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Diagnostic tests of medical conditions can have several types of results. The te

ID: 3062845 • Letter: D

Question

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 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.

(a) P(+ | condition present); this is known as the sensitivity of a test.

(b) P( | condition present); this is known as the false-negative rate.

(c) P( | condition absent); this is known as the specificity of a test.

(d) P(+ | condition absent); this is known as the false-positive rate.

(e) P(condition present and +); this is the predictive value of the test.

(f) P(condition present and ).

Condition Present Condition Absent Row Total Test Result + 101 29 130 Test Result 18 52 70 Column Total 119 81 200

Explanation / Answer

a)  P(+ | condition present)=101/119=0.8487

b) P( | condition present) =18/119 =0.1513

c) P( | condition absent)=52/81=0.6420

d)P(+ | condition absent) =29/81=0.3580

e) P(condition present and +) =101/200 =0.505

f) P(condition present and ) =18/200=0.09