Sensitivity

Sensitivity

Sensitivity, also known as Recall or the True Positive Rate (TPR), is a performance metric used in classification problems. It measures how well a model can identify actual positive instances.

Definition

$\text{Sensitivity}=\frac{TP}{TP+FN}$

Where:

• TP = True Positives – actual positives correctly predicted
• FN = False Negatives – actual positives incorrectly predicted as negative

Sensitivity answers the question: "Out of all real positive cases, how many did the model correctly identify?"

Alternate Names

• Recall
• True Positive Rate (TPR)
• Hit Rate (in signal detection theory)

Simple Example

A disease test is applied to 100 patients who have the disease. The model predicts:

• 90 correctly diagnosed as sick → TP = 90
• 10 wrongly predicted as healthy → FN = 10

$\text{Sensitivity}=\frac{90}{90+10}=\frac{90}{100}=0.9=90\mathrm{\%}$

This means the model successfully detected 90% of the sick patients.

Importance of Sensitivity

Sensitivity is **critical** in applications where missing a positive case can have serious consequences.

Real-World Scenarios

• Medical diagnosis: Missing a disease can be fatal.
• Security systems: Failing to detect a threat may be dangerous.
• Fraud detection: Missed fraud cases are costly.

Sensitivity vs Specificity

• Sensitivity measures how well you find actual positives.
• Specificity measures how well you avoid false alarms (negatives correctly identified).

Formula for Specificity (for comparison)

$\text{Specificity}=\frac{TN}{TN+FP}$

Where:

• TN = True Negatives
• FP = False Positives

Related Metrics

• Recall – Sensitivity is another name for Recall
• Specificity – Measures true negative rate
• Precision – Measures correctness of positive predictions
• F1 Score – Balances Sensitivity and Precision
• Confusion Matrix – Base table for all classification metrics

SEO Keywords

sensitivity in machine learning, true positive rate, recall vs sensitivity, disease test sensitivity, model evaluation metric, sensitivity formula, confusion matrix sensitivity