, and overwhelmingly sparse—are routinely excluded from EHR-based machine learning pipelines due to their incomplete availability. SCMTF challenges this exclusion, leveraging deep low-rank matrix and tensor models to incorporate temporal PROs, laboratory measures, and baseline features for robust patient stratification and outcome prediction (Minoccheri et al., 24 Jun 2025).

2. Mathematical Architecture: Supervised Coupled Matrix-Tensor Factorization

The SCMTF model assumes availability of a third-order tensor $\mathcal{X} \in \mathbb{R}^{I\times J\times K}$, where $I$ is the patient index, $J$ the set of time-varying variables (labs and PROs), and $K$ discrete time windows—here, seven bins of four months each, contextualized to key clinical events (e.g., medication initiation). Additionally, static feature matrices $M\in\mathbb{R}^{I\times D}$ (demographics, medication history, etc.) and binary outcome labels $y\in\{0,1\}^I$ (e.g., medication persistence at a specific time horizon) are provided.

The factorization posits a rank-$R$ coupled CANDECOMP/PARAFAC (CP) decomposition:

$$\mathcal{X}\;\approx\;[\![\,\mathbf{A},\mathbf{B},\mathbf{C}\,]\!] + \mathbf{B}_{\text{feat}} + \mathbf{B}_{\text{pat}},$$

where:

• $\mathbf{A} \in \mathbb{R}^{I\times R}$: patient–phenotype membership matrix
• $\mathbf{B} \in \mathbb{R}^{J\times R}$: variable–phenotype matrix (temporal features)
• $I$0: time–pattern matrix
• $I$1: feature bias (offsets per feature)
• $I$2: patient bias (offsets per patient)

The static matrix $I$3 is coupled via the patient mode:

$I$4

A neural classifier $I$5 with parameters $I$6 links $I$7 to clinical outcome via cross-entropy loss:

$I$8

where $I$9.

The total loss incorporates tensor and matrix reconstruction, $J$0 sparsity, bias regularization, and the supervised loss, subject to nonnegativity constraints on all factor matrices.

3. Missing Data: Masking and Imputation

EHR and PRO data are typically characterized by severe missingness (up to 90%), particularly in longitudinal symptom reporting. SCMTF introduces binary masks $J$1 and $J$2 to indicate observed entries in $J$3 and $J$4 respectively. Reconstruction losses are masked via Hadamard product, ensuring that only observed entries contribute to the objective:

$J$5

After optimization, missing entries in both $J$6 and $J$7 are naturally imputed using the learned low-rank and bias structure.

4. Optimization Strategies and Hyperparameters

Training proceeds as joint all-at-once gradient-based optimization implemented in PyTorch, leveraging TensorLy-Torch for tensor operations. All factors $J$8, biases $J$9, and classifier parameters $K$0 are updated simultaneously.

Key characteristics:

• Nonnegativity enforced by clamping factors after each step.
• Factor variables updated via Adam ($K$1); classifier via SGD ($K$2, momentum = 0.9)
• Learning rates decayed by $K$3 every $K$4 steps
• $K$5 sparsity handled by proximal-gradient/soft-thresholding
• Hyperparameters ($K$6, $K$7, $K$8, $K$9) selected through grid search on a held-out validation set, targeting AUC and imputation error

In the referenced work, the optimal configuration was $M\in\mathbb{R}^{I\times D}$0, $M\in\mathbb{R}^{I\times D}$1, and $M\in\mathbb{R}^{I\times D}$2 (Minoccheri et al., 24 Jun 2025).

5. Application: Ulcerative Colitis Computational Phenotyping

For UC, the SCMTF workflow was instantiated as follows:

• $M\in\mathbb{R}^{I\times D}$3 comprising 24 laboratory variables and 34 PRO items, binned into seven 4-month intervals centered on medication start.
• $M\in\mathbb{R}^{I\times D}$4 reflecting static demographics (age, sex, BMI), disease/therapy history, and baseline endoscopic scores.
• Labels $M\in\mathbb{R}^{I\times D}$5 marking medication persistence at 8 and 20 months.

Post-training, each rank component $M\in\mathbb{R}^{I\times D}$6 defines a distinct phenotype with interpretation derived from:

• $M\in\mathbb{R}^{I\times D}$7: per-patient phenotype strengths
• $M\in\mathbb{R}^{I\times D}$8: variable/PRO contributions
• $M\in\mathbb{R}^{I\times D}$9: temporal evolution
• $y\in\{0,1\}^I$0: static feature influences

Features with maximal loadings (e.g., arthritis pain, CRP, prior biologic use) and their corresponding time profiles informed clinical interpretations such as “chronic inflammation” or “episodic systemic symptoms.”

6. Predictive and Clinical Significance

The learned patient phenotypes, summarized by $y\in\{0,1\}^I$1, served as covariates for medication persistence prediction with high accuracy:

• Random Forest on $y\in\{0,1\}^I$2 yielded test AUC = 0.853 (8-month) and AUC = 0.803 (20-month)
• A subset of three dominant phenotypes preserved AUC > 0.80
• Imputation accuracy for missing tensor values was MAE $y\in\{0,1\}^I$3 0.145, RMSE $y\in\{0,1\}^I$4 0.197

Approximately 76% of tensor entries were missing (88% in PROs). The discovery of phenotypes featuring PROs indicates these data types, typically discarded for sparsity and subjectivity, contain clinically actionable information for outcome modeling in UC (Minoccheri et al., 24 Jun 2025).

7. Context and Implications

SCMTF represents the first tensor-based, supervised, and coupled factorization applied to the UC domain and to highly missing PRO data. It offers a unified, interpretable modeling framework capable of:

• Jointly factorizing static and temporal, multi-modal clinical data
• Absorbing patient and feature bias
• Integrating clinical supervision directly in the factorization
• Handling massive missingness via masked loss
• Yielding interpretable latent phenotypes with demonstrable predictive utility

A plausible implication is the extension of similar SCMTF-based factorizations to broader EHR phenotyping tasks and other highly missing clinical data domains, where integration of multiple data types and interpretability are crucial for precision medicine (Minoccheri et al., 24 Jun 2025).