Basic Cost-Effectiveness Model

Weinstein (1995) gives a very clear statement about the underlying logic of the cost-effective approach to medical decision-making. The analysis starts as follows. One is considering a menu of programs, where i identifies a typical program and is numbered from 1 to N. All programs are assumed Fundamentals of cost-effectiveness analysis 143

to be divisible with constant returns to scale. The programs are not repeat-able (or else one can just keep on doing one program over and over again if that one is the most cost-effective). All programs on the list must be fea-sible, such that if one is adopted, that does not preclude another being adopted later on (thus, for example, one program cannot be an alternative drug for a drug treating the same condition in another program). The deci-sion-maker selects an effect E that s/he is trying to maximize given a fixed budget cost C. One calculates all the programs C_ithat make up the budget cost C and one also measures each program effect E_i. If an E_iis negative, one simply deletes it from the list.

From this starting point, one proceeds to rank order (from lowest to highest) all the cost-effectiveness ratios C_i/ E_i. Programs are selected from the top of the list and working downwards until the entire budget has been exhausted. The set of programs so identified provide the most total effect for the budget. To illustrate the method, we will take Weinstein’s (1995) hypothetical example (Box 5.2), and add a column for the cumulative cost, to form our Table 6.1.

Table 6.1: Hypothetical example of the cost-effectiveness paradigm

Program Effect Cost ($) C/E ratio ($) Cumulative cost ($)

A 500 1 000 000 2000 1 000 000

B 500 2 000 000 4000 3 000 000

C 200 1 200 000 6000 4 200 000

D 250 2 000 000 8000 6 200 000

E 100 1 200 000 12 000 7 400 000

F 50 800 000 16 000 8 200 000

G 100 1 800 000 18 000 10 000 000

H 100 2 200 000 22 000 12 200 000

I 150 4 500 000 30 000 16 700 000

J 100 5 000 000 50 000 21 700 000

Source: Based on Weinstein (1995)

Say the budget available is $10 million. Program A is affordable and is the most cost-effective, so it must be chosen (if any one is chosen). Working down the list, we choose B and C and continue down to G, which corre-sponds to a $10 million cumulative cost. Program H would exceed the budget, so cannot be selected. By choosing programs A to G, the total effect obtained is 1700. This is the most effect that the $10 million can buy.

Although, as we have emphasized a number of times already, CEA cannot tell us whether any of the A to G programs are socially worthwhile

144 CEA and CBA

in absolute terms, Weinstein makes the important point that we are now at least in a position to identify better and worse programs in relative terms.

Program H’s cost of $18000 per effect is the benchmark or ‘cutoff’ ratio in this process. It tells us that if any new program wants to be adopted instead of any of the A to H, it must at least be able to lead to an effect that costs less than $18 000. If a new program costs $19 000 per effect, the money is best left in program G; while if the cost per effect of the new program is

$17 000 it can then replace project G. In this case, if G were worthwhile, then the new program would be even more worthwhile.

What happens if the programs are mutually exclusive (e.g., different treatments for the same condition are being considered, as with alternative drugs for dealing with hypertension) since this means that one program would be used at the expense of another, and thus not all programs are fea-sible? Weinstein points out that in these cases one needs to adjust the basic framework given above and turn from average cost-effectiveness ratios to incremental effectiveness ratios C/E. An incremental cost-effectiveness ratio for any two programs 1 and 2 can be defined as:

(6.1)

where C is the incremental cost and E is the incremental effect.

To see how this ratio is used in the context of mutually exclusive pro-grams, we refer to Weinstein’s Box 5.3, and add columns for average and incremental cost-effectiveness ratios, which become our Table 6.2.

Table 6.2: Hypothetical example of the cost-effectiveness paradigm with competing choices

Program Effect Cost ($) C/E ratio ($) C/E ratio ($)

K₀ 0 0 — —

K₁ 10 50 000 5000 5000

K₂ 15 150 000 10 000 20 000

Source: Based on Weinstein (1995)

The idea here is that we are adding to the list of J programs in Table 6.1 a possible new program K. There are three competing alternative candi-dates for this new spot. All three are identified by a subscript in Table 6.2 because only one of them can be chosen. Program K₀is the no-program option and this is why it has zero effect and zero cost. (Note that having no

C

EC₂ C1

E₂ E1

Fundamentals of cost-effectiveness analysis 145

program will not always involve zero costs and effects because illnesses sometimes improve on their own and untreated illnesses can still incur non-medical costs.) The incremental cost-effectiveness ratio for K₁is calculated relative to the no-program alternative and the ratio for K₂is calculated rela-tive to program K₁.

The key assumption is that the funds to finance the new program must come out of the original budget of $10 million. So program G is the one that would have to be sacrificed in order to allow the new program to be adopted. With a cost-effective ratio of $18000 for program G, this is the benchmark as before. But this is now to relate to incremental ratios and not average ratios. That is, any new project must produce a unit effect at an incremental cost lower than $18 000 in order to replace program G.

The decision-making process is as follows. Program K₁ is considered first. With an incremental cost-effectiveness ratio of $5000, it is well under $18 000 and so can be approved instead of program G. Now we consider program K₂. On the basis of the average ratio of $10 000, it would seem to be more cost-effective than G. But this ignores the fact that K₁has replaced G. Relative to K₁, that is, on the basis of its incremental ratio, it costs $20 000 per effect. This amount exceeds the critical value of

$18 000 and so K₂does not justify approval. The end result is that the

$50 000 to produce 10 units of E by K₁is used to replace the $50 000 that previously produced approximately 3 units of E in program G (this is where the assumption of program divisibility comes in) for a net gain of 7 units of E.