Calculate and interpret the sensitivity of mammograms for detecting breast cancer based on the provided data.
Understand the Problem
The question asks to calculate and interpret the sensitivity of mammograms for detecting breast cancer, given the results from a study in a provided table showing frequencies of individuals who screened positive or negative for breast cancer and non-cancer cases.
Answer
68%
Answer for screen readers
A total of 68% of individuals who have breast cancer test positive for breast cancer when using a mammogram as the primary diagnostic test for breast cancer.
Steps to Solve
- Understanding Sensitivity
Sensitivity is the ability of a test to correctly identify those with the disease (true positive rate). It's calculated as:
$$ \text{Sensitivity} = \frac{\text{True Positives}}{\text{True Positives + False Negatives}} $$
- Identify True Positives
From the table, the number of true positives (individuals with breast cancer who screened positive) = 17.
- Identify False Negatives
From the table, the number of false negatives (individuals with breast cancer who screened negative) = 8.
- Calculate Sensitivity
Using the formula:
$$ \text{Sensitivity} = \frac{17}{17 + 8} = \frac{17}{25} = 0.68 $$
- Convert to percentage
Convert the decimal to percentage by multiplying by 100:
$0.68 \times 100 = 68%$
A total of 68% of individuals who have breast cancer test positive for breast cancer when using a mammogram as the primary diagnostic test for breast cancer.
More Information
Sensitivity measures the proportion of actual positives that are correctly identified as such. A high sensitivity means fewer false negatives and a low sensitivity means more false negatives.
Tips
A common mistake is to mix up sensitivity and specificity. Specificity is the ability of the test to correctly identify those without the disease (true negative rate). Another common mistake is misidentifying true positives and false negatives from the table.
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