Calculate True Positive Rate Python

What is True Positive Rate?

The true positive rate, also known as sensitivity or recall, measures how well a classification model identifies positive cases. It's calculated as the number of true positives divided by the total number of actual positives.

In medical testing, for example, TPR would represent the proportion of sick patients correctly identified as having the disease. A high TPR indicates good model performance at detecting positive cases.

True Positive Rate Formula

Where:

• True Positives (TP) - Correctly identified positive cases
• False Negatives (FN) - Positive cases incorrectly identified as negative

The result is a value between 0 and 1, where 1 represents perfect detection of all positive cases.

Calculate True Positive Rate in Python

You can calculate TPR in Python using scikit-learn's classification metrics. Here's a complete implementation:

from sklearn.metrics import confusion_matrix

# Example confusion matrix
y_true = [1, 0, 1, 1, 0, 1, 0, 1, 0, 1]
y_pred = [1, 0, 1, 0, 0, 1, 0, 1, 0, 0]

# Calculate confusion matrix
tn, fp, fn, tp = confusion_matrix(y_true, y_pred).ravel()

# Calculate TPR
tpr = tp / (tp + fn)
print(f"True Positive Rate: {tpr:.2f}")

For a more complete implementation with model training, you would use:

from sklearn.model_selection import train_test_split
from sklearn.ensemble import RandomForestClassifier
from sklearn.metrics import classification_report

# Load your data
X, y = load_your_data()

# Split data
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2)

# Train model
model = RandomForestClassifier()
model.fit(X_train, y_train)

# Evaluate
y_pred = model.predict(X_test)
print(classification_report(y_test, y_pred))

Worked Example

Let's calculate TPR for a medical test with these results:

Using the formula:

This means the test correctly identifies 80% of actual positive cases.