Odds ratios frequently are used to present strength of association between risk factors and outcomes in the clinical literature. Odds and odds ratios are related to the probability of a binary outcome (an outcome that is either present or absent, such as mortality). The odds are the ratio of the probability that an outcome occurs to the probability that the outcome does not occur. For example, suppose that the probability of mortality is 0.3 in a group of patients. This can be expressed as the odds of dying: 0.3/(1 − 0.3) = 0.43. When the probability is small, odds are virtually identical to the probability. For example, for a probability of 0.05, the odds are 0.05/(1 − 0.05) = 0.052. This similarity does not exist when the value of a probability is large.
Norton EC, Dowd BE, Maciejewski ML. Odds Ratios—Current Best Practice and Use. JAMA. 2018;320(1):84–85. doi:10.1001/jama.2018.6971
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