There are two general ways to compare a treatment and a control group, relative comparisons and absolute comparisons. For a relative comparison, the basic computation is division. When the ratio A/B is larger than one, that implies that A is superior to B. For an absolute comparison, the basic computation is subtraction. When the difference A-B is greater than zero, that implies that A is superior to B. The distinction between relative and absolute is not the only important distinction, but it does represent a fundamental property of measures of effectiveness. Relative measures represent measures where the fundamental calculation is a division and absolute measures represent measures where the fundamental calculation is a subtraction.
Surprisingly, the choice between division and subtraction is critical. Relative and absolute comparisons often paint quite a different picture. There is substantial consensus in the evidence-based medicine community that relative measures of risk (such as an odds ratio or relative risk) tend to be misperceived by clinicians and patients and that they get a better sense of the value of a treatment when they receive information presented on an absolute scale (such as an absolute risk reduction or a number needed to treat). The general trend is that interventions appear more attractive when presented in relative terms, but less attractive when presented in absolute terms. The effect is strongest when the events being compared are relatively rare.
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