A Tea Party presentation on health care making the rounds in Montana claims that life expectancy is a smoke screen, and it’s death rates we should be looking at. The implication is that we shouldn’t envy Japan’s longer life expectancy, because the US has lower death rates, indicating superior performance of our health care system.
Which metric really makes the most sense from a systems perspective?
Here’s a simple, 2nd order model of life and death:
From the structure, you can immediately observe something important: life expectancy is a function only of parameters, while the death rate also includes the system states. In other words, life expectancy reflects the expected life trajectory of a person, given structure and parameters, while the aggregate death rate weights parameters (cohort death rates) by the system state (the distribution of population between old and young).
In the long run, the two metrics tell you the same thing, because the system comes into equilibrium such that the death rate is the inverse of the life expectancy. But people live a long time, so it might take decades or even centuries to achieve that equilibrium. In the meantime, the death rate can take on any value between the death rates of the young and old cohorts, which is not really helpful for understanding what a new person can expect out of life.
So, to the extent that health care performance is visible in the system trajectory at all, and not confounded by lifestyle choices, life expectancy is the metric that tells you about performance, and the aggregate death rate is the smokescreen.
It’s initialized in equilibrium. You can explore disequilbrium situations by varying the initial population distribution (Init Young People & Init Old People), or testing step changes in the death rates.