Odds Ratio (OR)
An Odds Ratio (OR) is a ratio that ...
- Context:
- range: Odds Score.
- It can be converted to a Log-Odds Ratio.
- See: Statistical Population, Risk Ratio, Absolute Risk Reduction, Case-Control Study, Rare Disease Assumption, Effect Size, Association (Statistics).
References
2015
- (Wikipedia, 2015) ⇒ http://en.wikipedia.org/wiki/Odds_ratio Retrieved:2015-1-15.
- In statistics, the odds ratio (usually abbreviated "OR") is one of three main ways to quantify how strongly the presence or absence of property A is associated with the presence or absence of property B in a given population. If each individual in a population either does or does not have a property "A", (e.g. "high blood pressure"), and also either does or does not have a property "B" (e.g. "moderate alcohol consumption") where both properties are appropriately defined, then a ratio can be formed which quantitatively describes the association between the presence/absence of "A" (high blood pressure) and the presence/absence of "B" (moderate alcohol consumption) for individuals in the population. This ratio is the odds ratio (OR) and can be computed following these steps:
- For a given individual that has "B" compute the odds that the same individual has "A"
- For a given individual that does not have "B" compute the odds that the same individual has "A"
- Divide the odds from step 1 by the odds from step 2 to obtain the odds ratio (OR).
- The term "individual" in this usage does not have to refer to a human being, as a statistical population can measure any set of entities, whether living or inanimate.
If the OR is greater than 1, then having "A" is considered to be "associated with having "B" in the sense that the having of "B" raises (relative to not-having "B") the odds of having "A". Note that this is not enough to establish that B is a contributing cause of "A": it could be that the association is due to a third property, "C", which is a contributing cause of both "A" and "B".
The two other major ways of quantifying association are the risk ratio ("RR") and the absolute risk reduction ("ARR"). In clinical studies and many other settings, the parameter of greatest interest is often actually the RR, which is determined in a way that is similar to the one just described for the OR, except using probabilities instead of odds. Frequently, however, the available data only allows the computation of the OR; notably, this is so in the case of case-control studies, as explained below. On the other hand, if one of the properties (say, A) is sufficiently rare (the “rare disease assumption"), then the OR of having A given that the individual has B is a good approximation to the corresponding RR (the specification "A given B" is needed because, while the OR treats the two properties symmetrically, the RR and other measures do not).
In a more technical language, the OR is a measure of effect size, describing the strength of association or non-independence between two binary data values. It is used as a descriptive statistic, and plays an important role in logistic regression.
- In statistics, the odds ratio (usually abbreviated "OR") is one of three main ways to quantify how strongly the presence or absence of property A is associated with the presence or absence of property B in a given population. If each individual in a population either does or does not have a property "A", (e.g. "high blood pressure"), and also either does or does not have a property "B" (e.g. "moderate alcohol consumption") where both properties are appropriately defined, then a ratio can be formed which quantitatively describes the association between the presence/absence of "A" (high blood pressure) and the presence/absence of "B" (moderate alcohol consumption) for individuals in the population. This ratio is the odds ratio (OR) and can be computed following these steps:
2000
- (Bland & Altman, 2000) ⇒ J. Martin Bland, and Douglas G. Altman. (2000). “The Odds Ratio.” In: Bmj, 320(7247).
- ABSTRACT: In recent years odds ratios have become widely used in medical reports — almost certainly some will appear in today's BMJ. There are three reasons for this. Firstly, they provide an estimate (with confidence interval) for the relationship between two binary (“yes or no”) variables. Secondly, they enable us to examine the effects of other variables on that relationship, using logistic regression. Thirdly, they have a special and very convenient interpretation in case-control studies (dealt with in a future note).
The odds are a way of representing probability, especially familiar for betting. For example, the odds that a single throw of a die will produce a six are 1 to 5, or 1/5. The odds is the ratio of the probability that the event of interest occurs to the probability that it does not. This is often estimated by the ratio of the number of times that the event of interest occurs to the number of times that it does not. The table shows data from a cross sectional study showing the prevalence of hay fever and eczema in 11 year old children.1 The probability that a child with eczema will also have hay fever is estimated by the proportion 141/561 (25.1%). The odds is estimated by 141/420. Similarly, for children without eczema the probability of having hay fever is estimated by 928/14 453 (6.4%) and the odds is 928/13 525. We can compare the groups in several ways: by the difference between the proportions, 141/561−928/14 453=0.187 (or 18.7 percentage points); the ratio of the proportions, (141/561)/(928/14 453)=3.91 (also called the relative risk); or the odds ratio, (141/420)/(928/13 525)=4.89.
- ABSTRACT: In recent years odds ratios have become widely used in medical reports — almost certainly some will appear in today's BMJ. There are three reasons for this. Firstly, they provide an estimate (with confidence interval) for the relationship between two binary (“yes or no”) variables. Secondly, they enable us to examine the effects of other variables on that relationship, using logistic regression. Thirdly, they have a special and very convenient interpretation in case-control studies (dealt with in a future note).