A researcher wishes to determine the association between oral contraceptive (OC)

Question

A researcher wishes to determine the association between oral contraceptive (OC) intake and cardiac disease. She plans to design a case-control study in which cases will be women who have experienced an MI and controls would be women with no MI. Suppose that the proportion PC of women who are exposed to OC among the controls is 45% and that the smallest OR the investigator will consider as clinically meaningful is 1.8. What is the value of POC (the proportion of women with MI who are exposed to OC) that corresponds to a clinically important difference, as defined by the investigator?

Explanation / Answer

Lets set up a basic 2x2 table. (+)MI (-)MI (+)OC A B (-)OC C D Next we find out how many people had MIs versus controls using the Odds Ratio. We are told the odds ratio is 1.8 for those exposed to OC. That means for every person exposed to OCs, they are 1.8 times as likely to have an MI than someone not exposed to OC. The odds ratio OR is related to the 2x2 table entries by the formula: OR = [A/(A+C)]x[(B+D)/B] We also know that B/(B+D) is the proportion of the control group that was exposed to OC, or 45%. But the question is looking for the POC, which is A/(A+C). So in other words, the odds ratio gives us all the invormation we need since: OR = POC x 1/0.45 This is because (B+D)/B is the reciprocal of the percentage of controls exposed to OC, given as 45% in the problem. Therefore, POC = OR*0.45, or 1.8*0.45 = 0.81, or 81%. Hope that helps! Jonathan

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