Signature
V_strat = sum_(x=1)^K (P_x * max(0, INMB_x)) - max(0, sum_(x=1)^K (P_x * INMB_x))
| Inputs | Definition | Unit |
|---|---|---|
P_x | Share of the decision population in subgroup x | proportion of the population |
INMB_x | Incremental net monetary benefit per patient of the treatment against the comparator in subgroup x, from HE-FM-NMB-002 at the chosen value per QALY | currency per patient |
V_strat | Gain in expected incremental net monetary benefit from deciding by subgroup rather than for the whole population | currency per member of the population, for example £ |
|---|
KNumber of non-overlapping subgroups that can receive separate decisions (count)
Function
Average treatment effect function
Maps the two potential outcomes of each patient in a stated population, Y(1) under the treatment and Y(0) under the comparator, to the mean of their difference. Only one potential outcome is observed for any patient, so the mean is computed from subgroup averages or by reweighting observed outcomes under stated conditions. Conditioning on the treated gives the average effect on the treated (ATT), and conditioning on baseline characteristics gives the conditional average effect (CATE). Applied to costs and to QALYs, the two averages are the incremental cost and incremental QALYs used by the pairwise ICER (HE-FM-ICER-001) and the incremental net monetary benefit (HE-FM-NMB-002).
Implementations
Excel
Static value of subgroup targeting in one cell
Excel adds the share-weighted positive subgroup INMBs and subtracts the population INMB when it is positive. The named ranges hold one share and one INMB per subgroup.
=SUMPRODUCT(SubgroupShares,(SubgroupINMB>0)*SubgroupINMB)-MAX(0,SUMPRODUCT(SubgroupShares,SubgroupINMB))
Assumptions
Treatment against one comparator in each subgroup
Each subgroup chooses between the treatment and one comparator, with INMB measured against the comparator, so not treating has an INMB of zero. With more options, each term takes the largest expected net benefit across the options.
Subgroup membership known at the point of decision
Subgroup membership is observable when treatment is decided, and the decision can restrict treatment to some subgroups. The shares P_x sum to 1.
Subgroup estimates under current information
The INMB_x values are treated as known expected values. The value of resolving uncertainty in them, the dynamic value of heterogeneity, needs value of information analysis and is not part of this formula.
Worked examples
Targeting the high-risk subgroup at £25,000 per QALY
At an illustrative £25,000 per QALY the INMB is minus £500 per low-risk patient and £6,000 per high-risk patient, and £2,100 for the population. Treating only high-risk patients yields £2,400 per member of the population, so targeting is worth £300 per member, the static value in the article.
K = 2; P_x = [0.6,0.4]; INMB_x = [-500,6000]; V_strat = 300
No targeting value at £35,000 per QALY
At £35,000 per QALY, the upper end of the NICE range, the subgroup INMBs are £500 and £10,000 per patient. Both are positive, so treating everyone is already the best decision and targeting adds nothing.
K = 2; P_x = [0.6,0.4]; INMB_x = [500,10000]; V_strat = 0
Common errors
Deciding on the population INMB when targeting is possible
The positive population INMB of £2,100 suggests treating everyone, yet each low-risk patient treated loses £500. Treating everyone gives up £300 per member of the population against treating only high-risk patients. Subgroup estimates are less precise than the population average, so the subgroups are preferably specified in advance.
Comparing a subgroup INMB with the population INMB
The high-risk INMB of £6,000 is per high-risk patient. Set against the population INMB of £2,100 it suggests a gain of £3,900 from targeting, when the high-risk-only policy yields £2,400 per member of the population and the gain is £300.
Sources
Espinoza and colleagues on the static value of heterogeneity
Espinoza MA, Manca A, Claxton K, Sculpher MJ. The value of heterogeneity for cost-effectiveness subgroup analysis: conceptual framework and application. Medical Decision Making. 2014;34(8):951-964. Section on net benefits for subgroup cost-effectiveness analysis under current information, which writes the total INB as the population-weighted sum of subgroup INBs and the gain from stratification as the weighted sum of each subgroup's maximum net benefit minus the maximum average net benefit.
Coyle and colleagues on stratified cost-effectiveness analysis
Coyle D, Buxton MJ, O'Brien BJ. Stratified cost-effectiveness analysis: a framework for establishing efficient limited use criteria. Health Economics. 2003;12(5):421-427. Abstract, which presents a framework for estimating the benefits from stratification when payers restrict reimbursement to a subgroup.
Canonical Identity
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