These observational studies look at two groups based on outcome; individuals with disease, or cases, and similar individuals without disease, or controls. Looking retrospectively, the study seeks to identify risk factors common among these groups and then calculate how much a given risk factor weighs on the outcome. This calculation is quantified as the odds ratio.
An odds ratio provides the probability that an individual with a disease or specific outcome was exposed to a risk factor at some point in the past.
The numerator of the formula compares the groups of people who have the disease and the odds that the people in these groups were exposed to a risk factor.
The numerator of the formula is calculated by dividing those with disease and exposure (a) by those with disease but without exposure (c).
This division step should be carried out last. First, divide the two terms found in the numerator and denominator respectively before dividing them altogether. Alternatively, you may rearrange the formula so that it becomes (a*d)/(b*c).
The denominator of the formula compares the groups of people who do not have the disease and the odds that the people in these groups were exposed to a risk factor.
The denominator of the formula is calculated by dividing those without disease but with exposure (b) by those without disease or exposure (d).
If the odds ratio is equal to one, then this implies that there is no association between the outcome and exposure, or in other words, exposure is not a risk factor for the outcome.
When the odds of exposure for those with the outcome (cases) is more than those without the outcome (controls), it implies that exposure may increase the risk of disease.
When the odds of exposure for those with the outcome (cases) is less than those without the outcome (controls), it implies that exposure may reduce the risk of disease.
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