Problem: Developed a diagnostic test designed to detect celiac disease (gluten intolerance) and that this test can have either a positive or a negative result.
To characterize this test, we use it on 200 persons with newly diagnosed celiac disease and 200 persons without celiac disease. Among persons with celiac disease, 190 had positive test results. Among persons without celiac disease, 50 had positive test results.
Required:
1. Calculate sensitivity and specificity for the diagnostic test described. Provide your overall assessment of how well the test identifies people with and without the disease.
2. Using the calculated sensitivity and specificity, determine the positive predictive value of the test in a population of 10,000 people where the disease prevalence is 1%. Next, determine the positive predictive value of the test in a population of 10,000 people where the disease prevalence is 5%. Discuss the effectiveness of this diagnostic test in terms of the disease prevalence. Provide justifications and citations for your responses.