Bottom line
Adding Sex and Delta days improves classification accuracy from the 73.0% baseline. The cleanest pattern: Delta days carries the most information of the two new variables, while Sex shifts the cutoff only slightly.
Approach A — Sex-stratified cutoffs (one cutoff per sex)
| Sex | n | # Positive | Cutoff (Result ≤) | Sens | Spec | AUC |
|---|---|---|---|---|---|---|
| Female | 60 | 31 | 5.326 | 90.3% | 55.2% | 0.758 |
| Male | 40 | 9 | 4.738 | 88.9% | 80.6% | 0.878 |
Combined performance using sex-specific cutoffs: accuracy 77.0%, sensitivity 90.0%, specificity 68.3%.
Approach B — Delta-days–stratified cutoffs (two cutoffs by time window)
We searched all candidate split points on Delta days that leave at least 10 subjects per side. The best split was Delta days = 0, giving:
- ΔDays < 0 (n=38, 2 positive): cutoff Result ≤ 2.967
- ΔDays ≥ 0 (n=62, 38 positive): cutoff Result ≤ 5.326
Performance: accuracy 83.0%, sensitivity 92.5%, specificity 76.7%.
Approach C — Grey-zone (two cutoffs on Result alone)
Targets: ≥ 95% specificity for the rule-in (positive) zone, ≥ 95% sensitivity for the rule-out (negative) zone.
- Rule-in zone (POSITIVE): Result ≤ 3.513
- Rule-out zone (NEGATIVE): Result ≥ 5.829
- Indeterminate band: 3.513 < Result < 5.829 (56 subjects, 56.0%)
On the 44 classified subjects: accuracy 86.4%, sensitivity 81.2%, specificity 89.3%, F1 0.812.
Caveat: the indeterminate band is large because the distributions overlap. A grey-zone rule is best used as a triage: confidently classify the easy cases, send the indeterminate band for confirmatory testing.
Approach D — Logistic regression (Result + Sex + Delta days)
| Feature | Coefficient |
|---|---|
| (Intercept) | +1.9673 |
| Result | -0.7711 |
| Sex_Female | +0.6103 |
| DeltaDays | +0.0471 |
The decision boundary in score space corresponds to logit = -0.186 (probability cutoff = 0.454). Held-out (5-fold CV) AUC = 0.934; CV accuracy at the CV-tuned threshold = 89.0% (sens 80.0%, spec 95.0%).
Approach E — Decision tree depth=3 (interpretable multi-cutoff rule)
|--- DeltaDays <= 24.00 | |--- DeltaDays <= -1.50 | | |--- class: 0 | |--- DeltaDays > -1.50 | | |--- Result <= 5.43 | | | |--- class: 1 | | |--- Result > 5.43 | | | |--- class: 0 |--- DeltaDays > 24.00 | |--- Result <= 4.07 | | |--- Result <= 3.70 | | | |--- class: 1 | | |--- Result > 3.70 | | | |--- class: 1 | |--- Result > 4.07 | | |--- class: 1
Held-out (5-fold CV) AUC = 0.926; CV accuracy = 85.0%.
Side-by-side comparison
| Approach | Accuracy | Sens | Spec | F1 | AUC | Note |
|---|---|---|---|---|---|---|
| Single global cutoff (Result ≤ 5.326) | 73.0% | 92.5% | 60.0% | 0.733 | 0.803 | iteration 1 baseline |
| Sex-stratified cutoffs (F: 5.326, M: 4.738) | 77.0% | 90.0% | 68.3% | 0.758 | — | in-sample |
| Delta-days split @ 0 (lo: 2.967, hi: 5.326) | 83.0% | 92.5% | 76.7% | 0.813 | — | in-sample |
| Logistic regression (Result+Sex+ΔDays) train | 89.0% | 80.0% | 95.0% | 0.853 | 0.938 | in-sample |
| Logistic regression (Result+Sex+ΔDays) 5-fold CV | 89.0% | 80.0% | 95.0% | 0.853 | 0.934 | honest out-of-fold |
| Decision tree depth=3 train | 88.0% | 97.5% | 81.7% | 0.867 | — | in-sample |
| Decision tree depth=3 5-fold CV | 85.0% | 87.5% | 83.3% | 0.824 | 0.926 | honest out-of-fold |
Recommendation
- If you want one simple rule: the Delta-days–stratified cutoff is interpretable, doesn't require a model at runtime, and delivers 83.0% accuracy — 10.0% points above the iteration-1 baseline.
- If you want maximum accuracy and have a way to compute a small score: the logistic regression on Result + Sex + DeltaDays gives CV AUC 0.934 and CV accuracy 89.0% — fairer estimate than the in-sample numbers and likely the most robust.
- If you want a triage strategy: the grey-zone rule confidently classifies 44.0% of subjects with high accuracy and flags the rest for follow-up.
- Sex alone is a weaker stratifier than ΔDays in this cohort. The two sex-specific cutoffs are close to one another, which suggests sex is mostly nuisance variation rather than a strong effect modifier.
All in-sample numbers (sex-stratified, delta-split, tree-train) are optimistic. The CV AUC of the logistic regression (0.934) is the most honest single-number summary of "what would this rule do on a fresh patient?"