Question

Difficulty: EasyDiagnostic and Screening Test Performance

A gastroenterology research team is evaluating a novel non-invasive breath test for the detection of early-stage liver cirrhosis. The gold standard for confirming the diagnosis is a liver biopsy. The researchers conduct a study involving 800800 adult patients with chronic liver disease.

The results of the study are as follows:
- Liver biopsy confirms early-stage cirrhosis in 200200 patients.
- Among these 200200 patients, 180180 have a positive breath test.
- Among the 600600 patients without cirrhosis on biopsy, 6060 have a positive breath test.

What is the positive predictive value of the novel breath test in this study cohort? Provide your answer as a whole number percentage.

Answer: 75 %

Answer

75
The positive predictive value (PPV) is calculated by dividing the number of true positive results by the total number of positive test results (true positives + false positives). In this study, there are 180 true positives and 60 false positives. Thus, the total number of positive tests is 240. The PPV is calculated as 180 / 240 = 0.75, which translates to 75%.

Step-by-Step Solution

1
Identify the number of true positives (TP).
TP = 180
These are the patients who actually have the disease (cirrhosis) and correctly tested positive.
2
Identify the number of false positives (FP).
FP = 60
These are the patients who do not have the disease but incorrectly tested positive.
3
Calculate the total number of positive test results.
Total Positive Tests = TP + FP = 180 + 60 = 240
The denominator for calculating positive predictive value is all positive test results.
4
Calculate the Positive Predictive Value (PPV).
PPV = (180 / 240) * 100 = 75%
PPV is the proportion of true positives out of all positive test results.

Key Concept

Positive predictive value (PPV) is the probability that a patient with a positive test result actually has the disease. It is calculated as True Positives / (True Positives + False Positives).
Estimated Time:1m 0s
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