A diagnostic screening test for a particular disease has been shown empirically

Question

A diagnostic screening test for a particular disease has been shown empirically to be fairly reliable: a positive result is recorded in 98% of cases where a patient actually has the disease, and in 5% of cases where the patient is healthy. The disease is known to afflict 1 person in 500.

(a) The proportion of patients screen positive on this diagnostic test is (i) 0.20% (ii) 4.99% (iii) 5.19% (iv) 37.79%

(b) The proportion of those screening positive that are actually suffering from the disease is (i) 4.99% (ii) 5.19% (iii) 3.78% (iv) 37.79%

Explanation / Answer

Ans:

Given that

P(positive/disease)=0.98

P(positive/not disease)=0.05

P(disease)=1/500=0.002

a)

P(positive)=P(positive/disease)*P(disease)+P(positive/not disease)*P(not disease)

=0.98*0.002+0.05*(1-0.002)

=0.0519 or 5.19%

Option iii is correct(5.19%)

b)

P(disease/positive)=P(positive/disease)*P(disease)/P(positive)

=0.98*0.002/0.0519

=0.0378 or 3.78%

Option iii is correct(3.78%)

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