Is partial AUC always between zero and one?

The scale depends on the definition; raw area over 0 to alpha is at most alpha.

Does it select the best threshold?

No; threshold selection is a separate decision.

Can two models reverse ranking compared with full AUC?

Yes, because they can perform differently in the restricted region.

AI Glossary / Statistics and probability / Intermediate

Partial Area Under the ROC Curve

Definition

Partial area under the ROC curve, or partial AUC, summarizes a classifier's ranking performance over a specified portion of the receiver operating characteristic curve. A common version integrates true-positive rate over a restricted false-positive-rate interval, such as 0 to 0.10, rather than averaging across the entire range from 0 to 1.

What it means

A classifier can have an attractive overall AUC while performing poorly in the operating region that matters. If a workflow can tolerate only a small false-positive rate, performance at very high false-positive rates may be largely irrelevant.
Partial AUC focuses evaluation on a defined region. Its numerical value depends on the interval and on whether the area is reported raw, divided by interval width, or standardized by another rule. Those conventions must be stated before comparing numbers.

How it works

Obtain scores and reliable binary labels from an appropriate evaluation sample. Specify which class is positive and ensure larger scores mean stronger evidence for that class. Construct the ROC curve by varying the classification threshold.
Choose the relevant false-positive-rate interval before using the evaluation results to favor a model. The choice should reflect operational requirements rather than whichever region makes a candidate look strongest.
Integrate true-positive rate over that interval. Empirical software commonly uses trapezoidal area with linear interpolation when a boundary falls between reported ROC points. Document interpolation, weighting, and treatment of tied scores.
For an interval from 0 to alpha, the maximum raw area is alpha. Dividing by alpha yields average sensitivity over that false-positive-rate interval, which is not the same as sensitivity at one selected threshold.
A different standardization, used by scikit-learn for its binary partial-AUC option, maps the diagonal reference to 0.5 and the maximal curve to 1. For raw area A, it uses one-half times [1 + (A - alpha squared/2)/(alpha - alpha squared/2)]. This is distinct from simply dividing by alpha.
Compare models on the same interval and convention, with uncertainty that respects shared evaluation cases and any clustering. Very low false-positive-rate regions require enough negative observations to resolve performance reliably.
Finally, choose and validate an actual operating threshold separately. Partial AUC does not directly supply precision, alert volume, calibration, or the cost of mistakes. Those depend on additional features of the deployment population and decision rule.

Three practical examples

Alert review: a team compares models within a false-positive-rate range compatible with its review capacity.
Quality inspection: evaluators focus on a region where false rejection of acceptable items must remain limited.
AI ranking evaluation: researchers report both whole-curve AUC and partial AUC to expose differences in an operationally relevant region.

Think of it this way

Think of comparing cars only over the speeds used on your daily route. An overall performance score may reward behavior in conditions you never encounter. A focused score is useful, provided everyone uses the same route and scoring convention.

Worked example

Consider an original illustrative ROC segment with points (false-positive rate, true-positive rate) equal to (0,0), (0.05,0.60), and (0.10,0.80). Use linear interpolation and the interval from 0 to 0.10.
The first trapezoid has area 0.05 times (0 + 0.60)/2 = 0.015. The second has area 0.05 times (0.60 + 0.80)/2 = 0.035. The raw partial AUC is therefore 0.050.
Dividing by interval width gives 0.050/0.10 = 0.50, the interval-average true-positive rate under this interpolation. It is not the endpoint true-positive rate, which is 0.80.
For the diagonal reference, raw area over this interval is 0.10 squared/2 = 0.005. The maximum raw area is 0.10. The stated standardized score is 0.5 times [1 + (0.050 - 0.005)/(0.10 - 0.005)] = 14/19, approximately 0.73684.
Thus 0.050, 0.50, and 0.73684 describe the same curve region under three different conventions. Reporting one without its definition can produce a misleading comparison. These values describe an invented ROC segment, not a measured model result.

Illustrative case study

Illustrative fictional case: Ash Alerts selects a model using full AUC, then finds that performance is weaker at the low false-positive rates its reviewers can support. The team defines an operational interval and compares candidate curves there using the same normalization.
It also estimates alert counts and precision at candidate thresholds on a suitable validation set. It records uncertainty because the low-rate region contains relatively few false-positive events. This fictional case illustrates complementary evaluation measures rather than a claimed improvement in alert quality.

Common misconceptions and mistakes

Do not compare raw partial AUC across different interval widths as though the scales were identical. Do not confuse standardized partial AUC with raw area or average sensitivity. A diagonal-reference score of 0.5 under one standardization does not mean every normalization has that baseline.
Avoid selecting the interval after inspecting which model wins. Do not assume a high partial AUC guarantees good calibration, high precision, or acceptable performance at every point inside the interval.

Business use

Partial AUC can align model comparison with a real operating constraint. Its business value depends on a justified region and a transparent definition. Reports should name the interval, positive class, scoring convention, interpolation, evaluation population, uncertainty, and the separate threshold-based measures used for deployment decisions.

Check your understanding

What is the raw area in the example?

Answer: 0.050.

Why is the standardized value approximately 0.73684?

Answer: It adjusts relative to the diagonal area and maximum area using the specified formula.

Is 0.50 the sensitivity at false-positive rate 0.10?

Answer: No; that endpoint sensitivity is 0.80.

Related terms

ROC (receiver operating characteristic) Curve
AUC (Area under the ROC curve)
False positive rate
Precision
Classification threshold
Calibration
ROC curve
AUC
sensitivity
specificity
model evaluation

Learn next

Next study uncertainty for ROC comparisons and the resolution of low false-positive-rate estimates. Then connect ranking metrics to prevalence, review capacity, and the costs of actual threshold decisions.

False positive rate

Sources

scikit-learn, roc_auc_score documentation: https://scikit-learn.org/stable/modules/generated/sklearn.metrics.roc_auc_score.html — official description of standardized partial AUC over a specified maximum false-positive rate. scikit-learn source, _binary_roc_auc_score: https://raw.githubusercontent.com/scikit-learn/scikit-learn/main/sklearn/metrics/_ranking.py — primary implementation of interpolation and McClish standardization. Both were checked; the ROC segment and exact arithmetic are original.

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