A life insurer is considering using electrocardiograms (EKGs) as an indicator of

Question

A life insurer is considering using electrocardiograms (EKGs) as an indicator of death due to heart disease. According to past studies, the insurer is expecting 7% of their insured population to die from heart disease. Since the insurer issues whole life policies it is assumed all policyholders that don't die from heart disease die from some other cause. That is, there are no canceled policies. The EKG manufacturer advertises that a death due to heart disease will have been noted by a previous abnormal EKG, performed at policy issue, 80% of the time. A non-heart disease death will also exhibit an abnormal EKG 10% of the time. What is the probability that an abnormal EKG will lead to a heart disease related death?

Explanation / Answer

HEre Pr (Randomly ensured person die from heart disease) = 0.07

so, Pr( Death by any other disease) = 1 - 0.07 = 0.93

Pr(Death due to heart disease noted by previous abnormal EKG) = 0.80

Pr(Death due to non- heart disease noted by previous abnormal EKG) = 0.10

Pr(abnormal EKG will lead heart disease related death)

= Pr(Heart Disease and lead by abnormal EKG) / [Pr(death by normal cause and abnormal EKG) + Pr(Death by hearrt disease and abnormal EKG) ]

= 0.07 * 0.80/ (0.07 * 0.80 + 0.93 * 0.1)

= 56/149

= 0.376

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