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The hazard ratio is the effect on this hazard rate of a difference, such as group membership (for example, treatment or control, male or female), as estimated by regression models that treat the logarithm of the HR as a function of a baseline hazard () and a linear combination of explanatory variables:
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.
In epidemiology, a rate ratio, sometimes called an incidence density ratio or incidence rate ratio, is a relative difference measure used to compare the incidence rates of events occurring at any given point in time. It is defined as:
It is computed as , where is the incidence in the exposed group, and is the incidence in the unexposed group. If the risk of an outcome is increased by the exposure, the term absolute risk increase (ARI) is used, and computed as I e − I u {\displaystyle I_{e}-I_{u}} .
In a proportional hazards model, the unique effect of a unit increase in a covariate is multiplicative with respect to the hazard rate. The hazard rate at time is the probability per short time dt that an event will occur between and + given that up to time no event has occurred yet. For example, taking a drug may halve one's hazard rate for a ...
It is computed as () /, where is the incidence in the exposed group, and is the incidence in the unexposed group. If the risk of an adverse event is increased by the exposure rather than decreased, the term relative risk increase (RRI) is used, and it is computed as ( I e − I u ) / I u {\displaystyle (I_{e}-I_{u})/I_{u}} .
Increase in incidence in the exposed group, such as "each daily alcoholic beverage increases the incidence of breast cancer by 11 cases per 1000 women." [ 9 ] Hazard ratio , such as "an increase in both total and invasive breast cancers in women randomized to receive estrogen and progestin for an average of 5 years, with a hazard ratio of 1.24 ...
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.