ADM Prediction (Made Before Running Models)
Predicted winner: ML, but for interaction discovery, not prediction accuracy. Published literature quantifies main effects well. Known interactions (metabolic syndrome) will add modestly. GradientBoosting's real contribution is discovering novel interaction pairs and their magnitudes — things not in standard clinical models.
Expected: Modest R² gain from interactions; primary value is discovery. Actual: Published interactions add 5%. GBM adds 12% more. Empirical analysis reveals obesity×diabetes (+2 mg/L synergistic) and sedentary×diabetes (+1.8 mg/L) — magnitudes not in standard CRP models. Prediction confirmed.
Clinical guidelines say "manage BMI, control blood pressure, stay active." They treat these as independent knobs. But what if the metabolic effect of weight depends on glycemic status? What if exercise doesn't just lower risk additively, but modulates how other risk factors compound? Main-effects models capture each factor in isolation. Interaction models capture how they combine.
Tier 1: Additive
Linear regression on published risk factors (obesity, smoking, exercise, diabetes). No interaction terms. R² = 0.208.
Tier 2: + Published Interactions
Same features + published interaction terms (obesity×diabetes, obesity×sedentary, obesity×smoking). R² = 0.218.
Tier 3: GradientBoosting
Full feature set (16 features including continuous BMI, biomarkers) with automatic interaction discovery. R² = 0.245.
The Real Finding
Empirical analysis: obesity×diabetes adds +2.1 mg/L beyond additive. Sedentary×diabetes adds +1.8 mg/L. Magnitudes not in standard clinical models.
All three models predict log(CRP) and are evaluated with 5-fold cross-validation on the same data. This ensures fair comparison — no model sees its own training data during evaluation.
Tier 1 uses linear regression on 10 published risk factors (age, sex, 6 binary lifestyle flags). This is what a textbook epidemiological model would include. Tier 2 adds 6 published interaction terms (obesity×diabetes, obesity×sedentary, etc.) — interactions that any clinical researcher would include based on metabolic syndrome literature.
Tier 3 uses GradientBoosting (300 trees) on 16 features including continuous BMI, waist circumference, and blood biomarkers. Tree-based models naturally capture interactions because each split conditions on previous splits.
The interaction discovery is done two ways: (1) empirically, by comparing mean CRP in the four groups defined by each factor pair (A=0/1, B=0/1), and (2) via SHAP interaction values from the GBM model. The empirical method is more reliable because it doesn't depend on model assumptions.
All three models evaluated on log-transformed CRP with identical 5-fold cross-validation. Published main effects explain 20.8%. Adding published interaction terms gains 5%. GradientBoosting with richer features and automatic interaction discovery gains another 12%. The progression shows where value comes from: features and nonlinearity, not just interactions.
Each cell shows the interaction strength between two lifestyle factors, computed from the GBM model. Positive values (green) mean the factors amplify each other's CRP effect. Negative values (red) mean they counteract. These are model-based; see the empirical interactions below for data-driven confirmation.
Computed directly from group means, not model assumptions. For each factor pair, we compare actual CRP in four groups (neither, A only, B only, both). The interaction is the difference between the combined effect and the sum of individual effects. Obesity×diabetes is the strongest: obese diabetics have CRP 2.1 mg/L higher than the sum of obesity-alone and diabetes-alone effects.
Domain knowledge captures the strongest interaction (obesity×diabetes) plus two others. The remaining interactions — sedentary×diabetes, exercise×sedentary, smoking×diabetes — are not in standard CRP prediction models. Domain knowledge identifies the biggest interaction; ML discovers the rest.
Three-tier comparison is fair but not perfect: All three models evaluated on log(CRP) with 5-fold CV. However, Tier 3 uses 16 features (including continuous BMI and biomarkers) vs Tier 1-2's 10 binary features. Part of the GBM advantage comes from richer features, not just interaction discovery.
Log-transform: All R² values reported on log(CRP+0.1). Raw CRP R² is substantially lower for all models due to extreme right skew. Log-transform is standard practice but changes the prediction task.
Empirical interactions are observational: The group-mean analysis shows obesity×diabetes interact, but this is association, not causation. Obese diabetics may have additional unmeasured confounders (medication use, disease severity) that drive the synergistic CRP elevation.
Cross-sectional design: NHANES provides a single snapshot per person. Interaction effects may differ in longitudinal data where within-person changes can be tracked.
No external validation: Results are within-NHANES cross-validation only. Replication on an independent cohort would strengthen claims.
- Fair comparison: 0.208 → 0.218 → 0.245 — when all models are evaluated on the same metric (log CRP, 5-fold CV), the progression is honest. Published interactions add 5%. GBM adds 12% more. No 5x gaps.
- Obesity × diabetes is the strongest interaction (+2.1 mg/L) — obese diabetics have CRP 57% higher than the sum of individual effects. This is known conceptually (metabolic syndrome) but the magnitude isn't in standard CRP models.
- Sedentary × diabetes is novel (+1.8 mg/L) — this interaction is not in published CRP interaction models. Sedentary behavior amplifies diabetic inflammation by 61% beyond what either factor predicts alone.