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Free Optimal Cut-off Calculator (Youden Index, Closest to Top-Left, Fixed Sensitivity or Specificity, Cost-Weighted)
Paste your marker values and true disease status, and get the optimal diagnostic cut-off by four criteria, each with sensitivity, specificity, predictive values and likelihood ratios. Exact confidence intervals and a DeLong AUC are included.
In Simple Words
A diagnostic marker is a number, such as a blood level or a score. To call someone positive or negative you need a cut-off. A low cut-off catches more true cases but raises false alarms. A high cut-off does the reverse. This calculator tries every possible cut-off in your data and reports the best one under the rule you choose.
Four rules are available. The Youden index maximises sensitivity plus specificity minus 1. The closest-to-top-left rule picks the point nearest perfect performance on the ROC plot. The fixed rule keeps sensitivity (or specificity) at a target and maximises the other. The cost-weighted rule lets you say how much worse a missed case is than a false alarm. The answer is always in your original units.
When to Use an Optimal Cut-off Calculator
Use it when you have a continuous or ordinal marker and a reference-standard result (disease present or absent) for each participant, and you need to turn the marker into a positive or negative call. Typical cases are a new biomarker, a symptom score or an imaging measurement, where the published threshold is missing, comes from another population, or does not suit your clinical purpose.
The criterion should follow the purpose. A rule-out screening test usually needs high sensitivity, so a fixed-sensitivity target fits. A confirmatory test usually needs high specificity. When the Youden index or the closest-to-top-left rule is used, you give sensitivity and specificity equal weight, which corresponds to equal error costs only at 50% prevalence and is rarely the case in practice. Use the cost-weighted option when the two errors clearly differ. If you only need the ROC curve and AUC without choosing a threshold, use the ROC curve tool linked below.
Expected: 2 columns: Disease status per subject | Marker value per subject
Drop a CSV here or click to choose. Parsed in your browser: nothing is uploaded.
Expected: 2 columns: Disease status per subject | Marker value per subject
status <- c({status})
score <- c({score})
higher <- "{dir}" == "Higher = more positive"
method <- "{method}"
target <- {target} / 100
cr <- {costratio}
prev <- suppressWarnings(as.numeric("{prev}")) / 100 # blank -> NA -> sample prevalence
P <- sum(status == 1); N <- sum(status == 0)
if (is.na(prev)) prev <- P / (P + N)
u <- sort(unique(score))
cut <- (head(u, -1) + tail(u, -1)) / 2 # candidates: midpoints between distinct values
posf <- function(s, c) if (higher) s >= c else s <= c
sens <- sapply(cut, function(c) mean(posf(score[status == 1], c)))
spec <- sapply(cut, function(c) mean(!posf(score[status == 0], c)))
obj <- if (grepl("Youden", method)) sens + spec - 1 else
if (grepl("top-left", method)) -((1 - sens)^2 + (1 - spec)^2) else
if (grepl("sensitivity", method)) ifelse(sens >= target - 1e-12, spec, -Inf) else
if (grepl("specificity", method)) ifelse(spec >= target - 1e-12, sens, -Inf) else
-(cr * prev * (1 - sens) + (1 - prev) * (1 - spec))
stopifnot(is.finite(max(obj))) # fixed methods: target must be attainable
i <- which(obj >= max(obj) - 1e-12)[1] # ties -> lowest cut-off
c(cutoff = cut[i], sensitivity = sens[i], specificity = spec[i], J = sens[i] + spec[i] - 1)
cp <- function(x, n) c(if (x == 0) 0 else qbeta(.025, x, n - x + 1), if (x == n) 1 else qbeta(.975, x + 1, n - x))
cp(round(sens[i] * P), P); cp(round(spec[i] * N), N) # exact (Clopper-Pearson) 95% CI
# AUC with DeLong CI: library(pROC); r <- roc(status, score, direction = ifelse(higher, "<", ">")); auc(r); ci.auc(r, method = "delong")User guide
When to use. Choose a single decision threshold for a continuous diagnostic marker, and see sensitivity, specificity, predictive values, likelihood ratios and AUC at that threshold. Five criteria are compared side by side: Youden index, closest to the top-left corner, fixed sensitivity, fixed specificity, and expected cost given prevalence and the relative cost of a false negative.
Assumptions. One marker value per subject with a true 0/1 reference-standard status; independent subjects. Cut-off candidates are the midpoints between consecutive distinct sorted marker values (the same thresholds pROC uses); a subject is test-positive when the marker is ≥ the cut-off (or ≤ if lower values are more positive). Predictive values at a different prevalence are only valid if sensitivity and specificity transfer to that population.
Common mistakes. The cut-off and its accuracy are chosen and estimated on the same data and are optimistic; validate in new data or by bootstrap, especially with fewer than about 30 subjects per class. Different criteria legitimately give different cut-offs (Perkins & Schisterman). Do not use sample prevalence for PPV/NPV when cases and controls were sampled separately; enter the true prevalence instead. The AUC confidence interval is a normal approximation (DeLong) truncated to [0, 1] and is unreliable near 1 or with very few subjects.
Worked example
Click Load example data above, then Run Analysis to see a fully worked result with figure, formula and interpretation for this test.
References
- Youden WJ. Index for rating diagnostic tests. Cancer. 1950;3(1):32-35.
- Clopper CJ, Pearson ES. The use of confidence or fiducial limits illustrated in the case of the binomial. Biometrika. 1934;26(4):404-413.
- DeLong ER, DeLong DM, Clarke-Pearson DL. Comparing the areas under two or more correlated receiver operating characteristic curves: a nonparametric approach. Biometrics. 1988;44(3):837-845.
- Perkins NJ, Schisterman EF. The inconsistency of “optimal” cutpoints obtained using two criteria based on the receiver operating characteristic curve. Am J Epidemiol. 2006;163(7):670-675.
- Robin X, Turck N, Hainard A, et al. pROC: an open-source package for R and S+ to analyze and compare ROC curves. BMC Bioinformatics. 2011;12:77.
Worked Example
The built-in example has 60 subjects with a marker where higher values suggest disease. The AUC is 0.760 (95% CI 0.632 to 0.889, DeLong). The Youden cut-off is 7.85, with sensitivity 58.3% (95% CI 36.6 to 77.9) and specificity 91.7% (95% CI 77.5 to 98.2). The Youden index J is 0.500, LR+ is 7.00 and LR- is 0.455. At the sample prevalence, PPV is 82.4% and NPV is 76.7%. The closest-to-top-left rule gives the same cut-off here.
Changing the criterion changes the answer. Asking for sensitivity of at least 90% moves the cut-off to 4.25, with sensitivity 91.7% but specificity only 33.3%. Asking for at least 95% sensitivity gives a cut-off of 3.4, with sensitivity 100% and specificity 27.8%. Asking for at least 95% specificity gives 9.35, with sensitivity 41.7% and specificity 97.2%.
Prevalence matters for predictive values. Entering a stated prevalence of 10% with the Youden cut-off of 7.85 gives PPV 43.8% and NPV 95.2%, compared with PPV 82.4% and NPV 76.7% at the sample prevalence. With a stated prevalence of 10% and a cost ratio of 0.5 (a false negative costs half as much as a false positive), the cost-weighted rule moves to 11.65, where specificity is 100% and sensitivity falls to 12.5%. This shows how strongly the chosen costs drive the result.
Assumptions to Check
- The reference standard is correct and was applied to every participant, independently of the marker result.
- The sample reflects the people in whom the test will be used. Spectrum bias shifts the optimal cut-off.
- One marker only. The tool does not adjust for covariates or combine markers.
- Observations are independent. Repeated measures on the same person need a different method.
- Positive means marker at or above the cut-off (or at or below it, if you select the lower direction). Check that the direction matches the biology.
- Predictive values at a stated prevalence assume that sensitivity and specificity carry over to the setting with that prevalence.
Common Mistakes
Treating a data-derived cut-off as validated
The cut-off and its sensitivity and specificity are estimated on the same data, so they are optimistic, especially in small samples. This calculator reports in-sample values only. It does not use bootstrap or cross-validation. Confirm the threshold in an independent sample before relying on it, and report it as exploratory until then.
Ignoring the uncertainty of the cut-off
The sensitivity and specificity have exact confidence intervals here, but the cut-off itself has none, and neither do PPV, NPV or the likelihood ratios. Several nearby cut-offs may perform almost equally well. Do not read the single number as precise.
Using Youden by default
Youden weights a missed case and a false alarm equally and ignores prevalence. For screening or confirmation, a fixed-sensitivity, fixed-specificity or cost-weighted rule often matches the clinical purpose better.
Applying the AUC interval near the extremes
The DeLong interval is a Wald interval truncated to 0 to 1. It is unreliable with very small samples or an AUC close to 1. With perfect separation the interval collapses and LR+ is infinite, which signals a small or unrepresentative sample more than a perfect test.
Reading predictive values from the wrong prevalence
PPV and NPV at the sample prevalence reflect how the study recruited its participants. In a case-control sample they say little about routine practice. Enter the prevalence of your target setting instead.
Frequently Asked Questions
How are candidate cut-offs chosen?
Midpoints between consecutive distinct observed marker values are used. Trivial thresholds that classify everyone as positive or everyone as negative are excluded. The result was checked against the pROC package in R, which uses the same midpoints.
What happens when two cut-offs tie?
The lowest cut-off value is returned. This is a convention of this tool. Other software may list all tied thresholds.
Why do the Youden and closest-to-top-left answers sometimes differ?
They optimise different quantities. Youden maximises sensitivity plus specificity, while the top-left rule minimises the squared distance to perfect sensitivity and specificity. In a lower-is-positive test dataset they gave 48.5 and 47.5 respectively. They often agree, as in the main example.
What if my target sensitivity or specificity cannot be reached?
The tool returns an error that states the maximum attainable value in your data.
Which confidence intervals are used?
Exact Clopper-Pearson intervals for sensitivity and specificity, and a DeLong-based Wald interval for the AUC.
Can I use this for a lower-is-positive marker?
Yes. Select the lower direction, and the tool classifies values at or below the cut-off as positive and computes the AUC in that direction.
Is this a substitute for a statistician?
No. It supports exploratory analysis and teaching. A threshold intended for clinical use needs validation, a pre-specified analysis plan and a reporting guideline such as STARD.
Related Calculators
ROC Curve and AUC CalculatorDiagnostic Accuracy Calculator (Sensitivity and Specificity)Youden Index: Optimizing Diagnostic Test AccuracyConfidence Interval CalculatorPrevalence CalculatorThreshold Effects on Diagnostic Accuracy
References
- Fluss R, Faraggi D, Reiser B. Estimation of the Youden Index and its associated cutoff point. Biometrical Journal. 2005. PMID 16161804.
- Unal I. Defining an optimal cut-point value in ROC analysis: an alternative approach. Computational and Mathematical Methods in Medicine. 2017. PMID 28642804.
- Mandrekar JN. Receiver operating characteristic curve in diagnostic test assessment. Journal of Thoracic Oncology. 2010. PMID 20736804.
- DeLong ER, DeLong DM, Clarke-Pearson DL. Comparing the areas under two or more correlated receiver operating characteristic curves: a nonparametric approach. Biometrics. 1988. PMID 3203132.
Need This Analysis Done for Your Manuscript?
Need help choosing a cut-off, planning validation or writing up a diagnostic accuracy study? Editverse biostatisticians can run the analysis and prepare the methods and results sections.