Signature
R = Delta_C / Delta_E; INMB = Delta_E * (lambda - R)
| Inputs | Definition | Unit |
|---|---|---|
Delta_C | Mean cost of the new option minus mean cost of the comparator | currency per patient |
Delta_E | Mean effect of the new option minus mean effect of the comparator, not zero | QALYs per patient |
lambda | Cost-effectiveness threshold | currency per QALY |
R | Incremental cost-effectiveness ratio Delta_C over Delta_E, whose sign alone does not identify the quadrant | currency per QALY |
|---|---|---|
INMB | Incremental net monetary benefit of the new option at lambda | currency per patient |
Function
Net benefit approach to a two-option cost-effectiveness decision and its sampling uncertainty
Maps a threshold lambda and the differences in mean effect and mean cost between a new option and its comparator, or the per-arm trial data behind them, to incremental net benefit, whose sign gives the adoption decision, and to the sampling uncertainty around it. Option-level and incremental net monetary benefit, the maximum net monetary benefit rule and expected net benefit from simulations are on the Net Monetary Benefit and Expected Net Benefit pages (HE-FM-NMB-001 to HE-FM-NMB-003, HE-FM-ENB-001 and HE-FM-ENB-002). Incremental net health benefit at a threshold is HE-FM-CET-002, the ICER is HE-FM-ICER-001 and dominance is HE-FM-DOM-001. A normal interval for incremental net benefit built from the standard errors of the two differences is HE-FM-AN-004 with HE-CF-AN-001, its bootstrap variance is HE-FM-BSE-003, the acceptability curve and frontier are HE-FM-CEAC-001 to HE-FM-CEAC-003 and EVPI is HE-FM-VOI-001. This package adds Stinnett and Mullahy's interval for incremental net health benefit from two independent trial arms, the identity that links the sign of incremental net benefit to the ICER in each quadrant of the cost-effectiveness plane, and net-benefit regression. Notation follows the Net Benefit Approach article.
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Implementations
Excel
Incremental net monetary benefit from a reported ICER and effect difference
With the ICER in ICER, the effect difference in IncrementalEffect and the threshold in Threshold, the first formula returns INMB and the second the decision, which reads the same way in every quadrant.
=IncrementalEffect*(Threshold-ICER); =IF(IncrementalEffect*(Threshold-ICER)>0,"Adopt new option","Keep comparator")
Assumptions
Non-zero effect difference in the quadrant identity
The identity divides by Delta_E. When the effects are equal the ICER is undefined but INMB is simply minus Delta_C, so INMB is computed directly from HE-FM-NMB-002 and the identity is used to read a reported ICER, not to replace that calculation.
One subtraction direction for the ratio and the net benefit
Delta_C, Delta_E and R are all new option minus comparator, as in HE-AS-NMB-003. Reversing the direction of both differences leaves R unchanged but reverses the sign of INMB, which is why R alone cannot show which option is favoured.
Worked examples
North-east quadrant with the ratio just above the threshold
Option C in draw 3 of the article's illustrative example costs GBP 3,000 more and gains 0.14 QALYs. R is about GBP 21,429 per QALY, above GBP 20,000, and INMB is minus GBP 200, as in the article's table.
Delta_C = 3000; Delta_E = 0.14; lambda = 20000; R = 21428.57; INMB = -200.00
North-west quadrant with a negative ratio
Option B in draw 4 of the article's illustrative example costs GBP 1,000 more and loses 0.02 QALYs. R is minus GBP 50,000 per QALY and INMB is minus GBP 1,400, as in the article, so here the negative ratio marks a worse option.
Delta_C = 1000; Delta_E = -0.02; lambda = 20000; R = -50000; INMB = -1400
South-east quadrant with a negative ratio
An illustrative option saves GBP 500 and gains 0.05 QALYs. R is minus GBP 10,000 per QALY, the same sign as in the north-west example, yet INMB is GBP 1,500 and the option dominates its comparator.
Delta_C = -500; Delta_E = 0.05; lambda = 20000; R = -10000; INMB = 1500
South-west quadrant with a positive ratio below the threshold
An illustrative option saves GBP 1,000 and loses 0.10 QALYs. R is GBP 10,000 per QALY, below the threshold, but each QALY given up saves only GBP 10,000 against the GBP 20,000 it is worth, so INMB is minus GBP 1,000 and the comparator is kept.
Delta_C = -1000; Delta_E = -0.10; lambda = 20000; R = 10000; INMB = -1000
Common errors
Positive ratio below the threshold accepted in the south-west quadrant
A cheaper, less effective option with R of GBP 10,000 per QALY looks acceptable at GBP 20,000 when its quadrant is ignored, yet INMB is minus GBP 1,000 because the saving per QALY forgone is below the value of that QALY. In this quadrant the option is acceptable only when R exceeds lambda, for example a saving of GBP 3,000 for 0.10 QALYs lost, which gives R of GBP 30,000 and INMB of GBP 1,000 (computed here for illustration). HE-ER-NMB-003 describes the same error in general terms.
Effect difference near zero read through the ratio
With an extra cost of GBP 10, an effect difference of 0.001 QALYs gives R of GBP 10,000 per QALY and a difference of minus 0.001 gives minus GBP 10,000, which reverses how the ratio is read, while INMB at GBP 20,000 per QALY moves only from GBP 10 to minus GBP 30 (computed here for illustration). Stinnett and Mullahy note that ratios of near-infinite size when the effect difference is close to zero also disturb bootstrap estimates of the ratio's mean and variance.
Sources
Stinnett and Mullahy decision rules for each quadrant
Stinnett AA, Mullahy J. Net health benefits: a new framework for the analysis of uncertainty in cost-effectiveness analysis. Medical Decision Making. 1998;18(2 Suppl):S68-S80. Section on the decision rules of cost-effectiveness analysis, which prefers the new option in quadrant I only if the ratio is below lambda, always in quadrant II, in quadrant III only if the ratio is above lambda and never in quadrant IV, and the section on ambiguity between quadrants, which states that a positive ratio below lambda is favourable in quadrant I but unfavourable in quadrant III. Checked in the NBER Technical Working Paper 227 version (1998).
Incremental net benefit plotted against willingness to pay
Hoch JS, Hay A, Isaranuwatchai W, Thavorn K, Leighl NB, Tu D, Trenaman L, Dewa CS, O'Callaghan C, Pater J, Jonker D, Chen BE, Mittmann N. Advantages of the net benefit regression framework for trial-based economic evaluations of cancer treatments: an example from the Canadian Cancer Trials Group CO.17 trial. BMC Cancer. 2019;19:552. Methods section, which states that a graph of incremental net benefit against willingness to pay has a y-intercept of minus Delta_C, a slope of Delta_E and an x-intercept at the ICER.
Canonical Identity
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