A researcher wants to determine the sensitivity of mammograms to determine how effective they are at diagnosing women who have breast cancer. Assume the researcher obtained the abo... A researcher wants to determine the sensitivity of mammograms to determine how effective they are at diagnosing women who have breast cancer. Assume the researcher obtained the above results from a study, calculate and interpret the sensitivity of mammograms for detecting breast cancer from the following data: | | Frequency of Breast Cancer Cases | Frequency of Non-Cancer Cases | | :------------------------------------- | :------------------------------- | :------------------------------ | | Frequency of Individuals Who Screened Positive | 17 | 5 | | Frequency of Individuals Who Screened Negative | 8 | 77 | Which of the following is the correct sensitivity? A total of 66.67% of individuals who have breast cancer test positive for breast cancer when using a mammogram as the primary diagnostic test for breast cancer. 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. A total of 70.59% of individuals who have breast cancer test positive for breast cancer when using a mammogram as the primary diagnostic test for breast cancer. A total of 92.77% of individuals who have breast cancer test positive for breast cancer when using a mammogram as the primary diagnostic test for breast cancer.
Understand the Problem
The question asks us to calculate the sensitivity of mammograms based on the provided data table. Sensitivity is calculated as the number of true positives divided by the sum of true positives and false negatives. In this case, true positives are the individuals who have breast cancer and screened positive (17), and false negatives are the individuals who have breast cancer but screened negative (8).
Answer
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.
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
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Identify True Positives (TP) and False Negatives (FN)
From the table, True Positives (TP) = 17 and False Negatives (FN) = 8.
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Calculate Sensitivity
Sensitivity = $TP / (TP + FN)$
Sensitivity = $17 / (17 + 8)$
Sensitivity = $17 / 25$
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Convert to Percentage
Sensitivity = $17 / 25 = 0.68$
Sensitivity (in percentage) = $0.68 * 100 = 68$%
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 (e.g., the percentage of sick people who are correctly identified as having the condition). High sensitivity means fewer false negatives and is essential for screening tests.
Tips
A common mistake is to confuse sensitivity with specificity. Specificity is the proportion of true negatives that are correctly identified. In this case, we are only calculating sensitivity.
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