Health Informatics Journal2026

Interpretable heart disease risk prediction via FCA-constrained logistic regression

A. Heydarian, H. R. Goudarzi, Z. F. Rad, A. Salehi

Interpretable MLFCALogistic RegressionHealthcare

A heart-disease risk score that a clinician won't trust is worse than useless — it gets ignored. That's the quiet failure mode behind a decade of medical machine learning: the most accurate models are ensembles whose reasoning no one can inspect, while the models doctors can read are often the least accurate. This paper asks whether that trade-off is really necessary, or just a habit.

Accuracy you can't explain

On the BRFSS-2015 survey — roughly 380,000 patients across 22 indicators — black-box ensembles comfortably clear an AUC of 0.84. But they can't tell a clinician why a patient is high-risk, and the dataset is badly imbalanced, so headline accuracy hides how rarely the positive cases are actually caught. Plain logistic regression is transparent, yet it treats each risk factor in isolation and misses the way they travel together.

Letting the data's structure speak

The key move is to let Formal Concept Analysis discover which clinical attributes co-occur, then force the model to respect those groupings. FCA builds a lattice of formal concepts — closed sets of attributes shared by real patients. Hover the lattice to see the concepts the method actually found:

Hover a node

Each filled node is a closed set of attributes that co-occur in real patients — for example metabolic syndrome in older adults. FCA finds these concepts automatically; the model then keeps the coefficients inside each one consistent.

These concepts aren't decoration — they become constraints. The training objective adds a closure penalty that keeps the coefficients of features inside one concept consistent with each other:

\omega^{*} = \operatorname*{arg\,min}_{\omega}\; \underbrace{\mathcal{L}(\omega)}_{\text{cross-entropy}}\; +\; \lambda\,\underbrace{\sum_{k} w_k\,\operatorname{Var}\!\bigl(\{\,\omega_j : j \in C_k\,\}\bigr)}_{R(\omega;\,C)\ \text{closure penalty}}

The penalty $R(\omega;C)$ shrinks the variance of coefficients within each concept $C_k$ . Slide $\lambda$ up and watch correlated risk factors stop fighting each other:

Coefficients in the “metabolic” conceptwithin-concept variance: 0.0103

HighBP

0.42

HighChol

0.31

Diabetes

0.58

Age ≥ 65

0.36

λ = 0.00

Slide λ up: the penalty pulls coefficients of co-occurring features toward a common value (the marker), so the model's reasoning stays coherent within each clinical concept instead of fragmenting across correlated indicators.

The model stays a single, readable logistic regression — every prediction still traces back to interpretable coefficients — but its reasoning is now organised around clinically coherent concepts rather than scattered across correlated columns.

The payoff: interpretable and accurate

Against L2 logistic regression, random forest and gradient boosting on the held-out ~76k test patients, the FCA model lands where you actually want to be:

Hover a model. FCA reaches the highest F1 while staying glass-box interpretable.

It posts the best F1 of any model, driven by far higher precision — crucial when a false positive sends a patient down an unnecessary diagnostic path:

0.1

0.2

0.3

0.4

0.5

FCA (ours)Random ForestLogistic Reg.Gradient Boost

0.906Accuracy

0.709Precisionhighest of all models

0.078Brier scorewell-calibrated

And because the coefficients are readable, the model tells you what drives risk — its largest contributors line up with clinical intuition:

0.1

0.2

0.3

0.4

StrokeGenHlthHvyAlcoholConsumpNoDocBcCost

Why it matters

Interpretability isn't a nicety in healthcare — it's a precondition for deployment. By baking the concept structure into the learning objective rather than explaining a black box after the fact, the method delivers auditable risk predictions a clinician can reason about, at accuracy that beats the opaque baselines. The honest caveats remain: binary feature encoding loses some signal, BRFSS is self-reported, and prospective external validation is the next step before any clinical use.

Cite this work

bibtex
@article{heydarian2026interpretable,
  title = {Interpretable heart disease risk prediction via FCA-constrained logistic regression},
  author = {A. Heydarian and H. R. Goudarzi and Z. F. Rad and A. Salehi},
  journal = {Health Informatics Journal},
  year = {2026},
  doi = {10.1177/14604582261444612}
}

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