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Notice that
So
if , and the answer would be C.
An actual two-by-two table is a tabular representation containing two rows and two columns.
- The columns consist of the tested True positive for prostate cancer and tested True Negative for prostate cancer
- The rows consist of the predicted positive screening and predicted negative values
Mathematically, the set-up of the two-by-two table for this data can be computed as:
Tested True Positive for cancer True Negative Total
Predicted Positive 800 3200 4000
Predicted Negative 100 95900 96000
Total 900 99100 100000
<h3>b)</h3>The prevalence rate of prostate cancer in this population is:
= 9 per thousand.
<h3>c)</h3>
The calculation of the sensitivity of this screening is as follows:
where;
- TP = True positive for cancer
- PN₁ = Predicted Negative for true positive cancer
∴
= 0.889
= 88.9%
The interpretation shows that 88.9% are correctly identified to be actual positive for prostate cancer.
<h3>d)</h3>The calculation of the specificity of this screening is as follows:
where;
- TN = True positive for cancer
- PN₂ = Predicted Negative for true negative cancer
∴
= 0.9677
= 96.77%
The interpretation shows that 96.7% of an actual negative is correctly identified as such.
<h3>e)</h3>
The positive predicted value of the screening test is computed as:
= 0.2
= 20%
The interpretation of the positive predicted value of this screening shows that 20% that are subjected to the diagnosis of positive prostate cancer truly have the disease.
Learn more about tabular representation here: