Incremental Net Monetary Benefit

Incremental Net Monetary Benefit and Its Link to the ICER

The equation for incremental net monetary benefit is INMB = λΔE − ΔC, where ΔE and ΔC are the differences in expected health and expected cost between a new option and its comparator and λ is the cost-effectiveness threshold. The result is a sum of money per patient, such as pounds per patient, accumulated over the whole time horizon of the analysis and discounted to present value. It is a figure for the full horizon, not an amount per year.

INMB is the quantity on which most two-option cost-effectiveness decisions turn once they are written as net benefit. Its sign gives the decision at the stated threshold, its size says how much value per patient is at stake, and because it is linear in costs and effects it can be averaged, regressed and scaled up to a population in ways an incremental cost-effectiveness ratio cannot. It is also the natural quantity to summarise across draws in a probabilistic sensitivity analysis. The option-level quantity is covered on the net monetary benefit page, the health-unit version on the net health benefit page, and the general family on the net benefit page.

The equation and what each term carries

INMB compares one option with one named comparator. It values the health difference at the threshold and subtracts the cost difference, which is the same as subtracting the comparator's net monetary benefit from the new option's.

$$\text{INMB} = \lambda \Delta E - \Delta C = (\lambda E_1 - C_1) - (\lambda E_0 - C_0)$$

where $\lambda$ is the threshold in money per unit of health (for example pounds per QALY), $E_1$ and $C_1$ are the expected health effect and expected cost per patient of the new option, $E_0$ and $C_0$ are those of the comparator, $\Delta E = E_1 - E_0$ is the incremental effectiveness and $\Delta C = C_1 - C_0$ is the incremental cost.

Read as a function of $\lambda$, INMB is a straight line. In their 2019 cancer trial example, Hoch and colleagues describe a graph of incremental net benefit against willingness to pay with a y-intercept of minus ΔC, a slope of ΔE and an x-intercept at the ICER. The line shows at a glance how the decision changes as the threshold moves, and Stinnett and Mullahy recommended reporting net benefit as a function of the threshold over a range of values, because the threshold is not known with certainty.

Units of money per patient over the time horizon

The units of INMB are inherited from its inputs. In a decision model or a trial-based analysis, $E$ and $C$ are expected values per patient, so INMB is money per patient. Results reported for a whole modelled cohort, such as 1,000 patients, carry that unit instead. Stinnett and Mullahy state that their net benefit measure is per patient, or more generally per unit of observation, and that the total for a programme is the per-patient value multiplied by the size of the target population.

The horizon and discounting fix what "per patient" covers. The NICE manual (PMG36) asks for a time horizon long enough to reflect all important differences in costs or outcomes, and for cost-effectiveness results to reflect the present value of costs and benefits over that horizon, with both discounted at 3.5% per year in the reference case. An INMB from a lifetime model is therefore the discounted lifetime value per patient, stated in a currency and price year. It is an annual figure only when the model horizon is itself one year.

Population totals need two further inputs, namely how many patients are treated and when. Claxton's value-of-information examples assumed 2,000 patients entering a decision problem each year for ten years, discounted at 6% a year, the same structure that underlies population EVPI.

INMB and the ICER, quadrant by quadrant

For a new option that costs more and gains health, a positive INMB and an ICER below the threshold are the same statement. In other quadrants of the cost-effectiveness plane the ratio rule changes direction or stops being needed, while the INMB rule reads the same everywhere. Stinnett and Mullahy set out the ratio rule for each quadrant.

In the north-east quadrant, dividing $\lambda \Delta E - \Delta C > 0$ by a positive ΔE gives $\lambda > \Delta C / \Delta E$. In the south-west quadrant ΔE is negative, so the division reverses the inequality. INMB is exactly zero when the ICER equals $\lambda$. The NICE manual (PMG36, section 4.10.8) notes that net health benefits may be particularly informative when technologies provide less health benefit at lower cost, the south-west quadrant.

Worked example from one patient to the eligible population

All numbers in this example are illustrative and do not describe a real technology. A lifetime model compares a new treatment with current care. Discounted at 3.5% per year, expected costs per patient are £18,400 and £12,000 and expected QALYs per patient are 6.82 and 6.50.

Increments (step 1). ΔC is £18,400 − £12,000 = £6,400 and ΔE is 6.82 − 6.50 = 0.32 QALYs per patient. The ICER is £6,400 / 0.32 = £20,000 per QALY, in the north-east quadrant.

INMB per patient at the two NICE values (step 2). The NICE manual (PMG36, section 4.2.16) asks for net health benefits at values of £25,000 and £35,000 per QALY gained and allows net monetary benefits alongside.

$$\text{INMB}_{25{,}000} = 25{,}000 \times 0.32 - 6{,}400 = 1{,}600$$

where 25,000 is $\lambda$ in pounds per QALY, 0.32 is ΔE in discounted QALYs per patient and 6,400 is ΔC in discounted pounds per patient. At £35,000 per QALY the same calculation gives 11,200 − 6,400 = £4,800 per patient. Both values are positive, matching the ICER of £20,000 per QALY lying below each threshold, and at £20,000 per QALY the INMB would be exactly zero.

The same result in health units (step 3). Dividing £1,600 by the £25,000 threshold gives an incremental net health benefit of 0.064 QALYs per patient. Option-level values agree, since the new treatment's NMB at £25,000 per QALY is £152,100 and current care's is £150,500, a difference of £1,600.

One year's patients (step 4). If 2,000 patients a year are eligible, one year's cohort gives the following.

$$\text{INMB}_{\text{cohort}} = N \times \text{INMB} = 2{,}000 \times 1{,}600 = 3{,}200{,}000$$

where $N$ is the number of patients treated and 1,600 is the per-patient INMB in pounds at £25,000 per QALY, giving £3.2 million.

Five annual cohorts in present value (step 5). If the treatment is used for five years, each later cohort is discounted back to the first year at 3.5%, as follows.

$$\text{INMB}_{\text{pop}} = \sum_{t=0}^{4} \frac{N \times \text{INMB}}{1.035^{t}} = 3{,}200{,}000 \times 4.67308 \approx 14{,}953{,}853$$

where $t$ is the year in which a cohort starts treatment, 1.035 reflects the 3.5% annual rate and 4.67308 is the sum of the five discount factors (1, 0.96618, 0.93351, 0.90194 and 0.87144). The undiscounted total would be £16 million.

Interpretation (step 6). At £25,000 per QALY, the new treatment yields about £15.0 million of net benefit in present value across five years of patients, meaning that the health gained, valued at the threshold, exceeds the extra cost by that amount. It is a value and not a cash saving, because each year's cohort still adds £12.8 million in discounted lifetime costs (2,000 × £6,400), and the year-by-year cash effect is a question for budget impact analysis.

INMB in probabilistic sensitivity analysis

In a probabilistic analysis, INMB is calculated in every simulation, and its distribution feeds the main uncertainty outputs. Because INMB is linear, Stinnett and Mullahy noted that the mean of its distribution equals INMB evaluated at mean costs and effects, which does not hold for a ratio. The decision at a given threshold rests on the expected value, the mean across draws, as on the expected net benefit page.

The share of draws with a positive INMB is the probability that the new option is cost-effective against its comparator. Stinnett and Mullahy noted that this probability, plotted against the threshold, gives a graph identical to the cost-effectiveness acceptability curve for the two options. For two options, the expected value of perfect information per patient also follows from INMB alone, as shown below.

$$\text{EVPI} = \frac{1}{S} \sum_{s=1}^{S} \max(\text{INMB}_s, 0) - \max(\overline{\text{INMB}}, 0)$$

where $S$ is the number of simulations, $\text{INMB}_s$ is the value in simulation $s$ and $\overline{\text{INMB}}$ is the mean across simulations. The comparator's net benefit cancels from both terms, so no other quantity is needed when only two options are compared.

Regression and confidence intervals with patient-level data

With patient-level trial data, INMB can be estimated with standard statistical tools. Tambour, Zethraeus and Johannesson noted that once effects are valued at a price per unit, standard techniques give a confidence interval for net benefit. Stinnett and Mullahy gave the variance for the health-unit form; multiplied by $\lambda^2$ it gives the money form, as follows.

$$\widehat{\sigma}^2_{\text{INMB}} = \sum_{i=0}^{1} \frac{\lambda^2 s^2_{E_i} + s^2_{C_i} - 2 \lambda r_i s_{E_i} s_{C_i}}{n_i}$$

where $i$ indexes the comparator (0) and the new option (1), $s^2_{E_i}$ and $s^2_{C_i}$ are the sample variances of effects and costs in arm $i$, $r_i$ is their sample correlation and $n_i$ is the number of patients in the arm.

Hoch, Briggs and Willan proposed net-benefit regression in 2002 as a way to bring established econometric techniques to cost-effectiveness analysis. Each patient's net benefit, $\lambda e_i - c_i$, is regressed on a treatment indicator, and the 2019 paper explains that the coefficient on the indicator equals the incremental net benefit and its 95% confidence interval is the interval for INMB. Covariates can be added, an interaction between treatment and a patient characteristic explores whether INMB differs across subgroups, and repeating the regression across thresholds traces the INMB line. The thresholds at which the confidence limits for INMB cross zero are the Fieller confidence limits for the ICER.

Choices that change an INMB result

An INMB figure is conditional on the choices behind its inputs, and two figures can be compared only when those choices match. The threshold is the most visible because it scales the health term. Other choices matter as much, and the main ones are listed below.

• the comparator, since INMB against one option says nothing about others not in the comparison;
• the time horizon and the discount rate, which set how much future cost and health enters ΔC and ΔE;
• the perspective, currency and price year of the costs;
• the unit of health, since a threshold per QALY cannot value effects counted in life years or events avoided.

The linear form also assumes every unit of health is worth $\lambda$ whatever its size or recipient. PMG36 relaxes this through decision-making modifiers, which can be applied quantitatively as QALY weights (section 6.2.11), and asks for net health benefits at £25,000 and £35,000 both with and without the weighting (section 6.3.2).

Common errors with INMB

Most errors come from losing track of direction, units or scale. Each of the following changes a reported INMB without any change in the underlying evidence.

• Subtracting in opposite directions for costs and effects, which flips the sign of one term.
• Reporting INMB without its threshold, or comparing figures calculated at different thresholds.
• Reading a per-patient lifetime INMB as an annual figure, or multiplying it by a population without stating how many patients and over what period.
• Adding undiscounted population totals across years, or mixing discounted QALYs with undiscounted costs.
• Treating a positive INMB as a cash saving or as proof of affordability.
• Judging each of several options by whether its INMB against one common baseline is positive, instead of choosing the option with the largest INMB against that baseline (equivalently the highest NMB); the net benefit page shows a case in which this picks the wrong option.
• Averaging ICERs across simulations instead of averaging INMB.

Sources

• 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. doi:10.1177/0272989X98018002S09. Also issued as NBER Technical Working Paper 227, 1998.
• Tambour M, Zethraeus N, Johannesson M. A note on confidence intervals in cost-effectiveness analysis. International Journal of Technology Assessment in Health Care. 1998;14(3):467-471. doi:10.1017/S0266462300011442
• Claxton K. The irrelevance of inference: a decision-making approach to the stochastic evaluation of health care technologies. Journal of Health Economics. 1999;18(3):341-364. doi:10.1016/S0167-6296(98)00039-3. Earlier version: CHE Technical Paper 8, University of York, 1997.
• 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. doi:10.1002/hec.678
• Hoch JS, Hay A, Isaranuwatchai W, et al. 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. doi:10.1186/s12885-019-5779-x
• National Institute for Health and Care Excellence. NICE technology appraisal and highly specialised technologies guidance: the manual (PMG36). Published 31 January 2022, last updated 13 October 2026. Sections 4.2.16, 4.5.1, 4.10.8, 6.2.11 and 6.3.2 and the reference case table.