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The relative risk (RR) or risk ratio is the ratio of the probability of an outcome in an exposed group to the probability of an outcome in an unexposed group. Together with risk difference and odds ratio, relative risk measures the association between the exposure and the outcome. [1]
Therefore, the relative risk is 1.28. Since rather large probabilities of passing were used, there is a large difference between relative risk and odds ratio. Had failure (a smaller probability) been used as the event (rather than passing), the difference between the two measures of effect size would not be so great.
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.
The rare disease assumption is a mathematical assumption in epidemiologic case-control studies where the hypothesis tests the association between an exposure and a disease. It is assumed that, if the prevalence of the disease is low, then the odds ratio (OR) approaches the relative risk (RR). The idea was first demonstrated by Jerome Cornfield. [1]
It is defined as the inverse of the absolute risk increase, and computed as / (), where is the incidence in the treated (exposed) group, and is the incidence in the control (unexposed) group. [1] Intuitively, the lower the number needed to harm, the worse the risk factor, with 1 meaning that every exposed person is harmed.
Calculation of probability (risk) vs odds. In statistics, odds are an expression of relative probabilities, generally quoted as the odds in favor.The odds (in favor) of an event or a proposition is the ratio of the probability that the event will happen to the probability that the event will not happen.
The relative risk reduction is 0.5 (50%), while the absolute risk reduction is 0.0001 (0.01%). The absolute risk reduction reflects the low probability of getting colon cancer in the first place, while reporting only relative risk reduction, would run into risk of readers exaggerating the effectiveness of the drug. [5]
Both the relative risk and odds ratio are relevant in retrospective cohort studies, but only the odds ratio can be used in case-control studies. Although most case-control studies are retrospective, they can also be prospective when the researcher still enrolls participants based on the occurrence of a disease as new cases occur. [citation needed]