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So, for instance, a CBA may compare building a \$20 million wall with building a \$10 million wall to protect a \$100 million building. Let us assume that the \$20 million wall would save the entire building during an explosion while the \$10 million wall would only save half of the building, or \$50 million. Then, a CBA would find the \$20 million wall (which would provide a net benefit of \$80 million = \$100 million - \$20 million) to be more favorable than the \$10 million wall (which would offer only a net benefit of \$40 million). The analysis in Chapter 29 is a CBA.

However, if all the potential rewards do not translate easily into pure monetary terms, a CEA (which measures rewards in simple clinical units such as life years saved, deaths avoided, or operations avoided) or a CUA (which measures rewards in health status measures such as QALYs or utilities) is more useful. Because it can be difficult to quantify the economic value of saving a single life or avoiding a medical procedure, a CEA and CUA will measure the costs and benefits of each alternative separately and compare the alternatives by using incremental cost-effectiveness (or cost-utility) ratios, described in the next section.

### 3.6. Marginal and Incremental Analyses

Incremental analyses quantify the resulting differences in choosing one alternative over others. An incremental analysis can tell you whether strategy A is more preferable than B, but will not tell you in absolute terms whether either strategy is better than doing nothing.

In CBAs, the incremental cost indicates the change in cost when moving from one alternative to another. For example, if cbx and cby are the net costs and rewards of strategies X and Y respectively, then the incremental cost of using strategy Y instead of X is cby - cbx. A negative incremental cost suggests that strategy Y is preferable over X, whereas a positive one favors X.

Similarly in CEAs, an incremental cost-effectiveness ratio (ICER) is the change in cost per change in effectiveness when shifting from one alternative to another, and in CUAs, an incremental cost-utility ratio is the change in cost per change in health status when shifting from one alternative to another. For example, if CA and CB are the costs of strategies A and B, respectively, and EA and EB are the resulting effectiveness (benefit) of A and B, respectively, then the ICER is (CB - CA)/ (Eb - Ea). Interpreting this ratio is somewhat more complicated than is interpreting an incremental cost. If the ICER is negative, then strategy B is favorable or dominant to strategy A. If the ICER is positive, then the magnitude of the ICER matters. If for instance, the ICER is \$10 per life year saved, then choosing strategy B requires only \$10 more for each life year saved. Most, except for the most penurious, would view this as a worthwhile investment and choose B. However, if the ICER

were \$100,000 per life year saved, then decision makers would have to debate over whether this reward is worth the investment. There is extensive literature debating the appropriate threshold dollar value per life year (Gold et al., 1996; Neumann et al., 2000; Hershey et al., 2003; Ubel et al., 2003).

Marginal cost and marginal cost-effectiveness studies can help reveal the implications of changing a certain parameter (e.g., number of medications given, dollars invested, items used, people employed) by a single unit. For example, in a CBA, to measure the added cost of giving every patient an extra day of a medication, if CN represents the net monetary value of giving a medication for N days and CN+1 is the net monetary value for giving it N + 1 days, then the marginal cost would be CN+1 - CN. In a CEA, if CN and EN represents the cost and effectiveness, respectively, of giving a medication N days and CN+1 and EN+1 represent the cost and effectiveness, respectively, of giving the medication N + 1 days, the marginal cost-effectiveness of an additional day of medication is (Cn+1 - Cn)/(En+1 - En). A similar calculation would yield a marginal cost-utility in a CUA.

### 3.7. Decision Analysis and CEA and CUA

The procedure to perform a CEA or CUA is similar to procedure described in Chapter 29, except that each branch in the decision tree has two sets of outcomes (i.e., costs and effectiveness measures or costs and utility measures) instead of just one (i.e., the net costs and benefits denominated in dollars). Therefore, you will need to fold back costs separately and then effectiveness or utilities separately before combining them in ICERs. By using the example in Chapter 29, Figure 31.1 shows the same decision tree structure as Figure 29.3 with one difference: each branch has a cost outcome (C1,C2,C3,C4) and an effectiveness outcome (E1,E2,E3,E4). So if C1 was equal to cb1 or -\$89,315,780.49, C2 was equal to cb2 or -\$8,025,000, C3 was equal to cb3 or -\$115,454,219.50, and C4 was equal to cb4 or -\$115,454,219.50, then folding back the costs would yield an expected cost value of act now of -\$11,357,922 and an expected cost value of wait of -\$4,733,623. Now, if both E1 was equal to 10,000 life years saved, E3 was equal to 10 life years saved, and both E2 and E3 were equal to 0 life years saved, then the expected life years saved for act now would be p•E1 + (1 - p) • E1 = 0.041 x 10,000 life years saved + 0.959 x 0 life years saved = 4.1 life years saved. The expected value of wait is p-E3 + (1 -p)- E4 = 0.041 x 10 life years saved + 0.959 x 0 life years saved = 0.41 life years saved. The ICER of act now would then be [Expected Costsactnow - Expected Costswait]/ [Expected Effectivenessactnow - Expected Effectivenesswait] or [-\$11,357,922 - (-\$4,733,623)]/[10,000 - 10] = \$16,173 per life year saved.