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Odds ratio - Primer in Literature Interpretation Risk...

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he most direct way to determine if an exposure is associated with a condition is to prospectively follow 2 groups, one exposed and one unex- posed, and observe the frequency with which each group develops the condition. Relative risk, dis- cussed in the first part of this 2-part series on risk as- sessment ( Hospital Physician , October 2005), reflects the magnitude of the difference in the frequency of an outcome between groups. For a given exposure (and exposure could mean exposure to a risk factor or exposure to a treatment), the relative risk of an out- come is calculated as: Relative risk = Risk of the outcome with exposure Risk of the outcome without exposure Consider a study of 1000 people in which 500 are treated with a new drug and 500 are treated with place- bo. If 5 in the treatment group (1%) and 10 in the placebo group (2%) have heart attacks, the relative risk of heart attack with treatment would be 0.01/0.02, or 0.5. The risk of heart attack with treatment is one half the risk without treatment. The relative risk tells us the precise proportional dif- ference in risk between groups, and, as we saw in the previous article, can be easily calculated when groups with known outcome frequencies are studied. There are situations (eg, case-control studies) when all the necessary information to calculate a relative risk may not be available, but we still wish to measure the associ- ation between a risk factor and an outcome. Another frequently presented measure of this association is the odds ratio. WHEN THERE IS NO DENOMINATOR Calculating relative risk requires knowing the risk of an outcome with and without exposure. To determine risk, you must know not only the frequency of an out- come but also the size of the groups at risk. If you fol- lowed a defined group prospectively, you could precise- ly calculate the proportion that develops a condition of interest. When you have a nearly “captive population” (eg, those with a particular kind of insurance who would almost certainly seek medical care in a particu- lar setting), you can make reasonable assumptions about the size of the population, and thus make rea- sonable estimates of the true risk. What if you are suspicious that a particular exposure might increase the risk of developing a particular con- dition? Say you identify a group of patients with a can- cer and wish to determine if a particular exposure is a risk factor. It would be impractical, particularly if you are dealing with a rare condition, and unethical, to expose disease-free individuals to the potential risk fac- tor and measure the frequency of cancer development. You could, however, review the records of those with cancer and determine how many of them were ex- posed to the potential risk factor. You could then cre- ate a group of people otherwise similar, but without cancer, and determine the proportion of this group that was exposed to the potential risk factor. By per- forming this case-control study and comparing the proportion of those exposed with cancer (the cases) to
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