Describing Magnitude of an Effect
the magnitude of the difference in outcome between an exposed group and an unexposed group is determined by the relative risk
The relative risk is the ratio of the probability of an outcome in an exposed group to the probability of an outcome in an unexposed group.
It is computed as , where is the incidence in the exposed group, and is the incidence in the unexposed group.[1]
, where 
is the incidence in the exposed group, and 
is the incidence in the unexposed group.Together with risk difference and odds ratio, relative risk measures the association between the exposure and the outcome.[2]
Relative risk — The relative risk (or risk ratio) equals the incidence in exposed individuals divided by the incidence in unexposed individuals. The relative risk can be calculated from studies in which the proportion of patients exposed and unexposed to a risk is known, such as a cohort study. (See 'Cohort study' below.)
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Odds ratio — The odds ratio equals the odds that an individual with a specific condition has been exposed to a risk factor divided by the odds that a control has been exposed. The odds ratio is used in case-control studies and is often generated in multivariate analyses as well. The odds ratio provides a reasonable estimate of the relative risk for uncommon conditions.
The relative risk and odds ratio are interpreted relative to the number one. An odds ratio of 0.6, for example, suggests that patients exposed to a variable of interest were 40 percent less likely to develop a specific outcome compared to the control group. Similarly, an odds ratio of 1.5 suggests that the risk was increased by 50 percent.
Absolute risk — The relative risk and odds ratio provide an understanding of the magnitude of risk compared with a standard. However, it is more often desirable to know information about the absolute risk (also known as risk difference). As an example, a 40 percent increase in mortality due to a particular exposure does not provide direct insight into the likelihood that exposure in an individual patient will lead to mortality. In some cases, a large relative risk reduction may not be clinically important. A 50 percent reduction in an outcome, for example, is much more impressive if the baseline rate of the outcome is 25 percent compared with 1 percent.
The "attributable risk" represents the difference in the rate of a disease in an exposed, compared with a non-exposed, population. It reflects the additional incidence of disease related to an exposure taking into account the background rate of the disease. The attributable risk is calculated by subtracting the incidence of a disease in non-exposed persons from the incidence of disease in exposed persons.
A related term, the "population attributable risk" is used to describe the contribution that an exposure has on the incidence of a specific disease in a population. It is calculated by multiplying the attributable risk by the prevalence of exposure to a risk factor in a population. The population attributable risk is particularly important when considering public health measures and the allocation of resources intended to reduce the incidence of a disease.
Number needed to treat — The benefit of an intervention can be expressed by the "number needed to treat" (NNT). NNT is the reciprocal of the absolute risk reduction (the absolute adverse event rate for placebo minus the absolute adverse event rate for treated patients). Its interpretation can be illustrated by the following sentence: "This study suggests that I would have to treat five patients with a drug to prevent one death."
As an example, consider a placebo-controlled trial involving 100 patients. Thirty patients died during the study period (10 receiving active drug and 20 receiving placebo) giving a mortality rate of 20 percent with active drug (10 divided by (10 +40)) versus 40 percent (20 divided by (20 + 30)) with placebo as shown in the left panel of the figure (figure 3). The difference between these two rates, the "risk difference", is used to calculate NNT.
●40 percent minus 20 percent = 20 percent = 0.2
●1 divided by 0.2 = 5
Thus, this study suggests that only five patients need to be treated with the drug (compared with placebo) to prevent one death.
Because it is intuitive, the NNT has become an increasingly popular expression of absolute benefit or risk, potentially allowing for comparison of the relative benefit (or harm) of different interventions. However, the NNT can be misleading:
●It implies that the option is to treat or not to treat rather than to treat or switch to another more effective treatment [1].
●There are variations on how NNT is determined; NNTs from different studies cannot be compared unless the methods used to determine them are identical [2]. This may be a particular consideration when NNTs are calculated for treatment of chronic diseases in which outcomes (such as mortality) do not cluster in time.
●Calculation of the NNT depends upon the control rate (ie, the rate of events in the control arm). The control rate can be variable (particularly in small controlled trials, which are more vulnerable to random effects). As a result, the NNT may not accurately reflect the benefit of an intervention if events occurred in the control arm more or less than would be expected based upon the biology of the disease. This effect can be particularly problematic when comparing the NNTs among placebo controlled trials (figure 3) [3].
When the outcome is a harm rather than a benefit, a number needed to harm (NNH) can be calculated similarly. As an example, if statin therapy causes myalgias in 5 percent of patients, then treating 20 patients with statins would be expected to cause one case of myalgia, for an NNH of 20. Other variations that sometimes appear in the medical literature include number needed to prevent and number needed to diagnose.