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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 ...
The above formula shows that once the are fixed, we can easily compute either the log-odds that = for a given observation, or the probability that = for a given observation. The main use-case of a logistic model is to be given an observation x {\displaystyle {\boldsymbol {x}}} , and estimate the probability p ( x ) {\displaystyle p({\boldsymbol ...
In fact, it can be shown that the unconditional analysis of matched pair data results in an estimate of the odds ratio which is the square of the correct, conditional one. [ 2 ] In addition to tests based on logistic regression, several other tests existed before conditional logistic regression for matched data as shown in related tests .
Suppose the odds ratio between the two is 1 : 1. Now if the option of a red bus is introduced, a person may be indifferent between a red and a blue bus, and hence may exhibit a car : blue bus : red bus odds ratio of 1 : 0.5 : 0.5, thus maintaining a 1 : 1 ratio of car : any bus while adopting a changed car : blue bus ratio of 1 : 0.5.
Formula Value Absolute risk reduction : ARR CER − EER: 0.3, or 30% Number needed to treat: NNT 1 / (CER − EER) 3.33 Relative risk (risk ratio) RR EER / CER: 0.25 Relative risk reduction: RRR (CER − EER) / CER, or 1 − RR: 0.75, or 75% Preventable fraction among the unexposed: PFu (CER − EER) / CER: 0.75 Odds ratio: OR (EE / EN) / (CE ...
The act of conditioning on the marginal success rate from a 2×2 table can be shown to ignore some information in the data about the unknown odds ratio. [22] The argument that the marginal totals are (almost) ancillary implies that the appropriate likelihood function for making inferences about this odds ratio should be conditioned on the ...
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.