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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.
Diagnostic odds ratios less than one indicate that the test can be improved by simply inverting the outcome of the test – the test is in the wrong direction, while a diagnostic odds ratio of exactly one means that the test is equally likely to predict a positive outcome whatever the true condition – the test gives no information.
Names of (fictional) studies are shown on the left, odds ratios and confidence intervals on the right. Wikimedia Commons has media related to Forest plots . A forest plot , also known as a blobbogram, is a graphical display of estimated results from a number of scientific studies addressing the same question, along with the overall results. [ 1 ]
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 ...
This exponential relationship provides an interpretation for : The odds multiply by for every 1-unit increase in x. [ 22 ] For a binary independent variable the odds ratio is defined as a d b c {\displaystyle {\frac {ad}{bc}}} where a , b , c and d are cells in a 2×2 contingency table .
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 ...
and = / / = While the prevalence is only 9% (9/100), the odds ratio (OR) is equal to 11.3 and the relative risk (RR) is equal to 7.2. Despite fulfilling the rare disease assumption overall, the OR and RR can hardly be considered to be approximately the same. However, the prevalence in the exposed group is 40%, which means is not sufficiently small