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Actual outcomes
Test values or scores
Compare by group (optional)

How-to

ROC Curve Calculator

Author: Dr. Mathias Jesussek
Updated:

Create one or more receiver operating characteristic (ROC) curves directly in your browser. numiqo calculates the area under the curve (AUC), DeLong uncertainty, cutoff performance and statistical comparisons while keeping the purpose of the analysis explicit.

Load single-curve example Load paired-curves example Load independent-curves example Load grouped-curves example Load missing-values example

Choose the ROC analysis that matches your question

Question Data selection Main results
How well does one test discriminate? One actual outcome and one test value or score ROC curve, AUC, DeLong SE, 95% CI and p-value
Which cutoff should I use? One actual outcome and one test value or score Youden, screening, confirmatory or existing-cutoff analysis
Which test discriminates better on the same participants? One actual outcome and several test values or scores Paired curves and paired DeLong comparisons
How do tests from separate samples compare? The same number of actual outcomes and test values or scores Independent curves and unpaired DeLong comparisons
Does performance differ between groups? One outcome, one test and one grouping variable One independent curve per valid group and pairwise comparisons

How to enter and select the data

  1. Paste or import the data into the table above.
  2. Select the binary variable under Actual outcomes.
  3. Select one or more metric variables under Test values or scores.
  4. Select the category that represents the Positive outcome.
  5. State whether high or low test values indicate that positive outcome.

If category value 1 is present, it is selected as the positive outcome initially. This is a convenience, not a statistical decision: confirm that the selected category matches the meaning of your data. Direction should likewise be chosen from subject-matter knowledge rather than whichever direction produces the larger AUC.

Cutoff selection for different purposes

Purpose Selection rule
Balanced cutoff Maximize the Youden index J = sensitivity + specificity − 1.
Screening or triage Reach the requested minimum sensitivity, then maximize specificity.
Confirmatory or rule-in testing Reach the requested minimum specificity, then maximize sensitivity.
Existing decision rule Evaluate the entered cutoff without optimizing it on these data.

The selected operating point includes sensitivity, specificity, likelihood ratios, predictive values and confusion-matrix counts as applicable. Stratified bootstrap 95% confidence intervals quantify uncertainty in the cutoff and performance measures. Read the cutoff-selection guide before treating a sample-derived threshold as a decision rule.

Missing observations and valid cases

Each curve uses outcome–test pairs for which both values are valid. The Case Processing Summary reports valid and excluded observations rather than silently treating missing values as a category or score. Paired curve comparisons use the rows that are complete for the two tests being compared; consequently, the AUC difference used in a comparison can differ slightly from the difference between AUCs calculated from all available rows for each test.

Results and publication output

  • ROC curve with reference line, optional cutoff point and selectable chart size
  • Optional pointwise 95% bootstrap confidence bands based on 2,000 stratified resamples
  • AUC with DeLong standard error, 95% confidence interval and test against AUC = 0.5
  • Paired and unpaired DeLong AUC comparisons
  • Holm-adjusted p-values when several pairwise comparisons are performed
  • ROC coordinates for every distinct observed cutoff
  • Tables, explanations and documentation export suitable for reporting

The confidence bands are pointwise intervals for sensitivity at fixed specificity values; they are not a simultaneous confidence region for the entire curve. Bootstrap results are calculated only when requested and then cached for the current analysis.

Interpretation limits

  • AUC describes discrimination, not calibration or clinical usefulness by itself.
  • A cutoff optimized and evaluated on the same sample can perform worse in new data.
  • PPV and NPV use the proportion of positive cases in this dataset and change with prevalence.
  • Very small or strongly imbalanced samples produce uncertain estimates.
  • A valid curve requires both positive and negative observations.

Learn more

Cite numiqo: numiqo Team (2026). numiqo: Online Statistics Calculator. numiqo e.U. Graz, Austria. URL https://numiqo.com