Our topic this week is cost-effectiveness analysis, which combines many of the things we've already considered, and explicitly includes issues of cost.

The guiding principles underlying cost-effectiveness analysis are these:

• There's not enough money to fund every possible treatment (screening program, etc.).
• We want to get the most for our money: fund the treatments that result in the best medical outcomes per dollar. "How can we allocate our resources to provide the most health we can afford?" (or "How cheaply can we provide our target level of health?"

The solution to the problem is to fund those treatments with the best cost-effectiveness ratios. The cost-effectiveness (CE) ratio is the ratio of cost (C) to health effect (E). For example, $100,000 per life saved, $75,000 per life year, or $45,000 per quality-adjusted life year (QALY).

Programs are ranked by their cost-effectiveness ratios, and we implement them in order from most cost-effective to least cost-effective until we run out of money or reach some other threshold beyond which we're not willing to pay. For example, if we had the money, we probably would be willing to pay $100 to gain a QALY, but might not pay $100 million dollars for a single QALY. Typical cutoff values today are $50,000/QALY or $100,000/QALY.

We can imagine a plot of all possible treatments on a graph like this:

In the upper-right quadrant we have programs that cost money and provide QALYs, like most medical treatments. The diagonal line is the $50k/QALY threshold. Programs below that line are more cost-effective than $50k/QALY; those above are less cost-effective.

In the lower-right quadrant are programs that are cost-saving; they provide QALYs and actually cost less than not doing the program would. Some medical treatments, particularly preventative programs, are like this, because the cost of the program (e.g. anti-tobacco education) is dwarfed by the future savings in medical costs to the medical establishment, patient, or society. We always want to implement cost-saving programs.

In the upper-left quadrant are programs that both cost money and reduce QALYs. We might call these "cost-defective" or destructive programs. A medical example might be unnecessary surgery.

In the lower-left quadrant are programs that save money but reduce QALYs. This is the "dark side" of cost-effectiveness: we may be able to save money (that we could use better elsewhere, perhaps) by doing something that is detrimental to health. For example, providing unhealthful food in the hospital cafeteria. Again, we can ask whether these programs save at least $50k per QALY lost, or some other threshold.

Technical note for the curious: The CE ratios in the lower-right and upper-left are negative (you're dividing negative costs by positive effectiveness or vice versa). Negative CE ratios do appear in studies of medical treatments and are a big problem if you're using them to make decisions. A treatment which saves $100k and provides 100 QALYs has a CE ratio of -1, and is better than saving $100k and getting 50 QALYs, which has a CE ratio of -2. But both are better than saving $50k and getting 50 QALYs, which has a CE ratio of -1! You can't just compare the CE ratios when they're negative.

That's all well and good if we can implement any combination of programs that we choose, and we're starting from scratch. But what if programs are mutually exclusive or we already have some other "standard" in place. Then we must evaluate programs based on how much more they provide than competing alternatives. This is done by computing "incremental" or "marginal" CE ratios. To compute an incremental CE ratio, we divide the incremental cost (how much more program B costs than A) by the incremental benefit (how many more QALYs program B provides than A), and see if it meets our threshold. If it doesn't, we don't fund it, arguing that A alone meets our threshold, but the extra value provided by B does not justify its extra cost "at the margin", even though B itself (when compared to nothing at all) might be cost-effective.

An example from Stinnett & Paltiel's CEA short course: Assume there are 5 programs, but only 1 can be implemented for some reason.

We immediately eliminate program D from consideration -- it costs more than C and provides fewer QALYs. It's dominated.

Now, we can ask, "how much more effective is each program than the one preceding it?"

We can now eliminate program B as well - it provides fewer additional QALYs than C does, at greater cost. We recalculate the incremental CE ratios again:

So, if our threshold is less than $3,600 per QALY, we should just implement program A, and we'll get 16.4 QALYs for $4,600. But if we're willing to $3,600 per QALY or more, we should instead implement program C, and get 17.9 QALYs for $5,400. Note that program C's average CE ratio is $559/QALY, but because A is available, its incremental CE ratio is higher -- $3,600 per QALY.

Doing CEA requires that we have some measure of effectiveness. If we're going to compare very different programs on which we can spend money, we'd like a measure of effectiveness that's comparable across programs.

The standard measure is QALYs -- quality-adjusted life years. We figure out how many additional years of life will be added by a treatment, and for each of those years, how good the quality of life will be, on a scale from 0 (as bad as death) to 1 (as good as perfect health). We add up these "quality adjustment coefficients" for all years gained, and that's the number of QALYs gained.

For example, if a treatment gives you 1 extra year of life in perfect health, you gain 1 QALY. If it gives you 2 years of life in a health state with quality 0.5, you've also gained 1 QALY (0.5 + 0.5 = 1). As you might guess, utilities assessed using standard gambles or time tradeoffs are often used for the quality adjustment coefficients.

A major question is whose utilities should be used. In an analysis from the "societal perspective", it's usually the utilities of people at large. From the "patient perspective", it's utilities of the patients with the condition.

Costs should be easier -- we measure them in dollars. But often the data we have are not truly costs, but charges -- which include the true costs plus some profits and other market features.

In addition, it's often very difficult to be sure that you're measuring all of the appropriate costs. Here are two common and controversial examples:

• When you extend someone's life, they may be able to work longer at their job, and thus contribute more productivity to society. Accordingly, this should reduce the cost of the treatment.
• When you extend someone's life, they will experience other medical problems that they wouldn't have experienced if they were dead. Accordingly, they will cost society more to care for in the future, and these future costs increase the cost of the treatment to society.

Finally, we want to discount future costs, but at what discount rate? The usual recommendation these days is 3%. (Actually, one is supposed to discount future utility as well...)