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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.
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 where a, b, c and d are cells in a 2×2 contingency table. [23]
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.
The curve represents the odds of an endpoint having occurred at each point in time (the hazard). The hazard ratio is simply the relationship between the instantaneous hazards in the two groups and represents, in a single number, the magnitude of distance between the Kaplan–Meier plots. [7] Hazard ratios do not reflect a time unit of the study.
The standard odds- or risk ratio of all strata could be calculated, giving risk ratios ,, …,, where is the number of strata. If the stratification were removed, there would be one aggregate risk ratio of the collapsed table; let this be R {\displaystyle R} .
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.
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. [21] 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 ...