Question 8.113

82. In the 1970s, a group of children in Lyme, Connecticut, developed rheumatoid arthritis. However, it took until the 1980s for researchers to determine the cause of their disease, now known as Lyme disease—deer ticks infected with Borrelia burgdorferi. ELISA (enzyme-linked immunosorbent assay) is a commonly administered first test for Lyme disease. It correctly identifies patients with Lyme disease (the test is positive) 93.7% of the time and gives false positive results (the test is positive for patients who do not have Lyme disease) 6% of the time.

  1. Suppose that in a community in the Northeast, the prevalence of Lyme disease is 0.5%. Given that a person from this community tests positive for Lyme disease, what is the probability that the person actually has Lyme disease?
  2. Most people are tested only when there is a suspicion that they may have been bitten by a tick. Suppose the prevalence of Lyme disease among those tested is 10%. Given that a person tests positive for Lyme disease, what is the probability that the person actually has Lyme disease?