Home / Science / Health and medicine / Biostatistics / ROC curve and AUCTool #468

ROC curve and AUC calculator with DeLong confidence interval, Youden cut-off and two-marker comparison

Paste a true outcome and one or two marker values to draw the ROC curve, get the AUC with its DeLong confidence interval, the Youden cut-off, sensitivity, specificity, PPV, NPV and likelihood ratios at every cut-off, and DeLong's test of two markers on the same subjects. Matches scikit-learn.

Keep it one tap away for everyday use.

Bookmark ROC curve and AUC?

Press Ctrl + D now. Your browser opens its own bookmark box, where you choose the name and folder.

  1. Paste data
  2. ROC curve
  3. Cut-off
  4. Report
Nothing is uploadedWorks offline once open

For study and teaching, not medical advice. Check with a qualified professional.

Data

The example is made up: 60 people, 25 with the condition, and two blood markers.

With higher values, a test is called positive when the marker is at or above the cut-off; with lower values, at or below it.

What it does

A blood test, a score or a scan measurement is only useful if it separates people who have a condition from those who do not. The ROC curve (receiver operating characteristic) shows how well it does this at every possible cut-off: each point is the sensitivity (share of true cases the test catches) against 1 − specificity (share of people without the condition who are wrongly flagged). The area under the curve (AUC) sums this up in one number from 0.5 (no better than a coin toss) to 1 (perfect). This tool draws the curve, gives the AUC with a DeLong confidence interval, finds the Youden cut-off, lists sensitivity, specificity, PPV, NPV and likelihood ratios at every cut-off, and compares two markers measured on the same people with DeLong’s test. Everything runs in your browser.

How to use it

  1. Paste or open a file with one row per subject: the true outcome (1/0, or two words such as case and control), then one or two marker columns. A header row names the markers.
  2. Has the condition: which outcome value means the condition is present.
  3. The condition goes with: higher values if a high marker points to the condition (most blood markers), lower values if a low one does (for example a low haemoglobin for anaemia).
  4. Level: 90, 95 or 99 % intervals.
  5. With two markers, pick which one the cut-off table shows. Download the table as CSV, or the whole report as an image, PDF or Word file.

What the numbers mean

  • AUC: the chance that a randomly chosen person with the condition has a more extreme marker than a randomly chosen person without it; ties count half.
  • DeLong interval: a standard error that needs no assumption about the shape of the marker’s distribution; the interval is AUC ± z × SE, cut at 0 and 1. The p value tests AUC = 0.5.
  • Youden’s J = sensitivity + specificity − 1. The cut-off with the largest J is the one that best balances the two, if misses and false alarms matter equally.
  • PPV and NPV use the share with the condition in your data, so they change if the prevalence differs where the test is used. LR+ and LR− do not depend on prevalence.
  • DeLong’s paired test compares two AUCs from the same subjects, allowing for the correlation between them.

Worked example

The example is 60 made-up people, 25 with the condition, each with two markers. The page shows:

  • Marker A: AUC = 0.895 (95 % CI 0.808 to 0.983, SE 0.045).
  • Youden cut-off ≥ 44: sensitivity 0.840, specificity 0.857 (21 of 25 cases caught, 5 of 35 false alarms), J = 0.697, LR+ = 5.88.
  • Marker B: AUC = 0.676 (0.532 to 0.820).
  • DeLong test: difference 0.219 (0.071 to 0.368), z = 2.892, p = 0.004, so marker A discriminates better.

Tips

  • Use the cut-off the same way it will be used in practice: choose it on one data set and check it on another, because the Youden cut-off from the same data is optimistic.
  • An AUC below 0.5 usually means the direction is the wrong way round.
  • The comparison needs both markers measured on every subject; rows with a blank are left out.

FAQ

Why do I get more points than other software? Every distinct value is a cut-off here (like scikit-learn’s roc_curve with drop_intermediate=False). Dropping the in-between points does not change the AUC.

Is this the same as d′ from signal detection? No. This is the empirical ROC of a clinical marker, without assuming normal distributions.

Is my data sent anywhere? No. Everything is worked out on your device and the page keeps working offline.

Where the numbers come from

  • Formulas: Hanley and McNeil (1982) Radiology 143:29 (AUC as the Mann-Whitney statistic); DeLong, DeLong and Clarke-Pearson (1988) Biometrics 44:837 (variance and paired test); Sun and Xu (2014) IEEE Signal Processing Letters 21:1389 (fast mid-rank form); Youden (1950) Cancer 3:32.
  • Example data: made up for this page.

Standard scientific values, such as constants, atomic weights and melting points, are facts found in every textbook; we name where ours were checked. If you are an author or publisher and want a value, a credit or a table changed or removed, tell us and we will act quickly.

Last updated 2026-11-09.

Related tools

Survival analysis (Kaplan-Meier, log-rank, Cox) #467 Paste time, event and group to draw Kaplan-Meier curves with Greenwood intervals, median survival with its interval, a number-at-risk table, the log-rank test for two or more groups and a Cox proportional hazards model with hazard ratios. Matches lifelines and statsmodels. Meta-analysis (forest and funnel plots) #469 Pool studies from 2×2 counts (odds ratio, risk ratio, risk difference), means and SDs (mean difference, Hedges' g) or an estimate with its SE or CI. Fixed effect and random effects (DerSimonian-Laird, REML, Paule-Mandel), Q, I², tau², prediction interval, Egger's test, forest and funnel plots. Matches statsmodels. Method validation statistics #87 Paste replicate results by day, analyst or instrument: mean, SD, RSD and confidence interval, the Grubbs outlier test, bias and recovery against a true value, repeatability and intermediate precision by ANOVA, and the Horwitz ratio. Calibration curve with LOD and LOQ #28 Paste your standards and get the calibration line, R², limits of detection and quantitation (ICH Q2), and the concentration of each unknown with a 95 % interval. Reliability and agreement #40 Check a questionnaire scale with Cronbach's alpha and item statistics, or rater agreement with Cohen's kappa (weighted too), Fleiss' kappa and all six intraclass correlations with 95 % intervals. Matches R's psych package. Sample size and power calculator #32 How many subjects, samples or survey responses do you need? Sample size for comparing two means, paired data, two proportions, or a survey's margin of error, with power curves. Matches R and G*Power. Publication plot maker #27 Paste columns or open a CSV or Excel file and get a clean scientific figure with error bars, sized for a journal column. Download vector SVG or PDF, or PNG at 300 or 600 dpi. Your data stays in your browser.