Youden Index for Optimal Cutpoints

Introduction

Many diagnostic and biomarker analyses begin with a continuous measurement. A laboratory concentration, imaging score, gene-expression value, risk score, or circulating biomarker may take hundreds or thousands of possible values.

Clinical decision-making, however, often requires a threshold.

For example, investigators may need to determine whether a biomarker value should be classified as:

• Positive or negative
• High risk or low risk
• Disease likely or disease unlikely
• Treatment eligible or treatment ineligible

Selecting that threshold is known as cutpoint selection or threshold optimization.

One of the most widely used statistical approaches is the Youden Index.

What Is the Youden Index?

Suppose a continuous biomarker is used to distinguish patients with disease from patients without disease. For any candidate threshold \(c\), patients can be classified as positive or negative.

That threshold produces two key diagnostic performance measures:

• Sensitivity: the probability of a positive test among patients with disease.
• Specificity: the probability of a negative test among patients without disease.

The Youden Index combines the two measures:

The selected cutpoint is therefore:

where \(c^*\) is the cutpoint that maximizes the Youden Index.

Why the Youden Index Is Useful

A diagnostic threshold always creates a trade-off.

Lowering a threshold can increase sensitivity but decrease specificity. Raising the threshold can increase specificity but decrease sensitivity.

The Youden Index provides a simple way to identify the threshold that provides the best combined discrimination under a criterion that gives equal weight to sensitivity and specificity.

The Confusion Matrix Behind the Youden Index

Every candidate cutpoint produces a classification table.

Sensitivity is:

Specificity is:

The Youden Index can therefore be written as:

Range of the Youden Index

Sensitivity and specificity each range from 0 to 1. Therefore:

A value of:

• 0 indicates no improvement over random classification under the usual interpretation.
• 1 represents perfect sensitivity and specificity.
• Values closer to 1 indicate stronger combined discrimination at that threshold.

For example, if:

then:

A Simple Worked Example

Suppose a biomarker is evaluated at five candidate thresholds.

The maximum Youden Index is:

Both 40 and 50 produce the same value in this simplified example.

This illustrates an important practical issue: the optimal cutpoint need not be unique.

Connection to the ROC Curve

The Youden Index is closely related to the receiver operating characteristic (ROC) curve.

For each possible threshold, calculate:

• Sensitivity
• False-positive rate
• Specificity

The false-positive rate is:

Therefore:

or:

where \(TPR\) is the true-positive rate.

This means that the Youden Index at a given threshold is the vertical distance between the ROC curve and the diagonal line representing random classification.

Geometric Interpretation

The ROC curve plots:

against:

For a candidate threshold:

Thus \(J\) is the vertical separation between the ROC point and the 45-degree no-discrimination line.

The Youden-optimal threshold is therefore the ROC point with the largest vertical distance above that diagonal.

Relationship to the AUC

The area under the ROC curve, or AUC, measures overall discrimination across all possible thresholds.

The Youden Index answers a different question.

A biomarker can have a high AUC but still require careful consideration when selecting a single operational threshold.

Worked Calculation From Raw Counts

Suppose a candidate threshold produces the following classification:

There are 100 patients with disease and 100 without disease.

Sensitivity is:

Specificity is:

Therefore:

The Youden Index for this cutpoint is therefore:

Comparing Multiple Cutpoints

In practice, the index is calculated across many candidate thresholds.

The maximum occurs at:

with:

Why Lowering the Threshold Changes Sensitivity

Suppose higher biomarker values indicate greater disease risk.

If the threshold is lowered, more patients are classified as positive.

This generally causes:

• More true positives
• Fewer false negatives
• Higher sensitivity
• More false positives
• Lower specificity

Raising the threshold generally produces the opposite pattern.

The Youden Index Does Not Use Prevalence

One useful property of sensitivity and specificity is that they are defined within disease-status groups.

Consequently, the Youden Index itself does not depend directly on disease prevalence in the study population.

This differs from predictive values.

Youden Index and Predictive Values

Positive predictive value is:

Negative predictive value is:

Unlike sensitivity and specificity, PPV and NPV depend strongly on disease prevalence.

Therefore, a cutpoint optimized using the Youden Index in a case-control dataset may not produce the expected PPV in routine clinical practice.

What Does "Optimal" Actually Mean?

The phrase optimal cutpoint can be misleading.

The Youden Index defines optimality according to one specific mathematical criterion:

It does not mean that the threshold is automatically:

• The safest threshold
• The most clinically useful threshold
• The least expensive threshold
• The threshold with the best patient outcomes
• The threshold with the best positive predictive value
• The regulatory-approved threshold

Equal Weighting of Sensitivity and Specificity

The standard Youden Index gives sensitivity and specificity equal mathematical weight.

For example:

A loss of 5 percentage points in sensitivity can therefore offset a gain of 5 percentage points in specificity.

But clinical decisions do not always have equal consequences.

Missing a patient with a dangerous disease may be substantially worse than performing an unnecessary confirmatory test.

In such situations, a sensitivity-prioritized threshold may be preferable to the Youden-optimal threshold.

When You Should Not Automatically Use the Youden Cutpoint

A purely statistical cutpoint should be questioned when:

• False negatives are much more harmful than false positives.
• False positives are much more harmful than false negatives.
• The treatment or intervention has substantial toxicity.
• The biomarker is used to determine treatment eligibility.
• The threshold is being used for population screening.
• There is a clinically established threshold already in use.
• The intended use requires a prespecified sensitivity or specificity.

Clinical Utility Versus Statistical Optimization

Suppose a cancer biomarker is used to identify patients who should undergo an invasive diagnostic procedure.

A Youden-optimal threshold might have:

But if missing a true case is considered unacceptable, investigators may instead choose a threshold with:

even if specificity falls substantially.

The latter threshold may have a lower Youden Index but greater clinical utility for the intended application.

Cost-Sensitive Threshold Selection

If the consequences of false positives and false negatives differ, threshold selection can explicitly incorporate those costs.

A general decision framework can consider:

• False-positive cost
• False-negative cost
• Disease prevalence
• Downstream treatment consequences
• Resource utilization
• Patient preferences

This is conceptually different from the standard Youden criterion.

Direction of the Biomarker Matters

The usual setup assumes that larger biomarker values correspond to greater probability of disease.

But this is not always true.

Some biomarkers have lower values in patients with disease.

For example, suppose:

• High values → disease likely
• Low values → disease likely

The definition of a positive test must be specified correctly.

A ROC analysis can account for the direction of the marker, but the final clinical rule should explicitly state whether the test is positive when:

or when:

Continuous Biomarker Example

Suppose a biomarker is measured in ng/mL. The candidate values are:

Each candidate threshold generates a sensitivity and specificity pair.

The analysis may produce:

The maximum occurs at:

with:

What Happens at the Cutpoint?

Suppose the classification rule is:

A patient with a biomarker value of 36.9 would be classified negative, whereas a patient with 37.0 would be classified positive.

This illustrates why cutpoint precision matters.

If the assay has substantial analytical variability around 37 ng/mL, the apparent sharpness of the threshold may not reflect a meaningful biological boundary.

Measurement Precision and Cutpoints

A statistically estimated threshold should always be considered alongside measurement error.

If the biomarker can fluctuate substantially because of:

• Analytical variation
• Biological variation
• Sampling variation
• Laboratory-to-laboratory differences

then a highly precise-looking cutpoint may not be operationally stable.

ROC Analysis and Candidate Thresholds

The ROC curve contains information about every candidate threshold.

The Youden Index evaluates them one by one:

What If Several Cutpoints Have Similar Youden Values?

This situation is common.

Suppose three thresholds produce:

There may be no meaningful statistical reason to prefer 39 over 40 or 41.

A clinically convenient threshold such as 40 may be preferable if it is consistent with assay reporting, clinical workflow, or an existing convention.

Confidence Intervals for the Cutpoint

A point estimate of the optimal threshold does not communicate its uncertainty.

Different samples from the same underlying population can produce different Youden-optimal thresholds.

Therefore, threshold estimation should ideally consider uncertainty through methods such as:

• Bootstrap resampling
• Cross-validation
• Independent validation datasets
• Confidence intervals for sensitivity and specificity
• Resampling distributions of the selected cutpoint

Bootstrap Stability Assessment

A useful exploratory analysis is to repeatedly resample the development dataset.

For each bootstrap sample:

1. Recalculate the ROC curve.
2. Recalculate the Youden Index.
3. Record the optimal threshold.

After many bootstrap samples, investigators can examine the distribution of selected thresholds.

For example, suppose 1,000 bootstrap samples produce:

with a broad central interval:

This suggests that the apparent cutpoint of 37 is not especially stable.

Overfitting in Cutpoint Selection

Cutpoint optimization is susceptible to overfitting.

If investigators search through many thresholds and select the one that gives the best apparent performance in the same dataset, the selected threshold may look better than it truly performs in new patients.

This is a form of data-driven model selection.

Training and Validation Framework

Why Re-Optimizing in the Validation Dataset Is a Problem

Suppose a threshold of 37 is identified in the development dataset.

In the validation dataset, the analyst searches again and discovers that 42 produces the highest Youden Index.

If the purpose is to validate the original threshold, the threshold should not simply be changed to 42.

The validation question is:

Re-optimizing the threshold answers a different question.

Youden Index in Biomarker Development

The Youden Index is commonly considered during biomarker development when a continuous biomarker must eventually support a binary classification.

Potential applications include:

• Disease detection
• Diagnostic classification
• Risk stratification
• Prognostic biomarker development
• Screening tests
• Laboratory assays
• Imaging-derived biomarkers
• Composite clinical scores

However, the development context matters.

A diagnostic biomarker used to detect disease is not necessarily evaluated in the same way as a prognostic biomarker used to predict survival.

Diagnostic Versus Prognostic Cutpoints

Time-to-Event Outcomes Require Additional Care

Suppose a biomarker is intended to predict overall survival. Simply defining:

If censoring is present, conventional ROC analysis may not appropriately represent the time-to-event structure.

Time-dependent ROC methods may be more appropriate.

Case-Control Sampling and the Youden Index

Diagnostic development datasets often contain intentionally selected numbers of cases and controls.

For example, investigators might analyze:

• 100 disease-positive participants
• 100 disease-negative participants

even though the disease prevalence in the intended population is much lower.

Sensitivity and specificity can still be estimated from such a design, but predictive values calculated from the sample should not automatically be interpreted as population predictive values.

Prevalence and Clinical Deployment

Suppose a Youden-optimal cutpoint produces:

In a high-prevalence population, the PPV may be relatively high.

In a low-prevalence screening population, the same threshold can produce a much lower PPV.

The threshold has not changed. The population has changed.

ROC Curves With a Perfect Classifier

For a perfect classifier, there exists a threshold with:

Therefore:

The ROC curve reaches the upper-left corner.

ROC Curves With No Discrimination

For a classifier with no discrimination, sensitivity and false-positive rate change together along approximately the diagonal.

Then:

and therefore:

This is why the Youden Index is closely connected to ROC discrimination.

Second ROC Example: A Threshold Trade-Off

Youden Index Versus Closest Point to the Top-Left Corner

Another commonly discussed ROC criterion selects the point closest to the perfect-classification corner:

A common Euclidean-distance criterion is:

The threshold minimizing \(D(c)\) is the closest-point criterion.

It is not identical to the Youden criterion.

When Youden and Closest-Point Criteria Agree

If the ROC curve has a favorable symmetric shape, different optimization criteria may select similar thresholds.

But they can diverge when the ROC curve is asymmetric.

This is another reason not to interpret the word "optimal" without specifying the criterion.

Fixed-Sensitivity Thresholds

In some clinical applications, investigators may specify a minimum acceptable sensitivity.

For example:

The selected threshold might then be the most specific threshold satisfying that requirement.

This may be more appropriate than maximizing the Youden Index when missing disease is particularly costly.

Fixed-Specificity Thresholds

Similarly, a diagnostic confirmation test might require:

The selected threshold would then prioritize specificity.

Again, this can result in a threshold different from the Youden-optimal value.

Choosing a Cutpoint for a Companion Diagnostic

Biomarker cutpoints can be particularly consequential when they determine whether a patient receives a targeted therapy.

In such settings, the threshold may affect:

• Who receives treatment
• Who is excluded from treatment
• Observed treatment benefit
• Safety exposure
• Assay reproducibility
• Clinical implementation

A Youden Index can be informative during exploratory development, but a treatment-selection threshold generally requires broader evidence than a single ROC optimization.

Cutpoint Selection Should Be Prespecified When Possible

If a cutpoint is used in a confirmatory clinical study, the analysis plan should clearly define:

• The biomarker variable
• Assay and measurement method
• Direction of the biomarker
• Population used for threshold development
• Cutpoint selection criterion
• Handling of ties
• Handling of missing values
• Validation strategy
• Primary and secondary performance metrics

Missing Biomarker Values

Missing values require an explicit analysis strategy.

Potential approaches include:

• Complete-case analysis
• Prespecified imputation
• Missingness indicators in appropriate modeling contexts
• Sensitivity analyses

The correct approach depends on why measurements are missing and what the estimand is.

Simply dropping missing values without considering the missingness mechanism can introduce bias.

Outliers and Extreme Biomarker Values

A few extreme biomarker values can influence ROC behavior and threshold selection.

Investigators should distinguish between:

• True biological extremes
• Analytical errors
• Unit errors
• Data-entry errors
• Specimen problems

Outliers should not be removed solely because they make the ROC curve less attractive.

Units Must Be Consistent

A cutpoint is meaningless without its measurement scale.

For example:

is not the same operational definition as:

A factor-of-1,000 unit error can completely invalidate threshold classification.

R Implementation Using pROC

The pROC package provides tools for ROC analysis and commonly supports Youden-based threshold selection.

library(pROC)

roc_obj <- roc(
  response = data$disease,
  predictor = data$biomarker,
  direction = ">"
)

coords(
  roc_obj,
  x = "best",
  best.method = "youden",
  ret = c(
    "threshold",
    "sensitivity",
    "specificity"
  )
)

The returned threshold is the candidate cutpoint according to the selected Youden criterion.

Calculating the Youden Index Explicitly in R

It is often useful to calculate the index directly so that the derivation is transparent.

roc_points <- coords(
  roc_obj,
  x = "all",
  ret = c(
    "threshold",
    "sensitivity",
    "specificity"
  ),
  transpose = FALSE
)

roc_points$youden <-
  roc_points$sensitivity +
  roc_points$specificity -
  1

best_row <-
  roc_points[
    which.max(roc_points$youden),
  ]

best_row

The key calculation is:

youden <-
  sensitivity +
  specificity -
  1

This explicit approach is useful for auditability because the analyst can inspect all candidate thresholds rather than only the final selected value.

Extracting the Optimal Cutpoint

best_threshold <-
  best_row$threshold

best_sensitivity <-
  best_row$sensitivity

best_specificity <-
  best_row$specificity

best_youden <-
  best_row$youden

A final report might therefore contain:

data.frame(
  Cutpoint = best_threshold,
  Sensitivity = best_sensitivity,
  Specificity = best_specificity,
  Youden = best_youden
)

Direction in pROC

The direction argument deserves particular attention.

For a biomarker where larger values indicate greater disease probability, the analysis may use a direction corresponding to:

If smaller values indicate disease, the direction must be handled accordingly.

Always inspect the ROC object and confirm that sensitivity and specificity correspond to the intended clinical classification rule.

Creating a Diagnostic Classification Variable in R

Once a threshold has been finalized, the operational classification rule can be generated explicitly.

cutpoint <- 37

data$test_positive <-
  ifelse(
    data$biomarker >= cutpoint,
    1,
    0
  )

The exact direction should reflect the scientific definition of a positive test.

Validating the Classification Rule

table(
  Predicted = data$test_positive,
  Observed = data$disease
)

From this table, sensitivity and specificity can be independently recalculated to verify the ROC output.

Manual R Calculation of Sensitivity and Specificity

tab <- table(
  Predicted = data$test_positive,
  Observed = data$disease
)

TP <- tab["1","1"]
FP <- tab["1","0"]
FN <- tab["0","1"]
TN <- tab["0","0"]

sensitivity <-
  TP / (TP + FN)

specificity <-
  TN / (TN + FP)

youden <-
  sensitivity +
  specificity -
  1

This is an excellent independent programming check.

R Workflow for Development and Validation

# Development set

roc_dev <- roc(
  development$disease,
  development$biomarker,
  direction = ">"
)

dev_best <- coords(
  roc_dev,
  x = "best",
  best.method = "youden",
  ret = c(
    "threshold",
    "sensitivity",
    "specificity"
  )
)

cutpoint <- dev_best$threshold


# Validation set

validation$predicted <-
  ifelse(
    validation$biomarker >=
      cutpoint,
    1,
    0
  )

table(
  Predicted =
    validation$predicted,
  Observed =
    validation$disease
)

Cross-Validation

When an independent validation dataset is unavailable, resampling methods can provide a more realistic estimate of threshold stability.

A cross-validation strategy can repeatedly:

1. Split the data into training and test subsets.
2. Estimate the Youden-optimal cutpoint in the training subset.
3. Apply that cutpoint to the held-out subset.
4. Evaluate sensitivity, specificity, and other metrics.

This helps quantify how much apparent performance depends on the particular sample used for threshold discovery.

Why Internal Validation Is Not the Same as External Validation

Bootstrap and cross-validation methods are valuable, but they do not replace an independent external validation population when one is needed.

External validation tests whether the threshold transports to a different sample, site, period, or population.

Potential sources of variation include:

• Different patient characteristics
• Different disease prevalence
• Different assay platforms
• Different specimen handling
• Different clinical settings
• Different treatment patterns

Cutpoint Drift

A biomarker threshold can perform differently over time.

For example, changes in:

• Assay calibration
• Laboratory procedures
• Patient selection
• Disease spectrum
• Reference standards

can affect the observed distribution of biomarker values.

Therefore, a cutpoint should be considered an operational measurement rule, not necessarily a permanent biological constant.

Spectrum Bias

Diagnostic accuracy can depend on the spectrum of patients included in the development dataset.

A biomarker may separate:

• Very healthy controls
• Patients with advanced disease

extremely well.

Its performance may be less impressive when distinguishing:

• Mild disease from no disease
• Borderline disease from healthy controls
• Closely related differential diagnoses

This is one reason external validation in the intended clinical population is important.

Verification Bias

Diagnostic studies can also be affected by verification bias.

If only participants with a positive screening result receive the definitive reference standard, disease status may not be known accurately for everyone.

That can distort estimates of sensitivity, specificity, and therefore the Youden Index.

Reference-Standard Quality

The Youden Index is only as meaningful as the disease classification used to define the outcome.

If the reference standard is inaccurate, the ROC curve may reflect disagreement with an imperfect reference rather than true disease discrimination.

Third Actual ROC Figure: Threshold Selection

Youden Index and Class Imbalance

Because the Youden Index uses sensitivity and specificity, it is not directly dominated by the numerical proportion of cases and controls in the dataset.

However, class imbalance can still matter indirectly through:

• Precision of the estimates
• Confidence intervals
• Number of available cases
• Number of available controls
• Sampling design
• Generalizability

A study with only a small number of disease-positive participants may produce a highly unstable threshold even if the Youden Index appears large.

Sample Size and Cutpoint Stability

Suppose the estimated Youden Index is:

That value alone does not indicate how precisely it has been estimated.

A dataset with thousands of participants can produce a very different level of certainty from a dataset containing 20 cases and 20 controls.

Therefore, threshold reporting should be accompanied by appropriate measures of uncertainty and validation.

What Should Be Reported?

A useful cutpoint analysis should report at least:

Suggested Reporting Language

Do Not Report Only the Cutpoint

A statement such as:

is incomplete.

The reader should know:

• What the biomarker measures
• The measurement units
• The disease definition
• The direction of positivity
• The optimization criterion
• The sensitivity
• The specificity
• The development population
• The validation strategy

Common Mistakes

1. Calling the Youden cutpoint universally optimal. It is optimal only with respect to the specified Youden criterion and dataset.
2. Ignoring biomarker direction. Positive may mean high values or low values depending on the marker.
3. Confusing AUC with the Youden Index. AUC summarizes overall discrimination; Youden selects a threshold.
4. Ignoring prevalence when interpreting predictive values. PPV and NPV depend on the target population.
5. Optimizing and validating in the same dataset. This can produce optimistic performance estimates.
6. Re-optimizing the threshold in validation data. This defeats the purpose of evaluating the original fixed threshold.
7. Reporting excessive numerical precision. A cutpoint such as 37.1842 may not be meaningful when assay precision is much lower.
8. Ignoring clinical consequences. A mathematically balanced threshold may not be appropriate when false negatives and false positives have very different consequences.
9. Ignoring uncertainty. A point estimate does not establish cutpoint stability.
10. Using ordinary ROC methods for censored time-to-event outcomes without consideration. The estimand and censoring structure must be addressed.

Youden Index Versus Sensitivity-Maximizing Cutpoints

Why the ROC Curve Should Be Shown

A cutpoint presented without the ROC curve hides important information.

For example, suppose the selected threshold has:

The reader should ideally be able to see where this point lies relative to the rest of the ROC curve.

If a broad range of thresholds produces nearly identical performance, the choice of a single threshold is less certain.

Flat ROC Regions

Some ROC curves contain broad regions in which performance changes very little.

For example:

and:

may indicate that there is little practical difference between the two thresholds.

A clinically convenient threshold may therefore be preferable.

Cutpoint Rounding

Suppose statistical optimization produces:

but the assay reports whole numbers.

The operational threshold may need to be:

The rounded threshold should then be evaluated directly because rounding can slightly change sensitivity and specificity.

Threshold Rounding Should Be Validated

Do not assume that a rounded threshold has exactly the same diagnostic performance as the unrounded value.

For example:

The operational difference may be negligible, but it should be demonstrated rather than assumed.

Clinical Interpretation of the Selected Threshold

Once a threshold has been selected, investigators should ask:

• Is the sensitivity clinically acceptable?
• Is the specificity clinically acceptable?
• What happens to PPV in the intended population?
• What happens to NPV?
• How stable is the threshold?
• Is the assay sufficiently precise?
• Does the threshold generalize across sites?
• Are there clinically important subgroups with different performance?

Subgroup Performance

A threshold can perform differently across subgroups.

Potential factors include:

• Age
• Sex
• Disease severity
• Comorbidities
• Treatment history
• Ethnic or geographic populations
• Assay platform
• Clinical site

The same cutpoint should therefore be evaluated for transportability when appropriate.

Subgroup Analysis Does Not Mean Re-Optimizing Every Subgroup

Suppose the overall development cutpoint is 37 ng/mL.

In subgroup A, the highest observed Youden Index occurs at 35. In subgroup B, it occurs at 41.

This does not automatically mean that three different clinical thresholds should be adopted.

The subgroup findings may instead indicate:

• Sampling variability
• Biological heterogeneity
• Assay differences
• True effect modification

Additional evidence is needed before operationalizing subgroup-specific thresholds.

Cutpoints Can Discard Information

Converting a continuous biomarker into a binary variable loses information.

Consider values:

If the cutpoint is 37, then 38, 60, and 100 may all become simply "positive."

Their underlying quantitative differences disappear from the binary analysis.

Continuous Modeling Versus Dichotomization

Example: A Prognostic Biomarker

Suppose a continuous biomarker is strongly associated with survival.

An investigator might find a Youden cutpoint for death within one year.

That cutpoint can be useful for describing discrimination at the one-year horizon.

However, it does not necessarily imply that the biomarker has a natural biological threshold at that value.

The underlying relationship with survival may be continuous.

Clinical Decision Curve Considerations

When the ultimate objective is clinical decision-making rather than classification alone, decision-analytic approaches may provide additional information.

For example, decision-curve analysis considers the clinical consequences of using different risk thresholds.

The resulting threshold may differ from the Youden-optimal threshold because the objectives are different.

Validation Checklist

Programming Quality Control

A cutpoint analysis should be independently checked.

At minimum, verify:

• All disease labels are correct.
• All biomarker values use the correct units.
• Missing values are handled according to the analysis plan.
• The biomarker direction is correct.
• The ROC curve has the expected orientation.
• Sensitivity is calculated using diseased participants.
• Specificity is calculated using non-diseased participants.
• The Youden formula is implemented correctly.
• The maximum is selected correctly.
• Ties are handled transparently.
• The operational cutpoint matches the reported cutpoint.
• Validation applies the frozen threshold.

Independent Manual Check

Suppose the selected threshold produces:

Then:

and:

Therefore:

The independently calculated value should agree with the programmed result.

How to Present the Result in a Table

The highlighted row is the Youden-optimal candidate.

How to Present the Result in a Figure

A useful figure package may contain:

• ROC curve
• AUC estimate
• Highlighted selected threshold
• Sensitivity at the threshold
• Specificity at the threshold
• Confidence intervals where appropriate

This allows the reader to understand both overall discrimination and the selected operating point.

Recommended Figure Footnote

Interpretation of a High Youden Index

Suppose:

This means that:

It does not mean that the probability of a correct classification is 80%.

For example, the same Youden Index could result from:

or:

Both have:

but they have different clinical trade-offs.

What the Youden Index Does Not Tell You

The Youden Index alone does not tell you:

• Positive predictive value
• Negative predictive value
• Clinical utility
• Cost-effectiveness
• Patient benefit
• Assay reproducibility
• Generalizability
• Performance under a different prevalence
• Performance in external populations

These questions require additional analyses.

Summary Workflow for a Clinical Biomarker Study

Practical Decision Framework

The Most Important Concept

The Youden Index is fundamentally a way to summarize the trade-off between sensitivity and specificity at a particular threshold.

Its formula is simple:

The corresponding cutpoint is:

But the simplicity of the formula should not obscure the complexity of the clinical decision.

A threshold selected from one dataset can be unstable. A statistically optimal threshold may not be clinically optimal. A threshold that performs well in a development cohort may perform poorly in external validation. And a binary cutpoint can discard information contained in the original continuous biomarker.

References

Youden, W.J. (1950). Index for rating diagnostic tests. Cancer, 3(1), 32–35.
Fluss, R., Faraggi, D., & Reiser, B. (2005). Estimation of the Youden Index and its associated cutoff point. Biometrical Journal, 47(4), 458–472.
Perkins, N.J., & Schisterman, E.F. (2006). The inconsistency of "optimal" cutpoints obtained using two criteria based on the receiver operating characteristic curve. American Journal of Epidemiology, 163(7), 670–675.
Pepe, M.S. (2003). The Statistical Evaluation of Medical Tests for Classification and Prediction. Oxford University Press.
Zou, K.H., O'Malley, A.J., & Mauri, L. (2007). Receiver-operating characteristic analysis for evaluating diagnostic tests and predictive models. Circulation, 115(5), 654–657.
Robin, X., Turck, N., Hainard, A., et al. (2011). pROC: an open-source package for R and S+ to analyze and compare ROC curves. BMC Bioinformatics, 12, 77.