Chapter 4.18, Problem 34E

In a January 15, 1998, article, the New England Journal of Medicine (338:141–146) reported on the utility of using computerized tomography (CT) as a diagnostic test for patients with clinically suspected appendicitis. In at least 20% of patients with appendicitis, the correct diagnosis was not made. On the other hand, the appendix was normal in 15% to 40% of patients who under- went emergency appendectomy. A study was designed to determine the prospective effectiveness of using CT as a diagnostic test to improve the treatment of these patients. The study examined 100 consecutive patients suspected of having acute appendicitis who presented to the emergency department or were referred there from a physician’s office. The 100 patients underwent a CT scan, and the surgeon made an assessment of the presence of appendicitis for each of the patients. The final clinical outcomes were determined at surgery and by pathological examination of the appendix after appendectomy or by clinical follow-up at least 2 months after CT scanning.

The 1996 rate of occurrence of appendicitis was approximately P(C) − .00108.

1. a. Find the sensitivity and specificity of the radiological determination of appendicitis.
2. b. Find the probability that a patient truly had appendicitis given that the radiological determination was definitely appendicitis (DA).
3. c. Find the probability that a patient truly did not have appendicitis given that the radiological determination was definitely appendicitis (DA).
4. d. Find the probability that a patient truly did not have appendicitis given that the radiological determination was definitely not appendicitis (DNA).