Treatment of patients whose injury might cause massive blood loss has involved giving them plasma transfusions after they had been admitted to the emergency room.

Sperry et al. (2018) investigated whether earlier use of this treatment—by emergency first responders before patients reached the hospital—could be effective. In a randomized control trial, patients with trauma either did or did not receive a plasma transfusion during air medical transport. (All patients also received standard care.) Of the 220 patients who received plasma, 53 died within 30 days after injury. Of the 261 patients who received only standard care, 89 died within 30 days.

a. Estimate the relative risk of death for trauma patients who have received plasma compared to those who did not.

b. By what amount is the relative risk of death reduced by the plasma treatment?

c. Calculate the odds ratio of death, comparing these two groups. What is the 95% confidence interval for that odds ratio?