Dictionary of Evidence-based Medicine.pdf

Dictionary of Evidence-based Medicine 143
Risk difference (see under Risk)
Risk ratio (see under Risk)
Risk reduction
In assessing and attributing risk, it is best to express the risk relative to a
control (see under Risk). For example, in estimating by how much an antibiotic
reduces the risk of traveller's diarrhoea, we could observe 100 patients
receiving it and report how many (say five) develop diarrhoea. The
estimate of absolute risk of diarrhoea would be 5/100 or 0.05. This figure,
however, does not tell us by how much the antibiotic has reduced the incidence
of diarrhoea. To do this, we may study a control group of patients
given a placebo to obtain another estimate of risk of diarrhoea for this
group of patients (say 10/100 or 0.1). The difference in the two rates (0.05)
gives us an estimate of the risk reduction in absolute terms. For this reason
this value is called the absolute risk reduction (ARR). On average, five
fewer patients out of 100 treated would develop diarrhoea than if they
received a placebo.
The reciprocal of the risk reduction gives us the number needed to treat
(see NNT), 20 in this instance. The NNT tells us that on average 20 patients
need to be given antibiotics for one more patient to be protected from
diarrhoea when compared to placebo.
The risk reduction may also be expressed as a proportion or percentage
of the risk in the control group to produce a relative risk reduction (RRR),
expressed as a proportion or percentage. In the above example, the relative
risk reduction is given by (0.1 - 0.05)/0.10 or 0.5. Expressed as a percentage
the RRR is 50%. This appears more impressive than the ARR of 0.05 or 5%.
It is worth noting that, perhaps confusingly, both the absolute and the
relative risk reduction terms are relative to a control group. The terms used
refer to how the values are expressed. The RRR is as a proportion or percentage
of the control rate or risk while the ARR is on its own.
Root mean square error
The root mean square error (RMSE) is an estimate of the standard deviation
associated with experimental error. For a sample of n observations
x v x x ,...,x n , the root mean square error or standard deviation is defined as: