Health Economics & Clinical Decision Analysis
ICER & Net Monetary Benefit (NMB) QALY Formula
Calculate the Incremental Cost-Effectiveness Ratio (C_1 - C_0)/(E_1 - E_0), Net Monetary Benefit lambda*Delta_E - Delta_C, and expose the South-West quadrant ICER sign trap.
Why raw ICER ratios mislead in Dominance and South-West quadrants — and how NMB fixes every case!
In health-technology assessment (NICE, ICER, WHO), comparing a New Therapy (cost C_1, quality-adjusted life-years E_1) against Standard of Care (C_0, E_0) at willingness-to-pay threshold lambda per QALY starts with Incremental Cost Delta_C = C_1 - C_0 and Incremental Effectiveness Delta_E = E_1 - E_0. While the Incremental Cost-Effectiveness Ratio ICER = Delta_C / Delta_E works cleanly in the North-East quadrant (Delta_C > 0, Delta_E > 0 -> cost-effective when ICER <= lambda), raw ratios fail catastrophically in two cases: (1) Dominated therapies (Delta_C > 0, Delta_E < 0) yield a NEGATIVE ICER that looks numerically "< lambda", and (2) South-West cost-saving trade-offs (Delta_C < 0, Delta_E < 0) yield a POSITIVE ratio (- / - = +) where you actually require savings per QALY lost to EXCEED lambda! Linearizing into Net Monetary Benefit NMB = lambda * Delta_E - Delta_C solves all four quadrants unambiguously: adopt iff NMB >= 0!
Build a clinical-trial comparison table FIRST: New_Cost_C1 = 28,000 (B2), Standard_Cost_C0 = 10,000 (B3 -> Delta_C = +18,000), New_QALYs_E1 = 6.60 (B4), Standard_QALYs_E0 = 6.00 (B5 -> Delta_E = +0.60 QALYs), and WTP_Threshold_Lambda = 50,000/QALY (B6). North-East ICER = 18,000 / 0.60 = 30,000.00/QALY (< 50,000), NMB = 50,000 * 0.60 - 18,000 = +12,000.00, and Net Health Benefit NHB = 0.60 - (18,000 / 50,000) = +0.2400 QALYs! Now test the South-West trap C1 = 4,000, E1 = 5.80 (Delta_C = -6,000, Delta_E = -0.20): raw ratio is STILL +30,000.00, yet NMB = 50,000*(-0.20) - (-6,000) = -4,000.00 < 0 (Reject!)!
| Cost-Effectiveness Plane Scenario (lambda = 50,000) | Raw Ratio Delta_C / Delta_E | NMB = lambda*Delta_E - Delta_C |
|---|---|---|
| Baseline North-East (+18,000, +0.60 QALY) | 30,000.00 / QALY | +12,000.00 (Cost-Effective!) |
| South-West Trap (-6,000, -0.20 QALY) | 30,000.00 (Misleading!) | -4,000.00 (Reject: QALY Loss Too High!) |
| North-West Dominated (+5,000, -0.10 QALY) | Dominated (Do Not Divide) | -10,000.00 (Strictly Dominated) |
| South-East Dominant (-2,000, +0.30 QALY) | Dominant (Cost-Saving) | +17,000.00 (Strictly Dominant) |
Quadrant-Safe Incremental Cost-Effectiveness Ratio (ICER) Formula
Suppress misleading negative ratios by labeling Dominated and Dominant quadrants explicitly before dividing Delta_C by Delta_E.
=LET(d_c, B2 - B3, d_e, B4 - B5, IF(OR(B2 < 0, B3 < 0, B4 < 0, B5 < 0, B6 <= 0), "Invalid HTA Input", IF(AND(d_e <= 0, d_c >= 0), "Dominated (Worse or Equal QALYs, Higher Cost)", IF(AND(d_e > 0, d_c <= 0), "Dominant (More QALYs, Lower or Equal Cost)", ROUND(d_c / d_e, 2)))))All-Quadrant Net Monetary Benefit (NMB = lambda * Delta_E - Delta_C) Formula
Because NMB is linear in (Delta_E, Delta_C) with zero division by Delta_E, confidence intervals and multi-arm rankings stay continuous across Delta_E = 0!
=IF(OR(B2 < 0, B3 < 0, B4 < 0, B5 < 0, B6 <= 0), "Invalid HTA Input", ROUND(B6 * (B4 - B5) - (B2 - B3), 2))Try the example
Use the original values or change them to test your understanding.