Useful Cost Effectiveness Summary Measures from Bivariate Distributions Conditioning on Threshold Values for Effect

Conditioning on threshold values per unit of effect, more useful and interpretable summary measures can be found across the full distribution at any threshold value. For two-strategy comparisons where there is only one comparator and one distribution to summarise on the CE plane, useful C-E summary measures informing decision makers across plausible threshold values include:

• (i) The cost effectiveness acceptability curve - the probability that a treatment is cost effective (has highest net benefit) across plausible threshold values for a unit of effect; and
• (ii) The incremental net benefit (INB) curve and 95% CI curves - the incremental net benefit expected and 95% CI for INMB across plausible threshold values for a unit of effect.

Figure 2.12 shows the LIPID CEA curve for the probability of pravastatin being cost effective in Australia at threshold values from A$0 to A$260,000 per life saved.

Fig. 2.12 LIPID cost effectiveness acceptability curve ($/life saved) - Fieller’s method

Fig. 2.13 LIPID net benefit curve with 95% CI - Fieller’s method

Similarly, an expected incremental net benefit curve conditional on potential threshold values and curves representing 95% confidence intervals around this expected NB line can also be presented. Figure 2.13 shows such INB curves for pravastatin relative to placebo from the LIPID study conditional on the same range of potential threshold values per life saved as Fig. 2.12.

Where threshold values for effect are 0, INMB (INMB = ХДЕ - ДС) simplifies to - AC. Hence, the expected value and 95% CI for INMB on the vertical axis in Fig. 2.13 with a 0 threshold effect value is simply negative incremental cost. In the case of LIPID, the point estimate for INMB at a 0 threshold value as shown in Fig. 2.13 is -$3246, with 95% CI from -$2637 to -$3854. More generally, INMB depends on the threshold value for incremental effects as well as incremental cost, with expected INMB changing with X at a rate of AE per unit of the threshold value. That is, the slope of the INB line as a function of X is AE. In the case of LIPID, the expected INB line has a slope of 0.03013 (reflecting the absolute 3.013% mortality reduction), increasing at a rate of $30.13 (=0.03013 x 1000) for every $1000 increase in the value of a life saved. On the horizontal axis, expected INMB is 0 at the threshold value where ХДЕ - ДС = 0, and hence at a threshold value where X = ДЕ/Д C, the ICER estimate. In the case of LIPID, the expected INB curve crosses the horizontal axis at $107,730 per life saved.

In general, the expected incremental net monetary benefit line INMB = ХДЕ - ДС passes through points of intersection on the vertical axis at INMB = - ДС and horizontal axis (X value with INMB = 0) at the expected ICER (X = AC/AE when INB = 0) and have slope AE. Hence, INMB lines will be upward sloping as a function of X where there is a positive expected treatment effect and downward sloping where there is a negative treatment effect. Expected INMB lines start with an implicit threshold value for valued of 0 on the vertical axis. Hence, INMB on the vertical axis simplifies to minus incremental cost, with negative INMB where the strategy has net additional costs, while starting with positive INMB if the strategy is cost saving. This in general leads to four types of expected INMB line (Willian and Briggs 2006) reflecting different potential combinations of cost and effects on the four quadrants of the CE plane:

• (i) INMB lines which start negative and become positive corresponding to positive incremental cost and effects (NE quadrant on CE plane).
• (ii) INMB lines which start positive and increase corresponding to negative incremental cost and positive effect (SE quadrant on CE plane), and indicate a new therapy dominates existing care.
• (iii) INMB lines which start positive and become negative corresponding to negative incremental cost and negative effects (SW quadrant on CE plane).
• (iv) INMB lines which start negative and decrease corresponding to positive cost and negative effect (NW quadrant on CE plane), and indicate the comparator (e.g. existing care) dominates then new therapy.

Similarly, the lower and upper 95% CI curves for INMB start on the vertical axis at minus the 95% CIs for incremental cost. The lower and upper 95% CI curves for INMB will cross the horizontal axis at the lower and upper 95% CI for the ICER unless they don’t arise - the new strategy dominates or is dominated at these points. Where new strategies are expected to dominate, expected INMB is positive for all feasible positive threshold values for a positive effect, while where new strategies are expected to be dominated, expected INMB is negative for all plausible threshold values. These curves do not cross the horizontal axis (have INMB=0) over feasible ranges for threshold values.