Best Informing Multiple Strategy Cost Effectiveness Analysis and Societal Decision Making: The Cost Disutility Plane and Expected Net Loss Curves and Frontiers

An Introduction to Multiple Strategy Comparison and Limitations of Fixed Comparator Two-Strategy Presentations and Summary Measures

Health economic analysis attempts to inform decision makers of relative effects and costs across potentially optimal alternatives in treating defined patient populations. Comparisons may be between a strategy and single comparator (bilateral) or between multiple strategies (multilateral). In the case of multilateral comparisons, consider, for example, the well-analysed comparison of six alternative strategies for gastro-oesophageal reflux disease (GERD) based on 1-year cost and outcomes in terms of weeks with or without GERD for patients presenting to their physician with endoscopically proven erosive esophagitis (Table 8.1) (Goeree et al. 1999; Briggs et al. 2002; Eckermann et al. 2008).

Multiple strategy cost effectiveness analysis for this example was first considered by Goeree et al. (1999) and then Briggs et al. (2002) on the incremental cost effectiveness plane (weeks without GERD) with a fixed comparator and more recently Eckermann (2004), Eckermann et al. (2005, 2008) and Eckermann and Willan (2011) on the cost-disutility plane with flexible axes (additional weeks of GERD to 1 year relative to the most effective strategy in each replicate).

Such multiple strategy comparisons are becoming increasingly important with diagnostic and genetic testing options as well as treatment of populations across multiple modalities and different strategies for combinations of therapies. Robust methods for multiple strategy comparisons that enable joint comparison of relative costs, effects and net benefit of multiple strategies against each other are required to satisfy coverage and comparability principles, and enable unbiased evidence-based cost effectiveness related decision making. Ideally presentation and summary measures of cost effectiveness evidence that directly inform societal decision making just as they were for two-strategy comparison. For two strategy comparisons, robust methods for joint presentation of costs and effect on the incremental cost

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S. Eckermann, Health Economics from Theory to Practice,

DOI 10.1007/978-3-319-50613-5_8

Table 8.1 Six alternative strategies for gastro-oesophageal reflux disease (GERD)








Cost per patient







Weeks without GERD (to 1 year)







Weeks with GERD (to 1 year)







A Intermittent PPI, B maintenance PPI, C maintenance H2RA, D step down maintenance PA, E step down maintenance H2RA, F step down maintenance PPI

effectiveness plane (relative to the fixed comparator at the origin) and summarising of cost effectiveness evidence with the INB curve (relative to the fixed comparator) and the CEA curve were identified in Chap. 2.

However, comparison of more than two strategies is conceptually and practically very different to two strategy, fixed comparator presentation of incremental costs and effects and cost effectiveness on the cost effectiveness plane and with incremental net benefit and CEA summary curves (Eckermann, Briggs and Willan 2008; Eckermann and Willan 2011). For bilateral (two strategy) comparisons, the appropriate comparator in maximising effect, minimising cost or maximising net benefit is simply the other strategy. This enables a fixed comparator as the origin in the C-E plane and for INB or CEA curves whether considered at expected values or under uncertainty, in any replicate or at any given threshold value. For multilateral comparisons (comparing more than two strategies), the appropriate comparator for any strategy in maximising effect, minimising cost or maximising net benefit can change across replicates, as well as with the threshold value in the case of net benefit.

To begin to see the problems and conceptual and practical issues such fixed comparator presentation and summary measures pose in attempting to accommodate multiple strategy comparison, we first consider the presentation of GERD evidence on the cost effectiveness plane. Conventionally, the cost effectiveness plane with two strategy comparisons presents evidence for a new therapy relative to current usual care. For multiple strategy comparison, Briggs et al. (2002) recognised that graphical interpretation of expected costs and effects on the incremental cost effectiveness plane is aided where the comparator is set to the excepted lowest cost strategy.

In particular, comparison of expected cost and effects of multiple strategies measuring incremental effects and incremental costs relative to the strategy with lowest expected cost strategy as a comparator enables a best practice efficiency frontier to pass through the origin (Fig. 8.1).

More generally the incremental cost effectiveness plane with the lowest cost strategy as the origin (Briggs et al. 2002) at least enables a starting point for considering some useful principles for comparisons of multiple strategies at their expected values in relation to:

  • (i) Excluding strategies with ‘extended dominance’ - convex combinations of other strategies have lower cost and greater effect (e.g. for GERD strategies D and F can move in SE direction to linear combination of other strategies).
  • (ii) An efficiency frontier being formed by remaining non-dominated strategies (e.g. strategies C, A, E and B can’t move in SE direction - reduce their cost and increase effect to any convex combination of other strategies);
GERD strategies on the incremental cost effectiveness plane (comparator origin strategy with expected least cost) (Source

Fig. 8.1 GERD strategies on the incremental cost effectiveness plane (comparator origin strategy with expected least cost) (Source: Eckermann et al. (2008))

  • (iii) At a given value for effect, net benefit of strategies can be compared with NB lines reflecting levels of incremental net benefit relative to lowest cost strategy comparator (e.g. $100/week of GERD avoided in Fig. 8.1).
  • (iv) The appropriate comparator for net benefit consideration changing with threshold values as one moves up the frontier (e.g. for GERD from C to A to E to B).

In relation to (iv), the appropriate comparator at any threshold value is that which maximises NB and hence for each strategy on the frontier reflects the range of threshold values for which they lie on the highest INB line, tangent to the frontier. For example, in the case of GERD strategies on the frontier maximising NB are C from a threshold value of 0 up to $10/week of GERD avoided (the slope of line AC), strategy A from $10 to $36, strategy E from $36 to $243 and strategy B beyond $243.

Nevertheless, presentation on the incremental costs effectiveness plane where performance improves in a south-east direction (cost reduces and effects increase), leads to unbounded consideration of net benefit and more generally poses distinct limitations for informing multiple strategy comparison for analysts and decision makers alike. The south-east direction for identification of dominance and performance improvement inherent in the CE plane does not permit radial properties in contracting to or expanding from a vertex. These radial properties are required to employ standard efficiency measures in identifying a frontier or relative performance of strategies off the frontier relative to the frontier. Efficiency frontiers on the C-E plane are consequently constructed ‘by hand’ and without being able to compare or interpret relative performance of strategies off the frontier (Eckermann 2004; Eckermann et al. 2008).

Frontiers and relative performance with radial properties on the cost disutility plane (Source

Fig. 8.2 Frontiers and relative performance with radial properties on the cost disutility plane (Source: Eckermann et al. (2008))

In contrast, comparison on the C-DU plane with flexible axes (Fig. 8.2) provides radial properties with performance improvement where cost and effects framed from a negative or disutility bearing perspective (e.g. mortality, morbidity, weeks with GERD, life years or QALYs lost) reduce and hence both contracting towards the origin or vertex. Combined with flexible axes where cost is measured relative to that of the lowest cost strategy in each replicate and disutility measured relative to the strategy with lowest disutility (highest effect) in each replicate, multiple strategy comparison on the C-DU plane enables:

  • (i) Technically simpler construction of efficiency frontiers and identification of net benefit-maximising strategies on the frontier and extended dominated strategies off it;
  • (ii) Degree of dominance (technical inefficiency) to be compared across dominated strategies;
  • (iii) A bounded comparison of net benefit (iso-net-benefit lines); and
  • (iv) Cost and effect inference under uncertainty prevented with multiple strategy comparisons on the C-E plane with fixed axes.

Advantages (i) to (iii) of the C-DU plane are explored in greater detail in Chaps. 9 and 10 where they have greater import to comparison and decomposition of provider efficiency following Eckermann (2004) and Eckermann and Coelli (2013) and multiple domain of effect cost effectiveness comparisons following McCafrey et al. (2015), while we focus on (iv) in this chapter following Eckermann and Willan (2011).

Multiple strategy cost and effect inference with fixed axes on the CE plane? (Source

Fig. 8.3 Multiple strategy cost and effect inference with fixed axes on the CE plane? (Source: Eckermann and Willan (2011))

In relation to cost and effect inference (iv), the fixed nature of all strategies being compared with a single comparator on the CE plane, whether the expected least cost comparator strategy or otherwise, frequently confounds even the simplest graphical inference under uncertainty (Eckermann and Willan 2011). For example, consider on the C-E plane what proportion of replicates each of the 6 GERD strategy maximises effect under uncertainty in Fig. 8.3, constructed from 1000 Mont-Carlo simulation model replicates across these strategies. While strategy B has the highest expected weeks without GERD (47.14 in Table 8.1 and as the highest effect strategy on the frontier in Fig. 8.1), it is not clear which of strategies B, F, E or even A have highest effect in any individual replicate or set of replicates across strategies on the C-E plane in Fig. 8.3. This lack of clarity arises given distributions for each of strategies F, E and even A, considered under uncertainty relative to the fixed expected least cost strategy C, overlap in terms of incremental effect.

This inability of the CE plane to enable even the simplest of graphical inferences reflects the added challenge in comparing multiple strategies of the appropriate comparator changing for cost minimisation and effect maximisation, let alone net benefit maximisation. Indeed, in the case of net benefit the appropriate comparator can change with threshold values for effects, as well as cost and effect evidence across strategies in each replicate, as we later highlight in identifying a solution with the flexible net loss statistic in Sect. 8.3. However, Sect. 8.2 first considers in overcoming more basic fixed comparator problems in considering cost and effect uncertainty and inference on the C-E plane, with flexible axes on the C-DU plane.

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