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An odds ratio (OR) is a statistic that quantifies the strength of the association between two events, A and B. The odds ratio is defined as the ratio of the odds of event A taking place in the presence of B, and the odds of A in the absence of B. Due to symmetry, odds ratio reciprocally calculates the ratio of the odds of B occurring in the presence of A, and the odds of B in the absence of A.
In practice the odds ratio is commonly used for case-control studies, as the relative risk cannot be estimated. [1] In fact, the odds ratio has much more common use in statistics, since logistic regression, often associated with clinical trials, works with the log of the odds ratio, not relative risk. Because the (natural log of the) odds of a ...
"OR" stands for "odds ratio" and "RR" stands for "relative risk". A prospective cohort study is a longitudinal cohort study that follows over time a group of similar individuals ( cohorts ) who differ with respect to certain factors under study to determine how these factors affect rates of a certain outcome . [ 1 ]
Although in classical case–control studies, it remains true that the odds ratio can only approximate the relative risk in the case of rare diseases, there is a number of other types of studies (case–cohort, nested case–control, cohort studies) in which it was later shown that the odds ratio of exposure can be used to estimate the relative ...
where N is the ratio of cases to controls. As the odds ratio approaches 1, the number of cases required for statistical significance grows towards infinity; rendering case-control studies all but useless for low odds ratios. For instance, for an odds ratio of 1.5 and cases = controls, the table shown above would look like this:
Both the relative risk and odds ratio are relevant in retrospective cohort studies, but only the odds ratio can be used in case-control studies. Although most case-control studies are retrospective, they can also be prospective when the researcher still enrolls participants based on the occurrence of a disease as new cases occur. [citation needed]
The simplest measure of association for a 2 × 2 contingency table is the odds ratio. Given two events, A and B, the odds ratio is defined as the ratio of the odds of A in the presence of B and the odds of A in the absence of B, or equivalently (due to symmetry), the ratio of the odds of B in the presence of A and the odds of B in the absence of A.
Odds-ratios are often used in analysis of clinical trials. While they have useful mathematical properties, they can produce counter-intuitive results: an event with an 80% probability of occurring is four times more probable to happen than an event with a 20% probability, but the odds are 16 times higher on the less probable event (4–1 ...