Signature
ACER_i = C_i / E_i
| Inputs | Definition | Unit |
|---|---|---|
C_i | Expected total cost of option i, including costs that would arise without it | currency per patient or per defined population |
E_i | Expected total health effect of option i, for example QALYs or life-years, including health that would occur without it | health-effect unit per patient or per defined population, above zero |
ACER_i | Average cost-effectiveness ratio of option i in total form | currency per unit of health effect, for example £ per QALY lived |
|---|
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 a total-form ACER
Excel divides the expected total cost by the expected total effect using named cells and returns #N/A when the total effect is not above zero.
=IF(TotalEffect>0,TotalCost/TotalEffect,NA())
Assumptions
Ratio of mean cost to mean effect for a total-form ACER
The ratio is formed from the expected (mean) total cost and the expected total effect of the same patient group, not by averaging ratios calculated for individual patients. Costs and effects share one population, perspective, time horizon, price year and discounting approach.
Descriptive use of a total-form ACER
The ratio describes one option on its own and involves no comparison. It does not show whether the option is worth its cost against any alternative, including doing nothing.
Worked examples
Total-form ACER for treatment A with background care
In the article's illustrative example, untreated patients live 5.00 QALYs and incur £1,000 of background care, so treatment A has totals of £3,000 and 5.40 QALYs. Its total-form ratio is about £556 per QALY lived, far below the £5,000 per QALY gained that A achieves against no treatment.
C_i = 3000; E_i = 5.40; ACER_i = 555.56
Total-form ACER for treatment B with background care
With the same background care, treatment B has totals of £10,000 and 5.60 QALYs, giving a total-form ratio of about £1,786 per QALY lived. Against no treatment B costs £15,000 per QALY gained, so the total form shrinks the ratio by spreading cost over health that would have occurred anyway.
C_i = 10000; E_i = 5.60; ACER_i = 1785.71
Common errors
Reporting a total-form ACER as cost per QALY gained
A total-form ratio treats every QALY lived as if the option caused it. In the article's example treatment A appears to cost about £556 per QALY when it costs £5,000 per QALY gained against no treatment, and the total-form figure falls further as the arbitrary background health grows.
Sources
Bang and Zhao on the ACER as a ratio of means
Bang H, Zhao H. Average cost-effectiveness ratio with censored data. Journal of Biopharmaceutical Statistics. 2012;22(2):401-415. Introduction, which writes the ACER as mean cost divided by mean effectiveness and the ICER as the ratio of differences in mean cost and mean effectiveness between groups.
Canonical Identity
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