Migraine with aura is a potentially debilitating condition, yet little is known about its causes. A case-control study compared 93 people who suffer from chronic migraine with aura (cases) to a sample of 93 healthy patients (controls; Schwerzmann et al. 2005). The researchers used transesophageal echocardiography to look for cardiac shunts in all of these patients. (A cardiac shunt is a heart defect that causes blood to flow from the right to the left in the heart, causing poor oxygenation.) Forty-four of the migraine patients were found to have a cardiac shunt, while only 16 of the people without migraine symptoms had this heart defect.

a. Is this an observational or experimental study?

b. Show the association between migraines and cardiac shunts with a mosaic plot.

c. How strong is the association between migraines and cardiac shunts? Calculate the odds ratio for migraine, comparing the patients with and without cardiac shunts.

d. What is the 95% confidence interval for this odds ratio?