Map of life expectancy at birth from Global Education Project.

Tuesday, September 08, 2009

Follow me deep into the wonkish weeds . . .

but wear protective gear. Here be serpents.

Before heading off to the Land That Time Forgot, I started to talk about probability theory and how most people's response to gambling propositions -- including the risks we take in daily life -- doesn't correspond very well to the way mathematicians and economists and weird people like that think about them. In addition, there is the vexed question of how we value possible outcomes. We know that ten bucks is ten times one buck, but how much more valuable -- if at all -- is ten years without arthritis in the left knee compared with ten years with arthritis? And would you be willing to give up some actual life -- say, die a couple of months earlier -- in order to avoid the arthritis?

That may sounds like a stupid or pointless question, but health economists ask it of people all the time. It's called the Time Trade-Off approach to measuring health utilities. Another, if anything even more popular approach drags the issue of probability right into the middle of the ring. It's called the Standard Gamble. What if there were a treatment that might cure your osteoarthritis, but it involved some risk of death? (Indeed there is such a treatment -- joint replacement surgery, like any surgery, involves a small but non-zero probability of killing you.) The Standard Gamble asks at what probability of death vs. certain cure you would be indifferent to the surgery. Another commonly used method is the Rating Scale, commonly presented as a so-called Visual Analogue Scale. If life in perfect health is a 10, what number is life with osteoarthritis of the knee? The VAS version of this has a horizontal bar and you point at the location on the bar, so you don't have to think in terms of numbers, which are yucky. The bar might even have a smiley face on one end and progressively less smiley faces as you move along until you get to a total yuck face.

Often, these questions are not asked about specific conditions such as osteoarthritis of the knee, but refer to vague, general states such as pain, mobility, mental acuity, etc. You can ask these questions of people who actually have a disease or symptoms of interest, or you can ask them of the general public in an even more hypothetical way.

Once you have this information from a sufficient number of people -- and how you define sufficient is an interesting question in itself -- you use it to calculate something called a Quality Adjusted Life Year, a QALY, usually pronounced "kwolly." Treatment A, let's say, that on average gets you 10 extra years of life but at 70% value based on the side effects of chemotherapy and the lack of a left lung, can then be compared either with another treatment -- say you skip the chemo in which case you can expect to live 8 years but at 90%, which is worth 7.2 QALYs and hence slightly better than the 7.0 you supposedly get from adding the chemo -- or to it its cost -- e.g. surgery + chemo costs \$250,000 so you're spending about \$35,700 per QALY.

It all sounds very scientific, no? Can you (or Betsy McCaughey) find anything wrong with this picture?