Benefit-Risk Ratio (BRR)
We conducted benefit-risk analysis using the benefit-risk ratio (BRR)with PASI75 as the benefit criterion and PML incidence as the risk criterion.
BRR method principle
BRR considers the increment of benefit (testing drug over its comparator or placebo) against the increment of risk. The risk increment, ∆R, and benefit increment, ∆B, will be taken as x-coordinate and y-coordinate into the following x-y plane.
Figure 5: Benefit-Risk plane and threshold line
If (∆R,∆B) falls in 'NW' quadrant, the drug under consideration is dominant over its comparator.If (∆R,∆B) falls in 'SE' quadrant, the comparator is dominant over the drug under consideration. If (∆R,∆B) falls in 'NE' quadrant, which is the most frequently observed, the decision depends on a pre-fixed choice of 'threshold' ?. If (∆B/∆R)>?, which means that when point (∆R,∆B) is over the threshold line, the drug's BRR under consideration is considered as positive , otherwise the drug’s BRR under consideration is considered as negative.
BRR analysis for efalizumab case study:
In this section, BRR method will be applied to the efalizumab case study. Since BRR deals with two criteria only, we chose PASI75 as the primary benefit criterion and PML as the primary risk criterion in this analysis. All secondary benefits and risks are excluded from the analysis.
1. Benefit increments (efalizumab - placebo)
Pooling five clinical trials in a Bayesian meta-analysis gives the increment of PASI75 benefit
Beware that the PASI75 effect is measured 12 weeks post treatment. In this analysis we assume this effect does not change over time.
2. PML risk increments (efalizumab - placebo) under two exposure estimations
The increment of PML risk is however time dependent. The data show clearly an increasing trend of PML risk over time. The patient exposure is hard to estimate precisely, so a low estimation and a high estimation are given in a PML risk table.
Table 7: Estimated number of patients and PML incidence by exposure
| Exposure to efalizumab | Estimated number of patients (Low - High) | PML cases | Incidence (per 1,000 pts) for high and low exposure estimates |
|
|---|---|---|---|---|
| On drug | 40,000 – 60,000 | 0 at <1 year | 0(0-0.06) | 0(0-0.09) |
| On > 1 year | 15,454 – 23,180 | 0 at 1-2 years | 0(0-0.16) | 0(0-0.24) |
| On > 2 years | 5,944 – 8,914 | 0 at 2-3 years | 0(0-0.41) | 0(0-0.62) |
| On > 3 years | 2,236 – 3,832 | 3 at 3-4 years | 0.78(0.16-2.29) | 1.34(0.28-3.92) |
| On > 4 years | 856 – 1,738 | 1 at >4 years | 0.58(0.01-3.20) | 1.17(0.03-6.49) |
With low exposure estimation, the PML risk after year 3 is 1.34 per 1000 pts. The increment of PML risk from placebo is:
With high exposure estimation, the PML risk after year 3 is 0.78 per 1000 pts. The increment of PML risk from placebo is:
For the PML risk before year 3, there is no observation of PML, so the estimation directly from data is 0. This will lead to a negative risk increment (although very tiny) since we have a positive estimation of background risk. In this analysis, we fit the data (number of PML cases and exposure each year) with an exponential risk increase model, which is more likely than fixed risk model and linear risk increase model in view of the data. The fitted curve of low exposure risk and curve of high exposure risk are shown below.
Figure 6: PML risk increase with time: low exposure risk (black) and high exposure risk (blue)
Based on this fitting, the PML risk increment in year 2 to year 3 for low exposure scenario is:
the PML risk increment in year 2 to year 3 for high exposure scenario is
3. Ratio of benefit increment and risk increment
The ratio of benefit increment and risk increment for year 3 - 4 in low and high exposure cases are
With the PML risk fitting in Figure 2, the ratio for year 2 - 3 in low and high exposure cases are
The ratio for year 1 - 2 and ratio for year 0 - 1 are much higher.
4 . Threshold determination
The threshold in this case study can be determined by considering the question: what is the benefit increment in order to tolerate 0.1% PML risk increase (or say, 1 more PML per 1000 patients). Consider the answer to different choices: 10%, 20% and 60% (i.e., out of 1000 patients, 100, 200 or 600 more patients benefiting more from efalizumab than placebo can compensate the risk of 1 more PML from efalizumab than placebo). The three thresholds are then:
Around these three thresholds, the first one is risky, the second may be fine but is still a little bit risky, the third is a safe choice (maybe a little conservative).
5. BRR decision
The decision is clearly dependent on which threshold a decision maker is going to use. The position of (∆R,∆B) for year 3 - 4 and year 2 - 3 and threshold lines are plotted in following figure.
Figure 7: Efalizumab case study (∆R,∆B) for year 3 – 4 (left) and year 2 – 3 (right)
The boxes in this figure are confidence range of position (∆R,∆B). Overall, year 2 - 3 show positive profile for all thresholds. Year 3 - 4 is however complicated. (∆R,∆B)of year 3 - 4 is over the middle threshold for high exposure estimation, but is under the middle threshold for low exposure estimation. Looking at the figure, an aggressive decision maker may approve the drug, but a conservative decision maker may reject the drug.