StATS: Economic evaluations (February 2, 2006)
Several years ago, BMJ had a whole series of articles on economic evaluations. I saved the references at the time, and am just now getting back to review them. There are a lot of important lessons in these articles, and like all articles in BMJ (except for their most recent 12 months of publications), the full free text is available on the web.
Economic data, such as costs or charges, often follow a skewed distribution. Normally I consider a log transformation anytime I suspect a skewed distribution, but there are good reasons to avoid the log transformation for economic data.
The outcomes in an economic evaluation can take three forms. First, you can analyze the cost required to prevent one event (if an intervention cost a million dollars and it was expected to prevent a total of 200 hip fractures, then you have to pay $5,000 per hip fracture). This analysis is somewhat simplistic and hard to compare across different studies. This analysis also fails to recognize that some medical gains come at the expense of quality of life. So quality of life is a second approach used in economic evaluations. Most measures of quality of life, however, do not allow relative comparisons. So you can't, for example, say that a new intervention that costs twice as much as the current standard is justified because it raised the average quality of life from 5 points to 10 points. So a third approach is to estimate a utility measure. This measure places relative values on certain events. For example, the "cost" of surgery might be five times as bad as having to endure a year of drug treatments, but only half as bad as having to put up with a year of dialysis treatment. There are standard approaches for interviewing patients to help discover their relative disdain of various medical events.
A very nice summary of the three forms for an economic evaluation appears in
Another important issue is discounting. Economists will typically include a discount calculation for economic benefits that don't appear until many years later. This makes sense because most people would rather have money today and would view a comparable amount of money six years down the road as less valuable. Even if they didn't want to spend the money right away, they would be able to invest the money and get a return on their investment. But should the future value of health benefits be discounted?
The main argument against discounting health benefits is that health, unlike wealth, cannot be invested to produce future gains. The Department of Health has thus recommended that health related benefits should not be discounted though more recent advice suggests future health benefits should be discounted but at a very low rate of 1.5%2%.5 An important reason for discounting future costs and benefits is “time preference,” which refers to the desire to enjoy benefits in the present while deferring any negative effects of doing so. Examples of human behaviour which implicitly discount future health effects abound. For instance smoking and drinking give current pleasure while incurring future (discounted) detrimental health effects. Indeed, research has indicated that smokers value future health benefits at a lower rate than nonsmokers.6 This desire to enjoy pleasurable benefits in the present time is often reflected in differential pricing of goods and services. Consider the hire of a video for home viewing. Despite the increased cost of newly released videos, many people are willing to pay the extra cost rather than wait until the price falls. Economic notes. Discounting. Torgerson DJ, Raftery J. Bmj 1999: 319(7214); 914-5. [Medline] [Full text] [PDF]
Another important consideration is prevalence costs versus incident costs.
Two methods of costing illness exist—the prevalence and incidence approaches. The prevalence method is the commonest and estimates the total cost of a disease incurred in a given year. The more data hungry incidence based approach involves calculating the lifetime costs of cases first diagnosed in a particular year, providing a baseline against which new interventions can be evaluated. Economic note: cost of illness studies. Byford S, Torgerson DJ, Raftery J. Bmj 2000: 320(7245); 1335. [Medline] [Full text] [PDF]
This is a subtle distinction, but very important. Prevalence will tend to give greater weight to those individuals who survive longer and less weight to those individuals who die quickly (or in another context, those who recover quickly).
Opportunity costs are important to an economic evaluation. Here's a nice definition:
The concept of opportunity cost is fundamental to the economist's view of costs. Since resources are scarce relative to needs,1 the use of resources in one way prevents their use in other ways. The opportunity cost of investing in a healthcare intervention is best measured by the health benefits (life years saved, quality adjusted life years (QALYs) gained) that could have been achieved had the money been spent on the next best alternative intervention or healthcare programme. Economic Notes: opportunity cost. Palmer S, Raftery J. Bmj 1999: 318(7197); 1551-2. [Medline] [Full text] [PDF]
Economic considerations can help derive an appropriate sample size. For example, transcervical endometrial resection cost 727 pounds, and has a 27% recurrence rate, yielding an average cost per patient of 923 pounds. Amore expensive procedure, endometrial laser ablation, costs 772 pounds, but if it has a lower recurrence rate, that would justify the added expense. How low would that rate have to be? Well, a bit of math will show you that a 19% recurrence rate is about the break even point. Any recurrence rate less than 19% would yield a lower overall average cost per patient. This analysis, of course, does not account for the non-economic costs associated with recurrence. But it does show that a study comparing the recurrence rate of the two procedures ought to have enough power to readily detect a shift from 27% to 19%, and perhaps even a smaller shift. Two more examples, cited in the same journal article, have fewer details, but illustrates the types of economic considerations used
Though it is not always possible to set sample sizes by economic criteria, economics can often usefully inform sample size calculations. For example, the minimum economic sample size for a clinical trial of thiazide diuretics for preventing hip fractures should be large enough to detect a 10% reduction in fracture rates as this is the point where cost savings due to averting hip fractures equal the costs of the intervention. Another point of economic importance might be where the cost effectiveness ratio is equal to that of the next best alternative treatment. For instance, a sample size calculation for a clinical trial of in vitro fertilisation compared with tubal surgery for treating infertility suggested that for the cost effectiveness ratios of the two treatments to be equal, then in vitro fertilisation must result in 12% more live births than tubal surgery. Cost effectiveness calculations and sample size. Torgerson DJ, Campbell MK. BMJ 2000: 321; 697. [Full text] [PDF]
Further reading
This page was written by Steve Simon while working at Children's Mercy Hospital. Although I do not hold the copyright for this material, I am reproducing it here as a service, as it is no longer available on the Children's Mercy Hospital website. Need more information? I have a page with general help resources. You can also browse for pages similar to this one at Category: Linear regression.