Benefit-risk ratio (BRR)

We calculate benefit-risk ratio (BRR) trade-off metric for each benefit criterion against each risk criterion for the purpose of directly comparing benefits and risks. Because the decision-maker's relative importance between benefit and risk criteria are unknown, we estimated BRR over a range of k values. In this setting, k is the scaling factor such that "benefit"=k×"risk" , that is, how much more important is the benefit when compared to risk.

The benefit-risk ratio of NEPP for benefit criterion i and risk criterion j is calculated as

The BRR for PIN-ER-t are calculated in the same way:

We present here the BRR(PIN-ER-t) for achieving 10% weight loss versus anxiety as an illustration of the method. The benefit-risk ratio is plotted against the relative importance of benefit to risk where the larger relative values refer to putting more weight on risks. This is equivalent to saying that a decision-maker prefers to avoid the risk more than gaining the benefit. The benefit-risk balance is achieved when BRR equals one that is when benefit equals risk. The green area shows the likely BRR values when rimonabant can be considered as a better option compared to placebo based on the two outcomes; and conversely the orange area shows the likely BRR values when placebo would be the better option.

Figure 1 The ratio of number of people in the population whose weight loss were attributable to rimonabant to the number of people who experienced anxiety as a result of taking rimonabant over one year (BRR of PIN-ER-1)

In this example (Figure 1), when a DM prefer achieving 10% weight loss twice as much than avoiding anxiety (or similarly prefer avoiding anxiety half as much as achieving 10% weight loss) i.e. relative importance of 0.5, the median ratio of benefit to risk is 7.0 (95% CI 4.5 – 11.9). This means 7 people would have lost weight by taking rimonabant for every person who experienced anxiety due to rimonabant. When weight loss is valued as important as avoiding anxiety, the median BRR drops to 3.5 (95% CI 2.3 – 5.9). On the other hand, if a DM greatly preferred to avoid anxiety, say with an extreme relative importance of 10, the BRR drops to 0.3 (95% CI 0.2 – 0.6) suggesting that rimonabant should be avoided. The benefit-risk balance of rimonabant in this situation reverses, BRR<1, when the relative importance of benefit to risk is between 3.4 and 3.5.