Signature
NB_1 = lambda * E_1 - C_1; NB_0 = lambda * E_0 - C_0; alpha = NB_0; beta = NB_1 - NB_0
| Inputs | Definition | Unit |
|---|---|---|
lambda | Threshold at which each patient's net benefit is computed before the regression is run | currency per QALY |
E_1 | Mean effect per patient in the new-option arm | QALYs per patient |
C_1 | Mean cost per patient in the new-option arm | currency per patient |
E_0 | Mean effect per patient in the comparator arm | QALYs per patient |
C_0 | Mean cost per patient in the comparator arm | currency per patient |
NB_1 | Mean of the patients' net benefit at lambda in the new-option arm | currency per patient |
|---|---|---|
NB_0 | Mean of the patients' net benefit at lambda in the comparator arm | currency per patient |
alpha | Fitted intercept, the mean net benefit of the comparator arm | currency per patient |
beta | Fitted coefficient on the treatment indicator, equal to incremental net monetary benefit 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
Net-benefit regression with Excel LINEST
With patient effects in Effect, patient costs in Cost and the indicator in TreatFlag, one row per patient, the first formula returns beta and the second its standard error from the LINEST statistics table. The array expression Threshold*Effect-Cost forms each patient's net benefit inside the function. LINEST pools the residual variance of the two arms, so its standard error equals lambda times SE_INHB of HE-FM-NBA-001 only when the arms are the same size or share one variance, and otherwise the per-arm form is the one to report.
=INDEX(LINEST(Threshold*Effect-Cost,TreatFlag),1); =INDEX(LINEST(Threshold*Effect-Cost,TreatFlag,TRUE,TRUE),2,1)
Assumptions
Treatment indicator coded 1 for the new option
T_i is 1 for patients given the new option and 0 for the comparator, so beta is new option minus comparator. Reversed coding reverses the sign of beta.
One threshold per net-benefit regression
The dependent variable changes with lambda, so the regression is re-run at each threshold. Hoch and colleagues use repeated regressions over willingness-to-pay values to show how the finding changes with lambda.
Unadjusted coefficient equals the difference in arm means
The equality of beta with the difference in arm mean net benefit holds for a regression on the treatment indicator alone. With baseline covariates added, beta is an adjusted incremental net benefit, and the arm-mean calculator returns the unadjusted value only.
Worked examples
Net-benefit regression for the illustrative trial at GBP 20,000 per QALY
Using the arm means of the illustrative trial in HE-EX-NBA-001, mean net benefit is GBP 10,000 in the new-option arm and GBP 9,500 in the comparator arm, so the intercept is GBP 9,500 and the treatment coefficient is GBP 500.
lambda = 20000; E_1 = 0.80; C_1 = 6000; E_0 = 0.70; C_0 = 4500; NB_1 = 10000; NB_0 = 9500; alpha = 9500; beta = 500
Net-benefit regression at a threshold equal to the ICER
At GBP 15,000 per QALY, the ICER of the illustrative trial, both arms have mean net benefit of GBP 6,000 and the treatment coefficient is zero, the check Hoch and colleagues recommend.
lambda = 15000; E_1 = 0.80; C_1 = 6000; E_0 = 0.70; C_0 = 4500; NB_1 = 6000; NB_0 = 6000; alpha = 6000; beta = 0
Net-benefit regression at a zero threshold
At a threshold of zero each patient's net benefit is minus the cost, so the coefficient is minus GBP 1,500, minus the difference in mean cost, a limiting case Hoch and colleagues also describe.
lambda = 0; E_1 = 0.80; C_1 = 6000; E_0 = 0.70; C_0 = 4500; NB_1 = -6000; NB_0 = -4500; alpha = -4500; beta = -1500
Common errors
Treatment indicator coded in reverse in a net-benefit regression
Coding 1 for the comparator returns a coefficient of minus GBP 500 for the illustrative trial at GBP 20,000 per QALY instead of GBP 500, and the intercept becomes the new arm's mean of GBP 10,000 (computed here for illustration).
Intercept read as incremental net benefit
The intercept is the comparator's mean net benefit, GBP 9,500 in the illustrative trial at GBP 20,000 per QALY, a level that depends on which costs and effects are counted. The incremental value is the treatment coefficient, GBP 500.
Sources
Net-benefit regression on a treatment indicator
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 on incremental net benefit regression, where each patient's net benefit is willingness to pay times the patient's effect minus the patient's cost, regressed on a treatment indicator with or without covariates, the coefficient b_TX equals incremental net benefit, and the checks that a willingness to pay equal to the ICER gives b_TX of zero and a value of zero gives minus Delta_C.
Hoch, Briggs and Willan proposal of net-benefit regression
Hoch JS, Briggs AH, Willan AR. Something old, something new, something borrowed, something blue: a framework for the marriage of health econometrics and cost-effectiveness analysis. Health Economics. 2002;11(5):415-430. Abstract (full text not checked), which places the net-benefit framework in a standard regression framework and lists the use of established econometric techniques, adjustment for imperfect randomisation and the identification of subgroups as practical advantages.
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