Critical evaluation: Usefulness and risk

Last updated: Monday, October 03, 2022

In assessing the usefulness of a trial there are two important considerations: are the results of the trial clinically important and what is the size of the benefit (and any harm)?

It is essential to judge the clinical importance of a result. We can do this by checking if the outcome measured was disease-oriented or patient-oriented. For example, if a new osteoporosis drug increases bone mineral density we would call this a disease-oriented outcome (DOO). If the drug reduces the risk of fractures we call this a patient-oriented outcome (POO). So an increase in bone mineral density of 1%, for example, may be statistically significant but if the rate of fractures is not improved is this clinically important?

To quantify the size of the benefit and harms of a new treatment, some of the key terms you’ll see are:

  • Absolute risk reduction (ARR)
  • Relative risk (RR) and hazard ratio (HR)
  • Relative risk reduction (RRR)
  • Number needed to treat (NNT) and Number needed to harm (NNH)

We’re going to use an example to help you understand what these terms mean and how to calculate them. Consider a fictitious randomised, double-blind trial of ‘anotheraban’ versus placebo for the prevention of stroke over 2 years. Each group contains 2,000 volunteers. At the end of the study, the number of patients suffering a stroke in the anotheraban group is 120 and the number in the placebo group is 160.

The absolute risk (AR) of an event is simply the chance it will happen. To work out the absolute risk of a stroke in each group, divide the number of strokes by the number of volunteers:

AR placebo group = 160 ÷ 2000 = 0.08 or 8%

AR anotheraban group = 120 ÷ 2000 = 0.06 or 6%

The absolute risk reduction (ARR) is the difference in risk of stroke between the two groups:

ARR = 0.08 – 0.06 = 0.02 or 2%

This means that anotheraban reduces the absolute risk of a stroke by 2%.

Relative risk (RR) tells us how many times more or less likely an event will occur in the treatment group relative to the placebo group. It is the risk of the outcome in the treatment group divided by the risk in the placebo group. From the above, AR anotheraban is 0.06 and AR placebo is 0.08, so:

RR = 0.06 ÷ 0.08 = 0.75

As this result is less than 1.0, anotheraban has made the risk of stroke less likely compared to placebo.

Some studies may use the term hazard ratio (HR) instead of relative risk – the two terms are broadly equivalent but hazard ratios are useful when the risk is not constant over time. It is weighted for the number of patients in the trial at different time points.

The relative risk reduction (RRR) is an alternative way of expressing the difference in risk; it is the reduction in risk of an event in the treatment group relative to the risk in the placebo group. Looking at the figures above you can see that the risk in the placebo group is 8% and the risk in the anotheraban group is 6%. Anotheraban has reduced the risk of a stroke by a quarter, from 8% to 6%. This is the relative risk reduction. Mathematically it is calculated like this:

RRR = (AR placebo group - AR anotheraban) ÷ (AR placebo group)

RRR = (0.08 - 0.06) ÷ (0.08) = 0.25 or 25%