Signature
r_H = (1 + r_C) / (1 + g_v) - 1; r_H_sub = r_C - g_v
| Inputs | Definition | Unit |
|---|---|---|
r_C | Social rate of discount for costs valued as consumption | proportion per year |
g_v | Growth in the money value of one QALY | proportion per year |
r_H | Rate at which the volume of future QALYs is discounted | proportion per year |
|---|---|---|
r_H_sub | Cost rate minus the growth rate, slightly above the exact rate when growth is positive | proportion per year |
Function
Differential discounting of incremental costs and health effects in a cost-effectiveness ratio
Converts the yearly streams of incremental costs and incremental QALYs to present values at two different annual rates, a cost rate and a usually lower health rate, before dividing one by the other. The package covers the ratio for a programme with costs and QALYs in different years, the exact health rate implied by growth in the money value of health, the effective cost rate implied by a growing cost-effectiveness threshold, and the factor by which delay changes the ratio. Separate discounting of two streams in general is HE-FM-DR-003 on the discount rate page and the two-option ratio HE-FM-ICER-001. Notation follows the Differential Discounting article.
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Implementations
Excel
Exact and subtraction health discount rates from named cells
With RateC and GrowthV named, the formulas return the exact health rate and the subtraction approximation, held in HealthRate and HealthRateSub.
=(1+RateC)/(1+GrowthV)-1; =RateC-GrowthV
Assumptions
Health measured in QALYs whose money value grows at a constant rate
Costs are valued as forgone consumption and discounted at r_C, health effects are counted in QALYs, and the money value of a QALY grows at the same rate g_v in every year; in the Gravelle and Smith welfare model g_v depends on growth in the direct utility value of health, income growth, the elasticity of the marginal utility of income and insurance against the income losses of ill health.
Gravelle and Smith framing with no binding health budget
The derivation values health in consumption terms; Claxton and colleagues show that with a fixed health budget and decisions based on incremental ratios the gap between the rates comes instead from growth in the threshold (HE-FM-DDIS-003).
Worked examples
Cost rate of 3 per cent and growth of 1.5 per cent in the value of health
The exact health rate is 1.03 divided by 1.015, minus one, or 0.0148, about 1.48 per cent, slightly below the 1.5 per cent given by subtraction, as in the article.
r_C = 0.03; g_v = 0.015; r_H = 0.0148; r_H_sub = 0.015
Growth at the low end of the Dutch estimate of 0.6 to 2.9 per cent
With growth of 0.6 per cent the exact health rate would be about 2.39 per cent and the subtraction rate 2.4 per cent (computed here for illustration); the Dutch guideline uses a growth rate of 1.5 per cent, slightly below the average of its range.
r_C = 0.03; g_v = 0.006; r_H = 0.0239; r_H_sub = 0.024
Common errors
Treating growth in the value of health as a reason for differential rates under a fixed budget
Claxton and colleagues show that, with a fixed budget, expecting growth in the consumption value of health does not on its own justify differential rates but implies a lower rate for both costs and health.
Allowing for the growing value of health twice
Attema and colleagues note that the growing value of health can also be handled through a monetary threshold that rises over time; an analysis that both lowers the health rate by g_v and raises the threshold at g_v counts the same growth twice.
Sources
Gravelle and Smith on the exact health rate in their technical paper
Gravelle H, Smith D. Discounting for health effects in cost benefit and cost effectiveness analysis. CHE Technical Paper 20. York: Centre for Health Economics, University of York; 2000 (full text read). Section 2.1, equation 6: (1 + rh)/(1 + rc) = v0/v1, and the discount rates on health and costs are the same only if the value of health is the same in both periods; with gv the growth rate of the value of health this rearranges to rh = (1 + rc)/(1 + gv) minus 1, approximately rc minus gv. Page 1: discounting the volume of health effects at rh = rc minus gv is equivalent to adjusting the volume of health effects by gv and discounting at the same rate as costs.
Gravelle and Smith 2001 on a lower health rate for the volume of health
Gravelle H, Smith D. Discounting for health effects in cost-benefit and cost-effectiveness analysis. Health Economics. 2001;10(7):587-599. doi:10.1002/hec.618 (abstract read). Abstract: when health effects can be valued in monetary terms they should be discounted at the same rate as costs; discounting the volume of health effects at a lower rate than costs is a valid method of taking account of the increase in the future value of health effects, whose growth depends on the direct utility effect of health, income growth, the elasticity of the marginal utility of income and insurance.
Zorginstituut Nederland 2024 on deriving the effects rate from growth in the value of health
Zorginstituut Nederland. Guideline for economic evaluations in healthcare (2024 version). Diemen: Zorginstituut Nederland; 16 January 2024 (full text read). Section 4.2: the discount rate for effects is calculated as the discount rate for costs minus the growth rate of the consumption value of health, estimated at 0.6% to 2.9% in the Netherlands; a growth percentage of 1.5% is used, slightly below the average of that range.
Claxton and colleagues on growth in the value of health with a fixed budget
Claxton K, Paulden M, Gravelle H, Brouwer W, Culyer AJ. Discounting and decision making in the economic evaluation of health-care technologies. Health Economics. 2011;20(1):2-15. doi:10.1002/hec.1612 (abstract read). Abstract: expecting growth in the consumption value of health does not itself justify differential rates but implies a lower rate for both.
Canonical Identity
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