Youden’s index, proposed by the statistician W. J. Youden in 1950, condenses the performance of a yes/no diagnostic test into one number. It adds the share of real cases the test catches (sensitivity) to the share of non-cases it correctly clears (specificity) and subtracts 1. A test that guesses at random scores 0, a perfect test scores 1, and a negative value means the test is doing worse than chance – usually a sign that the labels are reversed.
J is popular for choosing a cut-off on a continuous marker, such as a blood level or a risk score. Each possible threshold gives a point on the ROC curve; the threshold with the highest J is the one furthest above the diagonal line of chance, and it treats false negatives and false positives as equally costly. J is also the maximum difference between the true-positive and false-positive rates, so it is easy to explain.
Because sensitivity and specificity do not depend on how common the disease is, neither does J. Predictive values do, so the calculator also reports positive and negative predictive values for the prevalence in your sample.
How to use the Youden Index Calculator
- What do you know?
- True positives (TP)
- False positives (FP)
- False negatives (FN)
- True negatives (TN)
- Sensitivity
- Specificity
Results update as you type, and everything is calculated in your browser.
How it works
Enter the four counts of the confusion matrix, or switch to entering sensitivity and specificity. The calculator works out both rates, adds them and subtracts 1, and computes the likelihood ratios and – from counts – the predictive values and accuracy.
Worked example
A screening test is applied to 200 people, 50 of whom have the disease. It finds 42 of them (TP = 42, FN = 8) and wrongly flags 15 of the 150 healthy people (FP = 15, TN = 135).
Sensitivity = 42 ÷ 50 = 84% and specificity = 135 ÷ 150 = 90%, so J = 0.84 + 0.90 − 1 = 0.74. LR+ = 0.84 ÷ 0.10 = 8.4 and LR− = 0.16 ÷ 0.90 = 0.178. The positive predictive value is 42 ÷ 57 = 73.7% at this sample’s 25% prevalence.
Interpreting likelihood ratios
| LR+ | LR− | Effect on the probability of disease |
|---|---|---|
| > 10 | < 0.1 | Large, often conclusive change |
| 5 – 10 | 0.1 – 0.2 | Moderate change |
| 2 – 5 | 0.2 – 0.5 | Small change |
| 1 – 2 | 0.5 – 1 | Rarely important |
Inputs explained
| Field | What to enter |
|---|---|
| What do you know? | Choose one: Confusion matrix counts, Sensitivity and specificity |
| True positives (TP) | A number |
| False positives (FP) | A number |
| False negatives (FN) | A number |
| True negatives (TN) | A number |
| Sensitivity | In % |
| Specificity | In % |
What each result means
- Youden’s index (J) = ([Sensitivity (true positive rate)] + [Specificity (true negative rate)])÷100 – 1
- False positive rate (1 − specificity) = 100 – [Specificity (true negative rate)]
- False negative rate (1 − sensitivity) = 100 – [Sensitivity (true positive rate)]
- Positive likelihood ratio (LR+) = [Sensitivity (true positive rate)]÷(100 – [Specificity (true negative rate)])
- Negative likelihood ratio (LR−) = (100 – [Sensitivity (true positive rate)])÷[Specificity (true negative rate)]
- Positive predictive value (PPV) = [True positives (TP)]÷([True positives (TP)] + [False positives (FP)])×100
- Negative predictive value (NPV) = [True negatives (TN)]÷([True negatives (TN)] + [False negatives (FN)])×100
- Accuracy = ([True positives (TP)] + [True negatives (TN)])÷([True positives (TP)] + [False positives (FP)] + [False negatives (FN)] + [True negatives (TN)])×100
- Prevalence in the sample = ([True positives (TP)] + [False negatives (FN)])÷([True positives (TP)] + [False positives (FP)] + [False negatives (FN)] + [True negatives (TN)])×100
- Balanced accuracy = ([Sensitivity (true positive rate)] + [Specificity (true negative rate)])÷2
Formula
Sensitivity = TP ÷ (TP + FN) · Specificity = TN ÷ (TN + FP) · J = sensitivity + specificity − 1 · LR+ = sensitivity ÷ (1 − specificity) · LR− = (1 − sensitivity) ÷ specificity
Worked example
Inputs — What do you know?: Confusion matrix counts; True positives (TP): 42; False positives (FP): 15; False negatives (FN): 8; True negatives (TN): 135.
Results — Sensitivity (true positive rate) = 84 %; Specificity (true negative rate) = 90 %; Youden's index (J) = 0.74; False positive rate (1 − specificity) = 10 %; False negative rate (1 − sensitivity) = 16 %; Positive likelihood ratio (LR+) = 8.4; Negative likelihood ratio (LR−) = 0.178; Positive predictive value (PPV) = 73.68 %; Negative predictive value (NPV) = 94.41 %; Accuracy = 88.5 %; Prevalence in the sample = 25 %; Balanced accuracy = 87 %.
Key terms
- Sensitivity
- The share of people with the condition who test positive.
- Specificity
- The share of people without the condition who test negative.
- ROC curve
- A plot of sensitivity against 1 − specificity for every possible cut-off.
- Likelihood ratio
- How much a positive (LR+) or negative (LR−) result changes the odds of disease.
- Confusion matrix
- The 2×2 table of true and false positives and negatives.
Frequently asked questions
What is a good Youden index?
There is no universal cut-off, but J above 0.5 is often called good and above 0.7 very good. J = 0 means the test is useless and J = 1 means it is perfect.
How do I find the optimal cut-off with Youden's index?
Compute sensitivity and specificity for each candidate threshold and pick the one with the largest J. That point lies furthest above the chance diagonal of the ROC curve.
Can the Youden index be negative?
Yes, down to −1. A negative J means the test gets more cases wrong than a coin flip would – usually because positive and negative results were swapped.
Does the Youden index depend on prevalence?
No – it uses only sensitivity and specificity. Predictive values (PPV and NPV) do change with prevalence.
How is J related to balanced accuracy?
Balanced accuracy is the average of sensitivity and specificity, so J = 2 × balanced accuracy − 1.
What is J for sensitivity 84% and specificity 90%?
0.84 + 0.90 − 1 = 0.74.
When should I not use the maximum J cut-off?
When missing a case and a false alarm have very different costs – for screening a serious, treatable disease you may accept lower specificity to raise sensitivity.