Question 2. Diagnostic tests: A few calculations Purpose : This question attempt

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Question 2. Diagnostic tests: A few calculations

Purpose: This question attempts to help you understand some of the concepts surrounding diagnostic tests.

About 11.3% of the U.S. population aged 65 and over have Alzheimer’s disease. A medical research team wished to evaluate a proposed screening test for Alzheimer’s disease. The test was given to a random sample of 4,000 individuals who were 65 years of age or older. Alzheimer’s disease was confirmed in 450 of them (admittedly, confirmation was with an imperfect, but a well-accepted, standard). The results of the performance of the diagnostic test were as follows:

Alzheimer’s Diagnosis

Test Result

Yes

No

Positive

436

35

Negative

14

3515

Calculate AND provide an interpretation of the following (show your work):

Sensitivity:

Specificity:

False positive rate (or proportion):

False negative rate (or proportion):

Positive predictive value (predictive value of a positive test):

Negative predictive value (predictive value of a negative test):

Alzheimer’s Diagnosis

Test Result

Yes

No

Positive

436

35

Negative

14

3515

Explanation / Answer

A) sensitivity = 436/(436 + 14) * 100 = 436/450 * 100 = 96.89

B) specificity = 3515/(3515 + 35) * 100 = 3515/3550 * 100 = 99.01%

C) False positive = (1 - specificity) * ( 1 - prevalence)

= (1 - 0.9689) * ( 1 - (436 + 14)/(436 + 14 + 35 + 3515)) = 0.0311 * (1 - 0.1125) = 0.0311 * 0.8875 = 0.0276

D) False negative = (1 - sensitivity) * prevalence

= 0.0311 * 0.1125 = 0.0035

E) Positive predictive value = 436/(436 + 35) * 100 = 436/471 * 100 = 92.57%

F) Negative predictive value = 3515/(3515 + 14) * 100 = 3515/3529 * 100 = 99.60%

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