The number of cases of Lyme disease, a tick-borne illness, more than doubled between 2001 and 2015 in North America. A vaccine for Lyme disease was approved by the U.S. Food and Drug Administration in 1998, but it was then removed from the market just 3 years later (Nigrovic and Thompson 2007). Did it work? A clinical trial of the efficacy of this vaccine compared 5469 people who received the vaccine to 5467 people who received a placebo (Steere et al. 1998). Of these, 15 people with the vaccine had developed Lyme disease after 2 years, and 65 people in the placebo control group had developed the disease. In the same study, side effects were also tracked. The most severe possible side effect was joint pain. Of the vaccinated group, 71 people had joint pain, while in the control group 6 people had joint pain.

a. Calculate the relative risk of getting Lyme disease for patients who received the vaccine compared to those who did not.

b. Based on that relative risk calculation, by what amount does the vaccine reduce the rate of getting Lyme disease?

c. Do these data provide evidence that the vaccine was effective in reducing the rate of contracting Lyme disease? Carry out an appropriate hypothesis test.

d. What is the relative risk of joint pain for vaccinated patients compared to the controls?

e. Is there evidence that the probability of joint pain is different between vaccinated and control groups? Do a hypothesis test.