Youden Index Calculator & Formula: Find Cutoff (2026)

Q: What is the Youden Index in simple terms?

It is one number that combines how well a test finds people who have the condition (sensitivity) and how well it clears people who do not (specificity). J = sensitivity + specificity − 1. A useless test scores 0 and a perfect test scores 1.

Q: What is the formula for the Youden Index?

J = Se + Sp − 1, which is the same as Se − (1 − Sp), or the true positive rate minus the false positive rate. On a ROC curve it is the vertical distance from the diagonal chance line to the curve at a given cutoff.

Q: What range can the Youden Index take?

For a single test, J runs from −1 to 1. Zero means the test does no better than chance, and negative values mean the test labels are reversed. The maximum J over all cutoffs of a ROC curve cannot be below 0, because the corner (0, 0) already gives J = 0.

Q: What is a good Youden Index value?

There is no official threshold. Many papers treat J of 0.5 or more as good and 0.75 or more as high, but these are conventions, not standards. Judge J against the clinical cost of missed cases and false alarms, and report a confidence interval.

Q: How do I find the optimal cutoff with the Youden Index?

Calculate sensitivity and specificity at every candidate cutoff, compute J for each, and pick the cutoff with the largest J. In R, pROC does this with coords(roc_obj, "best", best.method = "youden").

Q: Is the Youden cutoff the same as the point closest to the top-left corner?

Not in general. The two criteria can select different cutoffs, and the gap grows when the ROC curve is asymmetric (Perkins and Schisterman, 2006). Choose the criterion before you look at the data and state it in your methods.

Q: When should I not use the Youden Index?

Avoid it as the only criterion when a missed case costs far more than a false alarm, as in screening for a serious treatable disease, or the reverse. J gives both errors equal weight. Cost-weighted or net-benefit approaches fit those settings better.

Q: Does prevalence change the Youden Index?

No. Sensitivity and specificity are estimated within the diseased and non-diseased groups, so J does not depend on prevalence. PPV and NPV do, which is why they can look very different between a specialist clinic and a screening programme.

Q: How should I report a Youden-based cutoff in a paper?

Report the cutoff, J, sensitivity and specificity with 95% confidence intervals (bootstrap intervals are common), the sample size in each group, and how the cutoff was chosen. Validate it in a separate sample when you can. STARD 2015 lists the items reviewers expect.

Published July 14, 2024 | Last updated October 27, 2026

In simple wordsThe Youden Index (J) turns sensitivity and specificity into one number: J = sensitivity + specificity − 1. A test that guesses scores 0 and a perfect test scores 1. Compute J at every possible cutoff and the cutoff with the highest J is the Youden-optimal threshold. It treats missed cases and false alarms as equally costly, which is the main thing to check before you use it.

The Youden Index is the most common way to pick a cutoff for a continuous diagnostic test or biomarker. Use the two calculators below to compute it, then read on for the formula, a worked example, how to choose the cutoff, and where the method breaks down.

On this page: Calculators · Formula · Worked example · Optimal cutoff · Interpretation · Real data case studies · Youden vs other criteria · Limitations · R code · FAQ

Youden Index calculator

Enter sensitivity and specificity if you already have them. If you have raw counts, use the 2×2 table version underneath.

Youden Index calculator: from sensitivity and specificity

Sensitivity (0 to 1)

True positive rate

Specificity (0 to 1)

True negative rate

Youden Index (J)	0.7500
Reading (rule of thumb)	High
False positive rate (1 − Sp)	10.00%
False negative rate (1 − Se)	15.00%

J = Se + Sp − 1. Try Se 0.92 and Sp 0.88 to reproduce the worked example below (J = 0.80).

Youden Index calculator: from a 2×2 table

Enter whole counts. You need at least one diseased and one non-diseased case.

True positives (TP)

Disease present, test positive

False positives (FP)

Disease absent, test positive

False negatives (FN)

Disease present, test negative

True negatives (TN)

Disease absent, test negative

Both calculators run in your browser and send nothing anywhere. We checked the 2×2 version against the R package pROC on edge cases such as zero cells and perfect separation.

Youden Index formula

J = Se + Sp − 1equivalently J = TPR − FPR = Se − (1 − Sp)

Youden proposed the index in 1950 as a single rating for a diagnostic test [1]. Three properties are worth knowing:

Range. For one test at one cutoff, −1 ≤ J ≤ 1. J = 0 means the test does no better than a coin toss, and J < 0 means the test points the wrong way. The maximum J across all cutoffs is never below 0.
Geometry. J is the vertical gap between the ROC curve and the diagonal chance line. The cutoff where that gap is largest is the Youden cutoff (Figure 1).
Prevalence. J does not change with disease prevalence, because Se and Sp are measured inside the diseased and healthy groups separately.

Figure 1. Youden Index on a ROC curve. The marked point is where Se + Sp − 1 is largest. In this illustration Se = 0.80 and Sp = 0.80, so J = 0.60.

Worked examples

Example 1: from Se and Sp

A test has sensitivity 0.92 and specificity 0.88. J = 0.92 + 0.88 − 1 = 0.80. It misses 8% of diseased patients and wrongly flags 12% of healthy ones.

Example 2: from a 2×2 table

Suppose 200 patients are tested against a reference standard. The table below is illustrative, not from a published study.

	Disease present	Disease absent
Test positive	TP = 85	FP = 10
Test negative	FN = 15	TN = 90

Sensitivity = 85 / (85 + 15) = 0.85
Specificity = 90 / (90 + 10) = 0.90
J = 0.85 + 0.90 − 1 = 0.75

The same counts give PPV 85/95 = 89.5%, NPV 90/105 = 85.7%, LR+ = 0.85 / 0.10 = 8.5 and LR− = 0.15 / 0.90 = 0.17. Type them into the second calculator to confirm.

How to find the optimal cutoff

With a continuous marker, each possible cutoff gives its own Se and Sp. The steps are:

List candidate cutoffs, usually every observed value or a clinically sensible grid.
At each cutoff, classify patients as positive when the marker is at or above it, and compute Se and Sp against the reference standard.
Compute J = Se + Sp − 1 at every cutoff.
Take the cutoff with the largest J, then add a bootstrap confidence interval for the cutoff and for J.

The table below uses made-up numbers for a biomarker measured in 100 diseased and 100 non-diseased people. J peaks at 0.70 at a cutoff of 25, so 25 is the Youden-optimal threshold here.

Cutoff	Sensitivity	Specificity	J
10	0.98	0.40	0.38
15	0.95	0.62	0.57
20	0.90	0.78	0.68
25	0.82	0.88	0.70
30	0.70	0.94	0.64
35	0.52	0.98	0.50

Notice what happens on either side of the peak. Lower cutoffs buy sensitivity at the price of specificity, and higher cutoffs do the opposite. Figure 2 shows that trade on simulated data, with J forming a hill whose top sits close to where the sensitivity and specificity curves cross.

Line chart of sensitivity, specificity and Youden Index across test thresholds for a simulated biomarker, with the best threshold of 5.4 and J of 0.74 marked — **Figure 2.** Sensitivity falls and specificity rises as the threshold increases. J peaks at the dashed line, a threshold of 5.4, where sensitivity is 0.85, specificity 0.89 and J = 0.74. Simulated data: 1,000 diseased and 1,000 healthy.

How to interpret the Youden Index

There is no agreed scale. The bands below are common rules of thumb, and the calculators above use them. Treat them as a starting point and judge J against the clinical stakes.

J	Reading	What it means in practice
0.75 to 1.00	High	Few errors of either kind
0.50 to 0.74	Good	Useful, but expect a visible error rate
0.25 to 0.49	Moderate	Weak alone, may help as part of a panel
0 to 0.24	Low	Close to chance
Below 0	Worse than chance	Check that the test direction is not reversed

Figure 3 compares three simulated ROC curves: a test with no information (J = 0.04), a moderate test (J = 0.42) and a strong test (J = 0.82). Even a strong test does not reach J = 1, which would need perfect separation of the two groups.

Three simulated ROC curves: no information (AUC 0.51, J 0.04), moderate test (AUC 0.78, J 0.42) and strong test (AUC 0.97, J 0.82), each with its best Youden point circled — **Figure 3.** Simulated ROC curves with the best Youden point circled on each. The grey curve hugs the chance diagonal (AUC 0.51, J 0.04), the dark blue curve is a moderate test (AUC 0.78, J 0.42), and the orange curve is a strong test (AUC 0.97, J 0.82). All curves are simulated, not patient data.

Common mistakeReporting the cutoff that maximises J in your own sample as if it were a validated threshold. That cutoff is chosen to fit the data you have, so sensitivity and specificity at that point are optimistic, most of all in small samples. Give a bootstrap confidence interval for the cutoff and check it in a second sample before anyone applies it in a clinic [2,9].

Real data case studies: two open-access PLOS ONE studies

Two recent studies in PLOS ONE report the Youden Index in full, and both are published under a CC BY 4.0 licence, which is why we can reproduce their ROC figures below. We rebuilt the tables from the published numbers and re-ran the arithmetic. Anything labelled as our analysis is our own calculation from those tables, not a result the authors reported.

Case 1: the HbA1c cut-off for diabetes in rural China

Wang and colleagues measured fasting plasma glucose (FPG) and glycated haemoglobin (HbA1c) in 3,547 adults aged 61 or older in rural China. Among the 3,122 without previously diagnosed diabetes, they used FPG of 7.0 mmol/L or higher as the reference standard and asked which HbA1c cut-off maximises J. The answer was 6.5% (48 mmol/mol), with sensitivity 88.9%, specificity 93.7% and J = 0.825 [12].

HbA1c cut-off	Sensitivity	Specificity	J (Se + Sp − 1)	PPV
6.1%	95.1%	78.8%	0.739	10.7%
6.4%	90.1%	91.5%	0.816	22.0%
6.5%	88.9%	93.7%	0.826	27.2%
6.6%	86.4%	95.4%	0.818	33.3%
6.9%	72.8%	97.9%	0.707	47.6%

Source: Wang et al. 2024, Table 2 [12]. We recomputed J from the rounded Se and Sp, which gives 0.826 at 6.5%; the paper reports 0.825 from unrounded values.

ROC curve of HbA1c against fasting plasma glucose for diagnosing diabetes in rural Chinese older adults — **Figure 4.** ROC curve of HbA1c for diabetes. Reproduced from Wang P et al., *PLOS ONE* 2024;19(1):e0296694, doi:10.1371/journal.pone.0296694. Licensed under CC BY 4.0.

Line chart of sensitivity, specificity and Youden Index for five HbA1c cut-offs, with J peaking at 6.5 percent — **Figure 5.** Sensitivity falls and specificity rises as the HbA1c cut-off rises; J peaks at 6.5%. Chart by Editverse from the published Table 2 data [12].

What this case shows

A clear peak. J climbs from 0.738 at 6.1% to 0.825 at 6.5% and falls to 0.707 at 6.9%. With a sharp peak, small changes in the sample are unlikely to move the cutoff far.
Two criteria, same answer here. In our calculation the point closest to the top-left corner is also 6.5% (distance 0.128, against 0.131 at 6.4%). They agree on this dataset, but nothing guarantees it [4].
High J does not mean high PPV. At 6.5% the PPV is only 27.2% even though specificity is 93.7%. Working back from the published Se, Sp and PPV, we estimate that about 2.6% of this screened sample had diabetes by FPG. When the disease is rare, even a good test produces many false positives. Report PPV with the prevalence it came from.

Case 2: the Morse Fall Scale in obstetrics and gynecology wards

Mao and colleagues compared 136 inpatients who fell with 120 who did not, across an obstetrics and gynecology hospital and a general hospital, and scored each on the Morse Fall Scale. The ROC curve had an AUC of 0.791, and the authors chose a cut-off of 40, with sensitivity 0.735, specificity 0.808 and J = 0.543 [13].

ROC curve of the Morse Fall Scale for predicting inpatient falls in obstetrics and gynecology wards, AUC 0.791 — **Figure 6.** ROC curve of the Morse Fall Scale. Reproduced from Mao B et al., *PLOS ONE* 2024;19(9):e0305735, doi:10.1371/journal.pone.0305735. Licensed under CC BY 4.0.

Cut-off	Sensitivity	Specificity	J (Se + Sp − 1)	Weighted loss (missed fall = 3× false alarm)
25	0.882	0.383	0.265	0.971
35	0.875	0.383	0.258	0.992
40	0.735	0.808	0.543	0.987
45	0.713	0.808	0.521	1.053
50	0.640	0.858	0.498	1.222
55	0.625	0.900	0.525	1.225
60	0.618	0.900	0.518	1.246

Source: Mao et al. 2024, Table 2 [13]. J and the last column are our calculation from the published sensitivity and specificity. Lower weighted loss is better.

Line chart of sensitivity, specificity and Youden Index across Morse Fall Scale cut-offs, with the highest J of 0.543 at 40 and a lower second peak near 55 — **Figure 7.** J across Morse Fall Scale cut-offs. The highest J is at 40, with a second, lower peak at 52.5 to 55. Chart by Editverse from the published Table 2 data [13].

What this case shows

Ties and a second peak. J is identical (0.543) for every score from 37.5 to 40, so several scores tie. After falling to 0.498 at 47.5 to 50, it rises again to 0.525 at 52.5 to 55. A single maximum can hide a second reasonable choice.
Equal weights are a choice. Suppose a missed faller counts three times as much as a false alarm. In our illustrative calculation, the lowest weighted loss then moves from 40 to 25 (0.971 against 0.987), where sensitivity is 0.882. J alone would never suggest that.
Prevalence is set by the design. With 136 fallers and 120 non-fallers, the sample is roughly balanced by design, so its PPV and NPV do not describe a real ward. J does not have this problem.
Recompute before you copy. In the published table, J at a cut-off of 20 is listed as 0.162, but 0.912 + 0.125 − 1 = 0.037. Check every J you take from a table.

The same check works on your own data: list Se and Sp at each cutoff, recompute J, then look for ties, second peaks and the cost of each error before you pick a number.

Youden Index vs other cutoff criteria

Criterion	What it optimises	Best when	Watch out for
Youden J	Se + Sp − 1	Missed cases and false alarms cost about the same	Ignores unequal costs
Closest to top-left	Distance to (FPR 0, TPR 1)	You want a point near perfect classification	Can pick a different cutoff than J [4]
AUC	Whole-curve discrimination	Comparing tests, not choosing a cutoff	Gives no threshold
Likelihood ratios	How much a result shifts probability	Bedside reasoning with pre-test probability	Needs a prior probability
Cost-weighted / net benefit	Expected harm or benefit	Costs of the two errors clearly differ	Needs cost or threshold-probability inputs

The Youden criterion and the closest-to-top-left criterion often agree, but not always. Perkins and Schisterman showed that they can point to different cutoffs and that the Youden cutoff is the one that maximises correct classification when the diseased and healthy groups are weighted equally [4]. Pick the criterion in advance and name it in your methods.

Limitations and fixes

Limitation	Why it matters	What to do
Equal weight on both errors	A missed cancer and a false alarm are rarely equal harms	Use a cost-weighted rule or decision-curve analysis
Optimism in the same sample	The best J in your data is biased upward	Bootstrap or cross-validate [2,9]
Measurement error in the marker	Noise flattens the ROC curve and lowers J	Use error-corrected estimators [3]
Values below the detection limit	Dropping them biases J and the cutoff	Use methods built for a lower limit of detection [5]
More than two classes	The two-group J does not extend directly	Use the three-class generalisation [6,7]
Prevalence in PPV and NPV	Predictive values shift with prevalence	Report Se and Sp, and recompute PPV and NPV for the target population

For broader reviews of cutoff methods, see Hajian-Tilaki’s introduction to ROC analysis [8] and the 2024 update by Hassanzad and Hajian-Tilaki [9].

Calculate the Youden Index in R

The pROC package returns the Youden cutoff directly [10].

library(pROC)
roc_obj <- roc(response = d$disease, predictor = d$marker)
coords(roc_obj, x = "best", best.method = "youden",
       ret = c("threshold", "sensitivity", "specificity"))
ci.coords(roc_obj, x = "best", best.method = "youden",
          ret = c("threshold", "sensitivity", "specificity"),
          boot.n = 2000)

When you write this up, follow STARD 2015 so the cutoff, how it was chosen and its uncertainty are all reported [11].

Free calculators for diagnostic accuracy work

These free tools cover the steps around the Youden Index.

ROC curve and AUC calculatorBuild the curve and read AUC Diagnostic accuracy calculatorSe, Sp, PPV, NPV, likelihood ratios Diagnostic meta-analysis (HSROC)Pool sensitivity and specificity Confidence interval calculatorPut an interval around your estimate Odds ratio and relative riskFrom a 2×2 table Statistical test selectorPick the right test for your data

Get your diagnostic accuracy analysis checked

A wrong cutoff method can sink a diagnostic paper in review. If you want a biostatistician to run or audit the ROC analysis, the cutoff choice and the methods paragraph, this is the service built for it.

Editverse

Youden Index FAQ

What is the Youden Index in simple terms?

It is one number that combines how well a test finds people who have the condition (sensitivity) and how well it clears people who do not (specificity). J = sensitivity + specificity − 1. A useless test scores 0 and a perfect test scores 1.

What is the formula for the Youden Index?

J = Se + Sp − 1, which is the same as Se − (1 − Sp), or the true positive rate minus the false positive rate. On a ROC curve it is the vertical distance from the diagonal chance line to the curve at a given cutoff.

What range can the Youden Index take?

For a single test, J runs from −1 to 1. Zero means the test does no better than chance, and negative values mean the test labels are reversed. The maximum J over all cutoffs of a ROC curve cannot be below 0, because the corner (0, 0) already gives J = 0.

What is a good Youden Index value?

There is no official threshold. Many papers treat J of 0.5 or more as good and 0.75 or more as high, but these are conventions, not standards. Judge J against the clinical cost of missed cases and false alarms, and report a confidence interval.

How do I find the optimal cutoff with the Youden Index?

Calculate sensitivity and specificity at every candidate cutoff, compute J for each, and pick the cutoff with the largest J. In R, pROC does this with coords(roc_obj, “best”, best.method = “youden”).

Is the Youden cutoff the same as the point closest to the top-left corner?

Not in general. The two criteria can select different cutoffs, and the gap grows when the ROC curve is asymmetric (Perkins and Schisterman, 2006). Choose the criterion before you look at the data and state it in your methods.

When should I not use the Youden Index?

Avoid it as the only criterion when a missed case costs far more than a false alarm, as in screening for a serious treatable disease, or the reverse. J gives both errors equal weight. Cost-weighted or net-benefit approaches fit those settings better.

Does prevalence change the Youden Index?

No. Sensitivity and specificity are estimated within the diseased and non-diseased groups, so J does not depend on prevalence. PPV and NPV do, which is why they can look very different between a specialist clinic and a screening programme.

How should I report a Youden-based cutoff in a paper?

Report the cutoff, J, sensitivity and specificity with 95% confidence intervals (bootstrap intervals are common), the sample size in each group, and how the cutoff was chosen. Validate it in a separate sample when you can. STARD 2015 lists the items reviewers expect.

References

Youden WJ. Index for rating diagnostic tests. Cancer. 1950;3(1):32-35. 10.1002/1097-0142(1950)3:1<32::AID-CNCR2820030106>3.0.CO;2-3
Fluss R, Faraggi D, Reiser B. Estimation of the Youden Index and its associated cutoff point. Biom J. 2005;47(4):458-472. 10.1002/bimj.200410135
Perkins NJ, Schisterman EF. The Youden Index and the optimal cut-point corrected for measurement error. Biom J. 2005;47(4):428-441. 10.1002/bimj.200410133
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. 10.1093/aje/kwj063
Ruopp MD, Perkins NJ, Whitcomb BW, Schisterman EF. Youden Index and optimal cut-point estimated from observations affected by a lower limit of detection. Biom J. 2008;50(3):419-430. 10.1002/bimj.200710415
Nakas CT, Alonzo TA, Yiannoutsos CT. Accuracy and cut-off point selection in three-class classification problems using a generalization of the Youden index. Stat Med. 2010;29(28):2946-2955. 10.1002/sim.4044
Luo J, Xiong C. Youden index and associated cut-points for three ordinal diagnostic groups. Commun Stat Simul Comput. 2013;42(6):1213-1234. 10.1080/03610918.2012.661906
Hajian-Tilaki K. Receiver operating characteristic (ROC) curve analysis for medical diagnostic test evaluation. Caspian J Intern Med. 2013;4(2):627-635. PMID 24009950
Hassanzad M, Hajian-Tilaki K. Methods of determining optimal cut-point of diagnostic biomarkers with application of clinical data in ROC analysis: an update review. BMC Med Res Methodol. 2024;24. 10.1186/s12874-024-02198-2
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. 10.1186/1471-2105-12-77
Bossuyt PM, Reitsma JB, Bruns DE, et al. STARD 2015: an updated list of essential items for reporting diagnostic accuracy studies. BMJ. 2015;351:h5527. 10.1136/bmj.h5527
Wang P, Li Y, Wang M, et al. Comparing glycemic traits in defining diabetes among rural Chinese older adults. PLoS ONE. 2024;19(1):e0296694. 10.1371/journal.pone.0296694
Mao B, Jiang H, Chen Y, et al. Re-evaluating the Morse Fall Scale in obstetrics and gynecology wards and determining optimal cut-off scores for enhanced risk assessment: a retrospective survey. PLoS ONE. 2024;19(9):e0305735. 10.1371/journal.pone.0305735

About this articlePrepared by the Statistics & Methodology Unit, Editverse. Calculator outputs were checked against the R package pROC. Last reviewed October 2026. Worked-example tables are illustrative and figures are simulated unless stated.