Saturday, January 22, 2011

Now, Let's Play "Get the Metric Defined Right"

Per the previous post, I'm still lost in parameter space trying to get the metric right on marginal utility for end-of-life health care.

First, it varies depending on how old you are. If you're ninety-five, a small amount of money is unlikely to prolong your life much. If you're twenty-three, a small amount of money may give you decades of extra life.

Second, as you move further out on the age axis, there is some point at which an infinite amount of money doesn't by you any more life. We might refer to this as the "your time is going to come" principle. So, on average, if you were to create a graph with the abscissa as "current age" and the ordinate as "cost per extra expected year of life", that graph has a vertical asymptote at some fairly advanced age.

Third, the shape of this graph has varied over time. Most important for our discussion, in days of yore, the graph bounced around at some fairly low value, rose a little bit as you got older, and then suddenly shot up sharply along the vertical axis as you reached your allotted three score and ten (or whatever it really was). Today, however, two things are happening:
  1. The vertical asymptote is moving further out.
  2. The rate of approach to that asymptote is shallower. In other words, you can actually extend your natural lifespan with some degree of medical intervention
Now, from that it's pretty easy to deduce that for any age 'a' and instantaneous medical expenditures as a function of your age:

sum(Medical expenditure(t))

is going to get bigger and bigger, the shallower and shallower that medical expenditure curve gets. But that's not the worst part.

The worst part (from a Medicare solvency standpoint--it's friggin' wonderful from the individual's standpoint) is that that vertical asymptote may be getting ready actually to tilt to the right. That pretty much means that if you want to live forever, a dollar value can be attached to what that will cost. It's likely a pretty high value, but it might no longer be infinite.

I wish somebody could produce this graph, and then animate it over time. I'll bet it would focus our conversation on health care considerably.

1 comment:

S. Loran Cook said...

I bet he can animate it. :) Interesting point(s).