Life expectancy is a population metric

You people sure love to argue about life expectancy. Short of physician salaries, no issue seems to draw more comments and hate mail for me.

Yesterday, I posted on the fact that life expectancy in NYC has been rising amazingly quickly over the last few decades, much faster than it has for the country as a whole. I also quoted from the author of the work, saying that he believed that many of the public health interventions are responsible. I finished by saying that while that is far from proven as the cause, it’s compelling.

And then all hell broke loose. I was inundated with comments, some tweets, and emails telling me it couldn’t be public health, it had to be some other reason. These included reduced traffic fatalities, reduced deaths from HIV/AIDS (or other illnesses), reduced death from homicides, or changes in demographics or population.

Let’s start with the latter. The beauty of NYC is that it’s not homogenous. The five boroughs contain different mixes of both race/ethnicity and socio-economic status. All of them saw a rise in life expectancy. So it can’t be because everyone is rich in NYC. The Bronx is still the poorest urban county in the US. The fact that this borough is closing in on the national average is amazing. Something is different in NYC. As for race, parts of NYC have less of a minority population, and the Bronx has an enormous minority population. Again, all went up way more than the average. Something is different in NYC.

But what about the other reasons? To think about that, you have to remember that life expectancy is a population statistic. It’s working at a huge level. The simplest way to increase the life expectancy of the roughly 8 million inhabitants of the city one year is to make them all live one year longer. If you want to try and affect life expectancy by improving things for a sub-group, though, it’s much harder. You need to save a lot more life.

That’s what you’re doing when you try and pin life expectancy increases on one cause. You’re identifying a sub group. So if you want to say that life expectancy has gone up so much because of reduced crime in NYC, then you need to prevent a lot of homicides. If you can save a 25 year old who would otherwise live to 75, you’ve added 50 person-years to the population. To increase the life expectancy of 8 million people one year, though, you need to add 8 million person years. In other words, we need to prevent 160,000 homicides of 25-year-olds (and then not let them die of any other causes) in order to get life expectancy for the city up one year. But that’s not all. Life expectancy rose more than 6 years more in NYC than the rest of the country. To see that kind of improvement at the population level, we’d need to prevent 960,000 25-year-olds from getting murdered.

In 1990, there were 2245 murders in NYC. Total. That’s dropped to less than 500 (which is awesome), but far from the number that would be needed to increase the life expectancy of the city that much above the rest of the country. Plus, all murders prevented likely don’t live for 50 years.

The same argument holds true for any other cause. You’d need to prevent 960,000 25-year-olds from dying of accidents and keep them alive for 50 years to see these results. But from 944 NYC traffic fatalities in 1970, the numbers have dropped to 247 in 2011 (which is awesome). Those numbers are even smaller than homicides.

HIV/AIDS? Much bigger numbers. Those peaked in 1994, when 8355 people died of the disease. And they have been coming down; by 2007, it was under 2000. But – again – you need to prevent many, many more deaths than this number in order to raise the life expectancy of the whole city. Moreover, when you’re talking about improving treatment for a disease, that should be happening nationally. It’s likely local things reducing homicides and traffic accidents, but treatment for HIV/AIDS improves things everywhere. I could rerun this argument with any disease, and you guys threw a lot of them at me.

Forget the numbers for a moment, though. Whenever I use life expectancy to talk about the quality of a health care system, some of you start screaming. You complain that life expectancy isn’t due to health care, it’s due to individual choices, public health, and things unrelated to medicine. Fine. There’s truth to that. But it’s ironic that when I put this up yesterday, many of the same people started throwing diseases at me, or things unrelated to public health. As if these things now accounted for the increase in life expectancy.

The truth is that a population metric measures, well, the public as a whole. And such a large increase at a local level likely involves something that affects the population as a whole. Relatively few people die of any one cause or disease, so it’s unlikely to be something that affects that one small thing. It likely has to be something that affects everyone, or at least most people.

There’s nothing in yesterday’s chart that proves it’s public health initiatives. But something is different in NYC, and it’s affecting a ton of people there. Whatever it is, it’s likely doing a lot of good.

@aaronecarroll

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