# Case control studies and odds ratio

Example: If the probability of an event is 0. The case-control design is very efficient.

### Case control study

We illustrate the technique with data from a nested case-control study of the risk of acute cardiac death associated with the use of bronchodilator drugs within a cohort of 12, asthmatics, with smoking as the confounder of interest. A study is done to examine whether there is an association between use of multivitamins and risk of coronary artery disease heart attacks. The odds are defined as the probability that the event will occur divided by the probability that the event will not occur. Odds ratios are used to compare the relative odds of the occurrence of the outcome of interest e. What the economist had actually said was, "Whether we reach the technical definition [of a double-dip recession] I think is probably close to The most logical approach would be to calculate the attributable risk percent of each of the drinking groups using the non-drinkers as a reference group. The probability that an event will occur is the fraction of times you expect to see that event in many trials. In other words, the exponential function of the regression coefficient eb1 is the odds ratio associated with a one-unit increase in the exposure. Wayne W. Risk difference can't be calculated because there is more than one risk category. In that situation, the fact of confounding can be verified by assessing the association between exposure and a confounder in the cases, but the data are insufficient to produce an adjusted estimate of the relative risk if confounding is found to be present. The investigators group the subjects into four risk categories: a non-drinkers, b less than two drinks per week, c less than two drinks per day, d greater than two drinks per day.

Compared to people who do not take vitamins, individuals who take daily multivitamins have a risk ratio of 0.

In that situation, the fact of confounding can be verified by assessing the association between exposure and a confounder in the cases, but the data are insufficient to produce an adjusted estimate of the relative risk if confounding is found to be present.

## Odds ratio vs relative risk

The odds ratio can also be used to determine whether a particular exposure is a risk factor for a particular outcome, and to compare the magnitude of various risk factors for that outcome. It was noted earlier in the module that the attributable proportion among the exposed in cohort type studies can also be calculated from the formula: Since the OR is an estimate of RR, then by analogy the attributable proportion among the exposed can be estimated in a case-control study from the formula: This can also be expressed as a percentage by multiplying by The investigators group the subjects into four risk categories: a non-drinkers, b less than two drinks per week, c less than two drinks per day, d greater than two drinks per day. In other words, the exponential function of the regression coefficient eb1 is the odds ratio associated with a one-unit increase in the exposure. A cohort study is conducted to investigate whether there is an association between alcohol consumption and esophageal cancer. So, I can't compute the probability of disease in each exposure group, but I can compute the odds of disease in each group. An odds ratio OR is a measure of association between an exposure and an outcome. What is an odds ratio? Risk difference can't be calculated because there is more than one risk category.

The risk difference in this study is 0. The investigators group the subjects into four risk categories: a non-drinkers, b less than two drinks per week, c less than two drinks per day, d greater than two drinks per day. Relative risk can't be calculated because there is more than one risk category. The most logical approach would be to calculate the risk difference of each of the drinking groups using the non-drinkers as a reference group.

It was noted earlier in the module that the attributable proportion among the exposed in cohort type studies can also be calculated from the formula: Since the OR is an estimate of RR, then by analogy the attributable proportion among the exposed can be estimated in a case-control study from the formula: This can also be expressed as a percentage by multiplying by

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