Diagnostic Test / Biomarker Accuracy Evaluation

Judge how well a test or biomarker discriminates disease — at a fixed cutoff (2×2) or across all cutoffs (ROC) — and turn a result into a probability of disease.

Which case are you in?

| You have… | Go to | |---|---| | A 2×2 table (TP/FP/TN/FN) at a fixed cutoff | Step 1 (Epidemiology_diagnostic) | | A continuous biomarker score + true labels | Step 2 (ROC / AUC / Youden, Python) | | A test's sens/spec + a patient's pre-test probability | Step 3 (Epidemiology_bayesian) |

Step 1 — Fixed-cutoff metrics from a 2×2 table

bash
tu run Epidemiology_diagnostic '{"operation":"diagnostic","tp":90,"fp":10,"tn":180,"fn":20}'

Returns sensitivity, specificity, PPV, NPV, accuracy, LR_pos, LR_neg, and the sample prevalence.

| Metric | Question it answers | Depends on prevalence? | |---|---|---| | Sensitivity = TP/(TP+FN) | Of those WITH disease, what fraction test positive? | No | | Specificity = TN/(TN+FP) | Of those WITHOUT disease, what fraction test negative? | No | | PPV = TP/(TP+FP) | If positive, what's the chance of disease? | Yes — strongly | | NPV = TN/(TN+FN) | If negative, what's the chance of being disease-free? | Yes | | LR+ = sens/(1−spec) | How much a positive raises the odds of disease | No | | LR− = (1−sens)/spec | How much a negative lowers the odds | No |

> The PPV/NPV trap. Sensitivity and specificity are properties of the test; PPV and NPV depend on the disease prevalence in the tested population. A test with great sens/spec has poor PPV in a low-prevalence (screening) setting. Never quote PPV/NPV from a case-control design (its 50/50 prevalence is artificial) — compute them for the real-world prevalence with Epidemiology_bayesian (Step 3). Report sensitivity, specificity, and likelihood ratios as the prevalence-independent summary.

Step 2 — ROC / AUC / optimal cutoff for a continuous biomarker

When the test is a continuous score, evaluate across all thresholds:

Prefer the ROC_analysis tool — one call returns structured JSON (AUC + bootstrap 95% CI, Youden-optimal cutoff with its sens/spec, optional metrics at a fixed cutoff, and the ROC curve), and works under the MCP server without a shell:

ROC_analysis(scores=[...], labels=[0,1,...])          # inline arrays
ROC_analysis(csv_path="scores.csv", cutoff=0.6)        # or a CSV (cols: label, score)

The bundled script is the equivalent CLI form:

bash
python skills/tooluniverse-diagnostic-test-evaluation/scripts/roc_analysis.py --input scores.csv
# scores.csv columns: label (1=disease, 0=healthy), score (continuous biomarker)

Both report AUC (with a bootstrap 95% CI), the Youden-optimal cutoff (max sensitivity+specificity−1) and its sens/spec.

| AUC | Discrimination | |---|---| | 0.5 | no better than chance | | 0.7–0.8 | acceptable | | 0.8–0.9 | excellent | | >0.9 | outstanding |

• The Youden cutoff weights sensitivity and specificity equally; if false negatives and false positives have different costs, pick the threshold from the clinical tradeoff, not Youden.
• Once you choose a cutoff, build its 2×2 and run Step 1 for the fixed-cutoff metrics at that operating point.

Step 3 — Post-test probability (Bayes)

Turn a result into the probability of disease for a given pre-test probability/prevalence:

bash
tu run Epidemiology_bayesian '{"operation":"bayesian","prevalence":0.10,
  "sensitivity":0.90,"specificity":0.95,"test_result":"positive"}'

Returns pre_test_odds, the LR, and post_test_probability. This is how you get the real-world PPV: plug the true prevalence in. (Example: a 90%/95% test at 10% prevalence gives a post-positive probability of only ~67%, not 95%.)

Gotchas (state these)

• PPV/NPV without a stated prevalence are meaningless — always give the prevalence they assume.
• AUC ignores the operating point. A high AUC doesn't tell you the test is useful at the threshold you'll actually use — report sens/spec at the chosen cutoff too.
• Class imbalance. With very few positives, ROC/AUC can look good while PPV is poor; consider a precision-recall curve and always report PPV at the real prevalence.
• Spectrum bias. Sens/spec measured on clearly-sick vs clearly-healthy subjects overestimate real-world performance on borderline cases.
• Single cutoff chosen on the same data it's evaluated on is optimistic — validate the threshold on a held-out set.

Honest limitations

• These are discrimination/accuracy metrics, not calibration — a well-discriminating model can still output poorly-calibrated probabilities.
• A single AUC compares nothing; to compare two tests on the same patients, use a paired AUC test (DeLong) — beyond the basic script here.

Related skills

• tooluniverse-statistical-modeling — logistic regression that produces the score, ORs.
• tooluniverse-epidemiological-analysis — population-level risk, screening program metrics.
• tooluniverse-meta-analysis — pool diagnostic accuracy across studies.