and it is theretore very important to obtain some estimate of disease prevalence. Exercises A medical research team wishes to assess the usefulness of a certain symptom (call it S) in the diagnosis of a particular disease. In a random sample of 775 patients with the disease, 744 reported having the symptom. In an independent random sample of 1380 subjects without the disease, 21 reported that they had the symptom. (a) In the context of this exercise, what is a false positive? (b) What is a false negative? (c) Compute the sensitivity of the symptom. (d) Compute the specificity of the symptom. (e) Suppose it is known that the rate of the disease in the general population is. 001. What is the predictive value positive of the symptom? (f) What is the predictive value negative of the symptom? (g) Find the predictive value positive and the predictive value negative for the symptom for the following hypothetical disease rates: .0001, .01, and .10. (h) What do you conclude about the predictive value of the symptom on the basis of the results obtained in part g? 3.5.1 SOME BASIC PROBABILITY CONCEPTS In an article entitled "Bucket-Handle Meniscal Tears of the Knee: Sensitivity and Speci- ficity of MRI signs," Dorsay and Helms (A-5) performed a retrospective study of 71 knees scanned by MRI. One of the indicators they examined was the absence of the "bow-tie sign" in the MRI as evidence of a bucket-handle or "bucket-handle type" tear of the menis- cus. In the study, surgery confirmed that 43 of the 71 cases were bucket-handle tears. The cases may be cross-classified by “bow-tie sign" status and surgical results as follows: 3.5.2 Tear Surgically Confirmed Tear Surgically Confirmed (D) As Not Present (D) Total 38 10 48 Positive Test (absent bow-tie sign) (T) 5 Negative Test (bow-tie sign present) (T) 18 23 43 Total 28 71 Source: Theodore A. Dorsay and Clyde A. Helms, "Bucket-handle Meniscal Tears of the Knee: Sensitivity and Specificity of MRI Signs," Skeletal Radiology, 32 (2003), 266–272. (a) What is the sensitivity of testing to see if the absent bow tie sign indicates a meniscal tear? (b) What is the specificity of testing to see if the absent bow tie sign indicates a meniscal tear? (c) What additional information would you need to determine the predictive value of the test?