Chapter 4.2, Problem 31P

Survey: Lung/Heart In an article titled “Diagnostic accuracy of fever as a measure of postoperative pulmonary complications” (Heart Lung, Vol. 10, No. 1, p. 61), J. Roberts and colleagues discuss using a fever of 38°C or higher as a diagnostic indicator of postoperative atelectasis (collapse of the lung) as evidenced by x-ray observation. For fever ≥38°C as the diagnostic test, the results for postoperative patients are

For the meaning of + and −, see Problem 30.

Complete parts (a) through (f) from Problem 30.

30. Survey: Medical Tests Diagnostic tests of medical conditions can have several types of results. The test result can be positive or negative, whether or not a patient has the condition. A positive test (+) indicates that the patient has the condition. A negative test (−) indicates that the patient does not have the condition. Remember, a positive test does not prove that the patient has the condition. Additional medical work may be required. Consider a random sample of 200 patients, some of whom have a medical condition and some of whom do not. Results of a new diagnostic test for the condition are shown.

Assume the sample is representative of the entire population. For a person selected at random, compute the following probabilities:

1. (a) P(+ | condition present); this is known as the sensitivity of a test.
2. (b) P(− | condition present); this is known as the false-negative rate.
3. (c) P(− | condition absent); this is known as the specificity of a test.
4. (d) P(+ | condition absent); this is known as the false-positive rate.
5. (e) P(condition present and +); this is the predictive value of the test.
6. (f) P(condition present and −).