## Relative and absolute differences

The HR or OR provides a measure of the chance of dying on the 'experimental' treatment compared to control. This is a relative benefit, giving an overall idea of how the experimental treatment compares to the standard treatment. It does not, however, provide information on what this means in absolute terms (see Section 10.4). Although there maybe a large relative effect of an intervention, if the absolute risk is small, it may not be worth adopting the intervention because the change in absolute terms is minimal (a big percentage of a small amount is still a small amount). Therefore it is generally useful to convert this relative difference to absolute differences at given points in time. This depends on both the baseline (control group) survival and the HR, and the way that the two inter-relate is not intuitively obvious.

The formulae required to convert HRs and ORs to absolute differences are shown below:

A = [exp (logePb x HR)] - Pb, A = Pb[(1 - Pb)(1 - OR)/(Pb + OR(1 - Pb))], where A is the absolute difference, Pb the baseline event rate on control group.

Table 11.6 provides examples of how HRs translate to absolute differences at various event rates. For example an HR of 0.7 will give a 6 per cent benefit on a baseline of 80 per cent, improving survival from 80 to 86 per cent. With a baseline of 50 per cent the same HR gives an absolute benefit of 12 per cent taking survival from 50 to 62 per cent and on a baseline of 5 per cent, survival will be improved by 7 per cent from 5 to 12 per cent.

 HR Baseline survival (%) 80 50 20 10 5 0.7 6 12 12 10 7 0.8 4 7 8 6 4 0.95 1 2 2 1 1
0 0