Signature
ACER_i0 = (C_i - C_0) / (E_i - E_0)
| Inputs | Definition | Unit |
|---|---|---|
C_i | Expected total cost of option i | currency per patient or per defined population |
C_0 | Expected cost when none of the options is provided, for example background care | the same currency basis as C_i |
E_i | Expected total health effect of option i, for example QALYs or life-years | health-effect unit per patient or per defined population |
E_0 | Expected health effect when none of the options is provided | the same health-effect unit as E_i |
ACER_i0 | Average cost-effectiveness ratio of option i against the do-nothing baseline, written ACER_{i,0} in the article | currency per unit of health effect gained, for example £ per QALY gained |
|---|
Function
Average cost-effectiveness ratio function
Maps the expected cost and expected health effect of one option, either in total or measured against a do-nothing baseline, to its cost per unit of health effect without reference to any competing option. Choices between mutually exclusive options rest instead on the pairwise ICER (HE-FM-ICER-001) and on net monetary benefit (HE-FM-NMB-001), which use the same cost and effect notation.
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Implementations
Excel
Calculate an ACER against doing nothing
Excel divides the cost difference from the baseline by the effect difference from the baseline using named cells and returns #N/A when the option does not gain health over doing nothing.
=IF(OptionEffect-BaselineEffect>0,(OptionCost-BaselineCost)/(OptionEffect-BaselineEffect),NA())
Assumptions
Stated and estimated do-nothing baseline
The baseline is stated and estimated with the same model, population, perspective and time horizon as the option, rather than assumed to be zero cost and zero effect.
Doing nothing as the real alternative
The ratio supports a decision only when doing nothing is the actual alternative, or when programmes are independent so that funding one does not prevent funding another. Mutually exclusive options are compared with incremental ratios after dominated options are removed.
Positive health gain over doing nothing
The difference E_i minus E_0 is greater than zero, so the ratio reads as cost per unit of health gained. Other sign combinations follow the quadrant rules for the ICER in HE-FM-ICER-001.
Worked examples
ACER against no treatment for treatment A
Treatment A has totals of £3,000 and 5.40 QALYs and no treatment has £1,000 and 5.00 QALYs. The extra £2,000 buys 0.40 QALYs, so A costs £5,000 per QALY gained against no treatment, the same figure as when costs and QALYs are recorded as differences from no treatment.
C_i = 3000; E_i = 5.40; C_0 = 1000; E_0 = 5.00; ACER_i0 = 5000
ACER against no treatment for treatment B and its ICER against A
Treatment B has totals of £10,000 and 5.60 QALYs, so it costs £15,000 per QALY gained against no treatment. Both average ratios are below an illustrative threshold of £20,000 per QALY, yet the ICER of B against A (HE-FM-ICER-001) is £35,000 per QALY, an extra £7,000 for an extra 0.20 QALYs. At that threshold the net monetary benefit (HE-FM-NMB-001) is £6,000 for A and £3,000 for B, so A is the right choice.
C_i = 10000; E_i = 5.60; C_0 = 1000; E_0 = 5.00; ACER_i0 = 15000
ACER against no treatment with a zero baseline
When costs and QALYs are already recorded as differences from no treatment, the baseline is zero cost and zero effect and the two forms of the average ratio coincide. Treatment A, at £2,000 and 0.40 QALYs, again costs £5,000 per QALY gained.
C_i = 2000; E_i = 0.40; C_0 = 0; E_0 = 0; ACER_i0 = 5000
Common errors
Testing an average ratio against the threshold when another option exists
An average ratio below the threshold shows cost-effectiveness only if doing nothing is the sole alternative. In the article's example B costs £15,000 per QALY gained against no treatment, below £20,000, but its ICER against A is £35,000 per QALY, so adopting B on its average ratio approves a poor-value option.
Choosing the option with the lowest average ratio
Ranking mutually exclusive options by average ratio ignores what the extra health from the more effective option costs. At £40,000 per QALY the lowest average ratio still picks A at £5,000, but the ICER of B against A is £35,000, below the threshold, and net monetary benefit is £15,000 for B against £14,000 for A, so B is the right choice.
Reading a table of average ratios as a funding ranking
Average ratios from separate studies each rest on their own baseline, population and time horizon, so placing them side by side and funding from the lowest upwards compares unlike quantities.
Sources
WHO-CHOICE plane with average and incremental ratios
Bertram MY, Lauer JA, Stenberg K, Tan Torres Edejer T. Methods for the economic evaluation of health care interventions for priority setting in the health system: an update from WHO CHOICE. International Journal of Health Policy and Management. 2021;10(Special Issue on WHO-CHOICE Update):673-677. Figure of the cost-effectiveness plane showing average and incremental ratios for two interventions, with the origin of no costs and no effects as the null position.
Average ratios against no screening compared with incremental ratios
Hershey JC, Asch DA, Jepson C, Baron J, Ubel PA. Incremental and average cost-effectiveness ratios: will physicians make a distinction? Risk Analysis. 2003;23(1):81-89. Abstract, which defines average ratios relative to a no-screening option and incremental ratios against the next best alternative.
Clinician guide to incremental rather than average ratios
Hoch JS, Dewa CS. A clinician's guide to correct cost-effectiveness analysis: think incremental not average. Canadian Journal of Psychiatry. 2008;53(4):267-274. Abstract, which names the ICER and incremental net benefit as correct summary measures in place of average ratios.
Canonical Identity
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