Screening Tests: A Cohort Of 10,000 Women Are Screened For B

Screening TestsA Cohort Of 10000 Women Are Screened For Breast Cancer

A cohort of 10,000 women are screened for breast cancer via mammography. A total of 500 women have a positive mammogram. Among these, 85 are confirmed to have the disease (true positives). Additionally, 15 women who have the disease are not detected by the mammogram (false negatives). To accurately evaluate the test's performance, we need to set up a contingency table based on these data and fill in all missing cells.

Constructing the contingency table involves defining the four possible outcomes: true positives (TP), false positives (FP), false negatives (FN), and true negatives (TN). From the given data:

• TP = 85 (women with the disease correctly identified)
• False negatives (FN) = 15 (women with the disease who had a negative mammogram)
• Total positive mammograms = 500 (TP + FP), so FP = 500 - 85 = 415
• Total women in the cohort = 10,000
• Number of women with the disease = TP + FN = 85 + 15 = 100
• Number of women without the disease = 10,000 - 100 = 9,900
• False positives (FP) are women who tested positive but do not have the disease, calculated as above: 415
• True negatives (TN) = total women without the disease - FP = 9,900 - 415 = 9,485

Filled Contingency Table

Calculations of Test Performance Metrics

1. Sensitivity

Sensitivity measures the proportion of actual positives correctly identified by the test. It is calculated as:

Sensitivity = TP / (TP + FN) = 85 / (85 + 15) = 85 / 100 = 0.85 or 85%

2. Specificity

Specificity measures the proportion of actual negatives correctly identified. It is calculated as:

Specificity = TN / (TN + FP) = 9,485 / (9,485 + 415) = 9,485 / 9,900 ≈ 0.957 or 95.7%

3. Positive Predictive Value (PPV)

PPV indicates the probability that subjects with a positive test truly have the disease. It is calculated as:

PPV = TP / (TP + FP) = 85 / (85 + 415) = 85 / 500 = 0.17 or 17%

4. Negative Predictive Value (NPV)

NPV reflects the probability that subjects with a negative test truly do not have the disease. It is calculated as:

NPV = TN / (TN + FN) = 9,485 / (9,485 + 15) = 9,485 / 9,500 ≈ 0.9984 or 99.84%

5. Prevalence of the Disease

The prevalence indicates the proportion of the population that has the disease:

Prevalence = (Number of people with the disease) / (Total population) = 100 / 10,000 = 0.01 or 1%

Impact of Increased Disease Prevalence on Test Metrics

If the prevalence of breast cancer increases within the population, the effects on various diagnostic performance metrics are substantial:

• Sensitivity: Typically remains unchanged because sensitivity is an intrinsic property of the test, representing its ability to identify true positives regardless of disease prevalence.
• Specificity: Also generally remains stable because it measures the test’s ability to identify true negatives and is not directly affected by disease prevalence.
• Positive Predictive Value (PPV): Will increase with higher prevalence because, as the disease becomes more common, a positive test result is more likely to be a true positive.
• Negative Predictive Value (NPV): Will decrease as prevalence increases because, with more cases in the population, the likelihood that a negative result is a false negative rises.

This emphasizes that PPV and NPV are prevalence-dependent metrics, whereas sensitivity and specificity are inherent to the test itself (Akobeng, 2007; Altman & Bland, 1994). Consequently, screening programs must consider disease prevalence to interpret predictive values accurately and optimize testing strategies.

References

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