Screening Tests A cohort of 10,000 women are screened for ✓ Solved
A cohort of 10,000 women are screened for breast cancer via mammography. A total of 500 women have a positive mammogram. Upon further study of these 500, only 85 are found to actually have the disease (true positives). An additional 15 women are found to have the disease but have had a negative mammogram.
A. Properly set up and label your table and fill in all missing cells.
B. Calculate the sensitivity of the test.
C. Calculate the specificity of the test.
D. Calculate the positive predictive value.
E. Calculate the negative predictive value.
F. Calculate the prevalence of the disease.
G. Explain what would happen to the sensitivity, specificity, positive predictive value, and the negative predictive value if the prevalence of the disease were to increase.
Paper For Above Instructions
Breast cancer screening is critical for early detection and improving survival rates among women. This paper provides a detailed statistical analysis based on a cohort of 10,000 women screened via mammography, detailing calculations for sensitivity, specificity, positive predictive value, negative predictive value, and disease prevalence. Additionally, it will discuss how changes in disease prevalence affect various test metrics.
Table Setup
To analyze the screening results effectively, we will set up a 2x2 table to categorize the outcomes:
| Result | Has Disease | No Disease | Total |
|---|---|---|---|
| Positive Test | 85 (True Positives) | 415 (False Positives) | 500 |
| Negative Test | 15 (False Negatives) | 9,485 (True Negatives) | 9,500 |
| Total | 100 | 9,900 | 10,000 |
Sensitivity Calculation
Sensitivity measures the proportion of actual positives that are correctly identified. It is calculated as follows:
Sensitivity = True Positives / (True Positives + False Negatives)
In our example:
Sensitivity = 85 / (85 + 15) = 85 / 100 = 0.85 (or 85%)
Specificity Calculation
Specificity measures the proportion of actual negatives that are correctly identified. The formula is:
Specificity = True Negatives / (True Negatives + False Positives)
Applying our numbers:
Specificity = 9,485 / (9,485 + 415) = 9,485 / 9,900 ≈ 0.9575 (or 95.75%)
Positive Predictive Value Calculation
Positive Predictive Value (PPV) indicates the probability that a person with a positive test result truly has the disease. The formula is:
PPV = True Positives / (True Positives + False Positives)
Thus:
PPV = 85 / (85 + 415) = 85 / 500 = 0.17 (or 17%)
Negative Predictive Value Calculation
Negative Predictive Value (NPV) reflects the probability that a person with a negative test result truly does not have the disease. The calculation is:
NPV = True Negatives / (True Negatives + False Negatives)
This gives us:
NPV = 9,485 / (9,485 + 15) = 9,485 / 9,500 ≈ 0.9984 (or 99.84%)
Prevalence Calculation
Prevalence measures the total number of cases of a disease in the population at a given time. It is calculated as:
Prevalence = (True Positives + False Negatives) / Total Population
Thus:
Prevalence = (85 + 15) / 10,000 = 100 / 10,000 = 0.01 (or 1%)
Impact of Increased Prevalence on Test Metrics
Increasing the prevalence of the disease would significantly affect the performance metrics of the screening tests:
- Sensitivity: Typically remains stable unless the test's methodology is flawed.
- Specificity: Also generally remains stable; however, with increased prevalence, the context in which this test is operating may mean more true positives.
- Positive Predictive Value (PPV): This will increase as more true positives are likely identified with higher prevalence.
- Negative Predictive Value (NPV): This can decrease with higher prevalence since the proportion of false negatives may rise, increasing the likelihood of false assurances in a more positive-biased population.
In conclusion, screening tests like mammography are essential tools in the fight against breast cancer, but they must be interpreted within the context of their statistical accuracy. Our analysis demonstrates key metrics that can guide clinical decisions and the impact of prevalence on these tests.