Fully Incremental Analysis

What fully incremental analysis does

It removes strategies ruled out by strict or extended dominance and recalculates incremental cost-effectiveness ratios between the remaining adjacent options.

This procedure answers which strategy becomes optimal as the decision maker's cost-effectiveness threshold increases. It differs from comparing every strategy only with a single baseline, because the relevant comparator for an efficient strategy is the next less effective strategy on the frontier.

The incremental cost-effectiveness ratio

For a more effective strategy $j$ and its relevant less effective comparator $i$, the incremental cost-effectiveness ratio, or ICER, is the additional cost divided by the additional health effect. Costs and effects must use consistent perspectives, time horizons, discounting, populations, and units before the ratio is calculated.

$$ICER_{j,i}=\frac{C_j-C_i}{E_j-E_i} =\frac{\Delta C_{j,i}}{\Delta E_{j,i}}$$

In a fully incremental analysis, $i$ is not automatically usual care. It is the adjacent surviving strategy after the ordering and dominance rules have been applied.

Why baseline comparisons can mislead

Pairwise ICERs against a common baseline do not reveal whether an intermediate strategy lies below the efficient frontier. They can therefore make a strategy look attractive even though a more efficient sequence of alternatives provides health gains at a lower marginal cost per unit of effect.

The fully incremental procedure treats the options as a mutually exclusive choice set. If technologies are not mutually exclusive, the strategies must first be defined as feasible combinations or treatment pathways rather than analysed as though only one could be selected.

The cost-effectiveness frontier

The cost-effectiveness frontier contains the non-dominated strategies that can be optimal for at least one range of threshold values. When plotted with effectiveness on the horizontal axis and cost on the vertical axis, these strategies form the lower convex envelope of the available options.

Successive ICERs along a correctly constructed frontier must increase as effectiveness rises. A fall in the ICER sequence signals extended dominance and requires removal of an inefficient intermediate strategy followed by recalculation.

Strict dominance

A strategy is strictly dominated when another available strategy is at least as effective and less costly, or at least as cheap and more effective. A strictly dominated option cannot maximise net benefit at any positive threshold under the same cost and effect assumptions.

For strategies $i$ and $j$, strategy $j$ is strictly dominated by $i$ when:

$$C_i\leq C_j,\qquad E_i\geq E_j$$

with at least one strict inequality. Strictly dominated strategies are removed before sequential ICERs are interpreted.

Extended dominance

A strategy is subject to extended dominance when a more efficient combination of other strategies can provide greater expected effectiveness at a lower incremental cost per unit of effect. Algebraically, it appears when the ICER for moving into a strategy is higher than the ICER for moving from that strategy to a more effective option.

For three effectiveness-ordered strategies $i$, $j$, and $k$, strategy $j$ is extendedly dominated when:

$$ICER_{j,i}>ICER_{k,j}$$

The intermediate strategy $j$ is removed, and $ICER_{k,i}$ is calculated directly. This process repeats until all remaining sequential ICERs increase monotonically.

A complete worked example

Consider five mutually exclusive strategies with discounted costs and QALYs per person. The table is already ordered from least to most effective, but dominance checks must still be applied.

Strategy D costs £2,000 more than C and produces $0.1$ fewer QALYs, so D is removed by strict dominance. The first sequential calculations for the remaining strategies are:

$$ICER_{B,A}=\frac{\text{£}15{,}000-\text{£}10{,}000}{5.3-5.0} =\frac{\text{£}5{,}000}{0.3}=\text{£}16{,}667\text{ per QALY}$$ $$ICER_{C,B}=\frac{\text{£}18{,}000-\text{£}15{,}000}{5.6-5.3} =\frac{\text{£}3{,}000}{0.3}=\text{£}10{,}000\text{ per QALY}$$

Because the ICER falls from £16,667 to £10,000 per QALY, strategy B is subject to extended dominance. After removing B, the comparison between C and A is recalculated:

$$ICER_{C,A}=\frac{\text{£}18{,}000-\text{£}10{,}000}{5.6-5.0} =\frac{\text{£}8{,}000}{0.6}=\text{£}13{,}333\text{ per QALY}$$

The final step from C to E is:

$$ICER_{E,C}=\frac{\text{£}30{,}000-\text{£}18{,}000}{6.0-5.6} =\frac{\text{£}12{,}000}{0.4}=\text{£}30{,}000\text{ per QALY}$$

The final ICER sequence increases from £13,333 to £30,000 per QALY. The cost-effectiveness frontier therefore contains A, C, and E; B is removed by extended dominance and D by strict dominance.

Reading the threshold ranges

Each final frontier ICER is the threshold at which two adjacent strategies have equal net monetary benefit. Away from exact ties, the optimal strategy changes as the threshold crosses these frontier values.

At exactly £13,333, A and C tie subject to unrounded values; at exactly £30,000, C and E tie. Rounding an ICER before applying the decision rule can move an apparent boundary, so calculations should retain full precision.

Cross-checking with net monetary benefit

Net monetary benefit provides a ratio-free way to confirm the incremental analysis at a chosen threshold $\lambda$. The strategy with the largest net monetary benefit is cost-effective for that threshold.

$$NMB_j(\lambda)=\lambda E_j-C_j$$

At $\lambda=£20{,}000$ per QALY, the worked example gives:

Strategy C has the highest NMB, consistent with the frontier because £20,000 lies between £13,333 and £30,000 per QALY. Strategies B and D never maximise NMB over positive thresholds in this example.

The full calculation algorithm

The analysis is iterative because removing one strategy changes which options are adjacent. A reliable implementation repeats the dominance and recalculation steps until the frontier no longer changes.

1. List every mutually exclusive and decision-relevant strategy with its expected cost and expected effect.
2. Sort the strategies from least to most effective using full-precision effects.
3. Remove exact duplicates according to a prespecified rule that retains the least costly strategy for an equal effect.
4. Remove every strictly dominated strategy.
5. Calculate incremental costs, incremental effects, and ICERs for adjacent remaining strategies.
6. Identify the first point at which a sequential ICER is less than or equal to the preceding ICER, subject to the stated tie rule.
7. Remove the intermediate strategy subject to extended dominance.
8. Recalculate all affected incremental results after every removal.
9. Repeat the strict- and extended-dominance checks until sequential frontier ICERs increase.
10. Verify the final frontier against net monetary benefit across relevant threshold values.

The final output should preserve both the original strategy set and the exclusion reason for each removed option. Silently deleting strategies prevents reviewers from reconstructing the analysis.

Handling equal costs, equal effects, and near-ties

Ties and very small differences require explicit rules because they can create zero denominators or unstable ratios. Full numerical precision should be used for calculations even when the published table displays rounded costs and effects.

• Equal effectiveness: Retain the least costly strategy and mark more costly strategies as strictly dominated.
• Equal cost: Retain the most effective strategy and mark less effective strategies as strictly dominated.
• Identical cost and effect: Retain one clearly identified representative or show the tie without calculating an ICER between duplicates.
• Zero incremental effect: Do not divide by zero; resolve dominance or equivalence before calculating an ICER.
• Near-zero differences: Report the numerical sensitivity and avoid interpreting an unstable ratio without the underlying increments.
• Equal sequential ICERs: Apply a documented convention because collinear strategies lie on the same frontier segment and may have equal net benefit at one threshold.

Rounding can falsely create or conceal dominance. Audit files should retain unrounded model outputs, and display rounding should occur only after the frontier is established.

What the analysis assumes

Fully incremental analysis is mechanically correct only when its inputs and strategy set are appropriate. It does not repair missing comparators, inconsistent models, biased estimates, or an incoherent decision problem.

• Mutual exclusivity: The decision maker chooses one defined strategy from the evaluated set.
• Comparable outcomes: Every strategy's effect is measured in the same unit, commonly QALYs.
• Consistent scope: Costs and effects use the same population, perspective, time horizon, discount rates, and price basis.
• Relevant comparators: All feasible strategies that could alter the frontier are included.
• Expected values: The deterministic frontier uses expected costs and effects, with uncertainty assessed separately.
• Divisibility for extended dominance: The frontier interpretation assumes resources can be allocated across strategies or populations in a way consistent with the decision context.

The divisibility interpretation can be difficult when a strategy must be adopted for an indivisible population or system. Net-benefit analysis still provides a coherent threshold rule, but the meaning of a probabilistic mixture used to explain extended dominance should be stated carefully.

Uncertainty around the frontier

The deterministic frontier uses mean costs and effects and does not show the probability that each strategy is optimal. Sampling, parameter, structural, and methodological uncertainty can change dominance status and the preferred strategy.

Probabilistic sensitivity analysis should calculate costs, effects, and net benefit jointly for every strategy in every simulation draw. Cost-effectiveness acceptability curves or frontiers then summarise decision uncertainty, while the expected-value decision remains the strategy with the highest expected net benefit at the chosen threshold.

An ICER confidence interval is often difficult to interpret because the ratio is discontinuous when incremental effectiveness is near zero. The joint cost-effectiveness plane and net-benefit framework usually provide clearer uncertainty summaries.

Subgroups and treatment sequences

The efficient strategy can differ across clinically meaningful subgroups because baseline risk, treatment effect, cost, or utility may differ. A pooled frontier should not be assumed to apply to every subgroup when a decision can be targeted.

For treatment sequences, each feasible sequence is a strategy and its total expected costs and effects enter the fully incremental table. Comparing individual drugs without modelling downstream sequencing can omit displacement, switching, and subsequent treatment consequences.

Spreadsheet implementation and audit checks

A spreadsheet can implement the algorithm transparently when raw strategies, working calculations, and final frontier outputs remain distinct. Manual row deletion is risky because it obscures provenance and can leave ICER formulas pointing to the wrong comparator.

• Preserve the source table with stable strategy identifiers, unrounded costs, and unrounded effects.
• Create an ordered working table that records strict-dominance and extended-dominance flags without deleting source records.
• Calculate adjacent differences from the currently surviving strategies rather than from fixed row positions.
• Recalculate after each exclusion until the frontier and sequential ICERs are stable.
• Check monotonicity so effectiveness, cost on the frontier, and frontier ICERs increase in the required order.
• Cross-check NMB over thresholds below, at, between, and above the frontier ICERs.
• Flag zero or negative increments and exact or near-ties for review rather than suppressing errors.

A robust audit should confirm that every excluded strategy has one traceable reason and that every surviving ICER uses the correct adjacent comparator. Hard-coded exclusions should be avoided unless the decision and rationale are explicitly documented.

Interpreting and reporting the result

The final frontier describes efficient expected cost-effect combinations for the stated strategy set and model assumptions. It does not prove that a selected technology is affordable, equitable, clinically acceptable, or feasible to implement.

Reporting should show all strategies, ordered costs and effects, dominance classifications, incremental differences, recalculated frontier ICERs, threshold, NMB cross-check, and relevant uncertainty analyses. Common errors include retaining an extendedly dominated option, failing to recalculate after removal, comparing every strategy only with baseline, omitting a relevant comparator, rounding too early, and interpreting an ICER without its incremental cost and effect.