Researchers collected data from an observational study to investigate the association between smoking status and the presence of aortic stenosis, a narrowing of the aorta that impedes blood flow to the body.

(a) What percentage of the 215 participants were both smokers and had aortic stenosis? This percentage is one component of the joint distribution of smoking and stenosis; what are the other three numbers of the joint distribution?

(b) Among the smokers, what proportion have aortic stenosis? This number is a component of the conditional distribution of stenosis for the two categories of smokers. What proportion of non-smokers have aortic stenosis?

(c) In this context, relative risk is the ratio of the proportion of smokers with stenosis to the proportion of non-smokers with stenosis. Relative risks greater than 1 indicate that smokers are at a higher risk for aortic stenosis than non-smokers; relative risks of 1.2 or higher are generally considered cause for alarm.
Calculate the relative risk for the 215 participants, comparing smokers to non-smokers. Does there seem to be evidence that smoking is associated with an increased probability of stenosis?

Transcribed Image Text:

Smoking Status Non-smoker Smoker Total Absent 67 43 110 Disease Status Present 54 51 105 Total 121 94 215