Differential Discounting

Differential Discounting of Costs and Health Effects

Most economic evaluations convert future costs and future QALYs to present values at one shared rate, but a long-running argument in health economics holds that health effects should be discounted at a lower rate than costs. The choice matters most for prevention and vaccination, where costs fall early and health gains arrive decades later, so the pair of rates can change which programme looks better value. The case for a lower health rate is tied to growth in the cost-effectiveness threshold, and the NICE manual (PMG36), Dutch and Belgian guidelines and the Green Book answer the question differently; in an illustrative example below, two programmes swap places under different rate pairs. Present-value basics are on the discount rate page and a single-ratio example at 3.5% and 1.5% on the cost per QALY page.

Two rates inside one incremental ratio

When costs and health effects are discounted separately, each stream is converted to a present value with its own rate before the options are compared. The incremental cost-effectiveness ratio then divides one discounted sum by the other.

$$ICER = \frac{\sum_{t=0}^{T} \Delta C_t \,(1 + r_C)^{-t}}{\sum_{t=0}^{T} \Delta Q_t \,(1 + r_H)^{-t}}$$

where $\Delta C_t$ is the difference in cost between the two options in year $t$, $\Delta Q_t$ is the difference in QALYs in year $t$, $r_C$ is the annual discount rate for costs, $r_H$ is the annual discount rate for health effects and $T$ is the last year of the time horizon. Equal discounting sets $r_H = r_C$; differential discounting usually sets $r_H < r_C$.

The lower health rate raises the weight on late QALYs relative to late costs. A QALY gained in year 20 keeps about 50% of its undiscounted value at 3.5% and about 74% at 1.5%. Under differential rates, even a cost and a QALY that fall in the same year $t$ change the ratio by the factor $(1 + r_H)^{t} / (1 + r_C)^{t}$, so the effect depends on when both streams fall relative to the discount base year and grows with $t$.

The growing value of health as the case for a lower rate

The main argument starts from the fact that QALYs are counted in physical units while costs are counted in money. Gravelle and Smith showed that when health effects are valued in money, as in cost-benefit analysis, they should be discounted at the same rate as costs. In cost-effectiveness analysis, a rising money value of a unit of health can instead be allowed for by discounting the volume of health at a lower rate, which is equivalent to inflating the health effects at the growth rate and discounting them at the cost rate.

$$\frac{v_0 (1 + g_v)^{t} Q_t}{(1 + r_C)^{t}} = \frac{v_0 Q_t}{(1 + r_H)^{t}} \quad \text{when} \quad 1 + r_H = \frac{1 + r_C}{1 + g_v}$$

where $v_0$ is the money value of one QALY today, $g_v$ is the annual growth in the consumption value of health, $Q_t$ is the number of QALYs in year $t$, and $r_C$ and $r_H$ are as defined above. Gravelle and Smith derive this exact form and summarise it as the cost rate minus the growth rate. With a cost rate of 3% and growth of 1.5%, the exact health rate is as follows.

$$r_H = \frac{1.03}{1.015} - 1 = 0.0148$$

where the result is the annual health rate as a decimal, about 1.48%, slightly below the 1.5% given by subtraction.

In their welfare model the growth rate depends on growth in the direct utility value of health, income growth, the elasticity of the marginal utility of income and how far people are insured against the income losses of ill health. Brouwer, Niessen, Postma and Rutten used the argument in 2005 to criticise NICE's change from 6% for costs and 1.5% for effects to 3.5% for both, arguing that differential discounting is more appropriate when outcomes such as QALYs are not expressed in money and that a lower weight on future health makes preventive care look less cost effective.

Fixed budgets and the link to the threshold

Claxton, Paulden, Gravelle, Brouwer and Culyer reframed the debate in 2011 by asking what the decision maker is trying to maximise and whether the health budget is fixed. With a fixed budget, spending on a new technology displaces other care. The opportunity cost of spending in a given year is then the health forgone, which depends on the cost-effectiveness threshold in that year.

$$PV_{\text{forgone}} = \sum_{t=0}^{T} \frac{\Delta C_t}{k_0 (1 + g_k)^{t} (1 + r_H)^{t}}$$

where $PV_{\text{forgone}}$ is the present value, in QALYs, of the health displaced by the extra spending, $k_0$ is the threshold today in money per QALY, $g_k$ is its annual growth rate and the other terms are as defined above. If the threshold grows, a pound spent later displaces less health, so costs carry an effective rate $r_C^{*}$ with $(1 + r_C^{*}) = (1 + r_H)(1 + g_k)$, approximately the health rate plus the threshold growth.

The authors showed that, with a fixed budget and decisions based on incremental ratios, discounting costs and health at the same rate is correct only if the threshold stays constant, and that expected growth in the consumption value of health does not on its own justify differential rates but implies a lower rate for both. A later review by Attema, Brouwer and Claxton combines the strands. The health rate equals the social time preference rate for consumption minus the growth in the consumption value of health, and the cost rate adds the threshold growth to that health rate. On those expressions the effective cost rate equals the consumption rate only if the threshold and the consumption value of health grow at the same rate. In this framing the gap between the rates comes from a growing threshold, whereas in the Gravelle and Smith framing, with costs valued as forgone consumption, it comes from the growing value of health.

Consistency and the postponement paradox

Two arguments have been used to defend equal rates. The consistency argument compares programmes that differ only in timing. Brouwer and colleagues illustrate it with a programme costing £30,000 for 1 QALY this year and the same programme 40 years later, which should receive equal priority if the money value of a QALY stays constant, and whose ratios are equal only when the two rates are equal. The second is the postponement paradox of Keeler and Cretin, who showed in 1983 that if health benefits are left undiscounted, a programme is always improved by delay unless the ability to produce the health effect diminishes too quickly. Delaying a whole programme by $s$ years multiplies its ratio by the factor below.

$$\left(\frac{1 + r_H}{1 + r_C}\right)^{s}$$

where $s$ is the delay in years and the rates are as defined above. The factor is below one whenever the health rate is below the cost rate, so the ratio improves with every year of delay.

In reply, Gravelle and Smith argued that the paradox reveals a difficulty with cost-effectiveness analysis itself and is irrelevant to the choice of the health rate, Brouwer and colleagues cited the criticism that the consistency argument fails once the money value of health changes and judged infinite postponement hardly relevant in the real world, and Attema and colleagues noted that it was never observed in the UK before 2004 or the Netherlands since 2004, when both used differential rates.

Rates in the NICE manual and in guidelines that use two rates

Jurisdictions divide into those that apply one rate to both streams and those that set a lower rate for health effects. The table summarises four sets of guidance checked on 1 October 2026, with the Green Book rates rechecked on 3 October 2026, which can change before any given analysis.

The NICE manual (PMG36) states in section 4.5.1 that "For the reference case, costs and health effects should be discounted at the same rate of 3.5% per year." Under section 4.5.3 the committee "may consider analyses using a non-reference-case discount rate of 1.5% per year for both costs and health effects" only when all three criteria are met. The technology must be for people who would otherwise die or have a very severely impaired life, it is likely to restore them to full or near-full health, and the benefits are likely to be sustained over a very long period. Because the lower rate applies to both streams, this exception is uniform discounting at a lower rate rather than differential discounting; sections 4.5.4 and 4.5.5 add conditions that the discount rate page sets out.

The Dutch guideline from Zorginstituut Nederland requires, for the reference case, a constant 3% for future costs and a constant 1.5% for future effects. It derives the health rate as the cost rate minus the growth of the consumption value of health, estimated at 0.6% to 2.9% a year in the Netherlands, and it uses 1.5%, slightly below the average of that range. It lists the change of the cost rate to 3% among its main changes from the 2016 version; the review by Attema and colleagues records the earlier Dutch pair as 4% and 1.5%. The Belgian KCE guideline sets the outcome rate below the cost rate to avoid penalising too strongly interventions that generate most of their outcomes in the future, such as screening and vaccination. The figures themselves are kept for consistency, with 3% chosen to allow comparison with previous evaluations and 1.5% to stay consistent with previous guidelines, since the change in the value of health over time is highly uncertain.

Worked example with a prevention programme and a treatment under three rate pairs

The figures below are illustrative. Two independent programmes are each compared with no intervention, all amounts are increments over that comparator, and year 0 is the start of treatment. Programme A, a prevention programme, costs £12,000 in year 0 and £12,000 in year 10 and gains 1.2 QALYs in year 20. Programme B, a treatment, costs £20,000 in year 0 and gains 0.8 QALYs in year 1.

1. Both streams at 3.5%. The discounted cost of programme A is calculated first.

$$C_A = 12000 + \frac{12000}{1.035^{10}} = 12000 + 8507.03 = 20507.03$$

where $C_A$ is the discounted incremental cost of A in pounds. The discounted QALY gain and ratio follow.

$$ICER_A = \frac{20507.03}{1.2 / 1.035^{20}} = \frac{20507.03}{0.60308} = 34004$$

where $ICER_A$ is the cost in pounds per discounted QALY gained by A. B has its whole cost in year 0, so only its QALYs are discounted.

$$ICER_B = \frac{20000}{0.8 / 1.035} = 25875$$

where $ICER_B$ is the cost in pounds per discounted QALY gained by B.

2. Both streams at 1.5%. The same steps give a cost for A of £22,340.01, a QALY gain of 0.89096 and a ratio of £25,074, while B's ratio becomes £25,375.

3. Costs at 3% and health at 1.5%. Only the year-10 cost of A changes from step 2 when the ratio is recalculated.

$$ICER_A = \frac{12000 + 12000 / 1.03^{10}}{0.89096} = \frac{20929.13}{0.89096} = 23490$$

where $ICER_A$ is as above. B stays at £25,375, because its cost falls in year 0.

Under the 3.5% pair the treatment has the lower ratio; under either pair with a 1.5% health rate the prevention programme does, so the reversal comes from the health rate. The 1.5% row shows arithmetic only, since NICE applies that rate just when all three of its criteria are met.

4. Delaying the prevention programme. If every cost and QALY of A moved 10 years later under the 3% and 1.5% pair, the ratio would change as follows.

$$23490 \times \left(\frac{1.015}{1.03}\right)^{10} = 23490 \times 0.86355 = 20285$$

where the result is A's cost in pounds per discounted QALY gained after the delay. The programme is unchanged, yet its ratio falls by about 14%; under equal rates it would not move.

Reading ratios produced under different rate pairs

A ratio calculated with one pair of rates is a different measure from a ratio calculated with another, even for the same programme. NICE's threshold range applies to ratios discounted at 3.5%, not to a ratio discounted at 3% and 1.5%, and cross-country comparisons need the rate pair behind each published figure.

Reports should therefore state both rates, the guideline followed and the discount base year, and show equal-rate scenarios, which the Belgian guideline makes mandatory. Attema and colleagues note that the growing value of health can also be handled through a monetary threshold that rises over time, which in a net monetary benefit calculation gives the same result as the equivalence above.

Common misreadings of differential discounting

A common error is to treat a rate pair as one number or to mix up different reasons for changing a rate. NICE's 1.5% option can be mistaken for differential discounting, but PMG36 applies it to costs and health effects alike. A lower health rate also does not make future health count more than present health. Compared with discounting at a cost rate of 3.5%, a QALY in year 20 rises in weight from about 0.50 to about 0.74, relative both to costs and to a QALY today, but still weighs less than one gained today.

Differential discounting varies the rate by type of consequence, covered stream by stream in the dictionary entries for discounting health and discounting costs, whereas hyperbolic discounting varies it with the length of delay and the Green Book schedule with the year of the appraisal. Attema and colleagues also warn that placing the discount base year before the actual start of a programme lowers its ratio through the same arithmetic as step 4, so a fixed rule such as the start of treatment is needed. How society should weight later outcomes at all is a question of time preference.

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