Question

Baldness Screening Test tests for the presence of a biomarker that predicts future baldness in men. The true positive rate of the test is 85%, and the false positve rate is 25%. It is estimated that 60% of men will go bald in their lifetime. (A) This test costs $5000 per individual. If you were an insurance company, why would/would not you cover this test. Include calulations to justify your answer. ("Baldness is not a serious illness" may be part of your answer, but is not sufficient) (B) If your sister tested positive, explain why should she not be worried about going bald. Use a Bayesian argument ("She's a she, not a he" may be part of your answer, but is not sufficient). No calculations necessary.

Answer 1

Given

The true positive rate of the test = 85%

The false positive rate of the test = 25%

It is estimated that 60% of men will go bald in their lifetime

(a) The cost of the Test = $5000 per individual

As per the given problem true positive rate of the test is more than the false positve rate of the test. Which means every one will go for test again to check the baldness.

This way more than actual baldness patient will go for the test and can burden the company.

(b)

	Positive	Negative	Probabiiity
Bald	0.51	0.09	0.6
Not Bald	0.1	0.3	0.4
Total	0.61	0.39	1.00

The Probability of actual bald = Bald/total

= 0.51/0.61

= 0.8360

Which means that 83.60% of chances to get she is bald.