Question

A research study estimated that under a certain condition, the probability a subject would be referred for heart catheterization was 0.906 for whites and 0.847 for blacks. a. A press release about the study stated that the odds of referral for cardiac catheterization for blacks are 60% of the odds for whites. Explain how they obtained 60% (more accurately, 57%). b. An Associated Press story21 that described the study stated "Doctors were only 60% as likely to order cardiac catheterization for blacks as for whites." What is wrong with this interpretation? Give the correct percentage for this interpretation. (In stating results to the general public, it is better to use the relative risk than the odds ratio. It is simpler to understand and less likely to be misinterpreted.)

Answer 1

Answer and Step-by-step explanation:

a) The press release uses some weird relative risk method to arrive at this value.

P(B) = 0.847, Probability that a black is safe from being referred for cardiac carthetirization, P(B') = 1 - 0.847 = 0.153

P(W) = 0.907, P(W') = 1 - 0.907 = 0.094

The press release's relative risk = (0.847/0.153)/(0.907/0.094) = 0.574 = 57.4%

b) This is interpretation for relative risk, not the odds ratio. The actual relative risk is

(0.847/0.906) = 0.935: i.e., 60% should have been 93.5%.

Hope this helps!