• 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.


    • Quite right. I thought it was interesting that one of the reports referenced in the comments referred to HIV as one of the main drivers. Maybe they got the math wrong, but for HIV to be one of the main drivers of the Bronx’s rise in life expectancy, I imagine it would have had to be a generalized epidemic (like in sub-Saharan Africa, where it’s mainly heterosexual transmission), people had no access to treatment and were therefore dropping like flies, but then the Feds stepped in and we’re in much better shape.

      To state the obvious, it’s good that HIV death rates have dropped and we should try to get them to zero. But those couldn’t have been a major cause of life expectancy improvements in the Bronx. Likely it was a mishmash of small things adding up. HIV rates were a party of that. But again, there is a case to be made that Bloomberg’s public health efforts also played a role. And while I strongly disapprove of some of his other efforts (especially stop and frisk), I think that some degree of authoritarianism is justifiable in public health. People acting voluntarily don’t often adopt the steps they should, so exerting a limited amount of compulsion may be justifiable.

    • I kind of see it as a case where you can’t have things both ways. This seems unlikely to be just noise. These are large increases (Manhatten looks to be a decade) and large increases relative to a generally increasing US life expectency.

      Something like AIDS would have to be affecting ~10-20% of the population to be the sole driver. Population changes could matter, as well, but that is one heck of a healthy immigrant effect.

      Finally, a safer city with fewer crimes, accidents and less transmission of disease is one that has improved on key public health metrics (maybe just not the ones we think of like sanitation and obesity).

    • Life expectancy changes over time are driven by fewer deaths in the youngest population (as this gains the most life-years). Worldwide improvements in life expectancy are generally explained by mass reduction in childhood deaths due to diseases (like smallpox) and poor health. Examining the life expectancy of all individuals who are 10 years or older will show that how long we live hasn’t changed much… just that a greater number of us live to be 10 in the first place.

      New York’s trend could be explained by lower infant mortality and higher birth rates than the national average… coupled with more in-migration than other places (migrants tend to be young and not dead).

    • What if it is population change, specifically a marked decrease in immigration from the south and rise in immigration form other places with a healthier culture. (and assimilation of those from the south).

      Just for white people, the south has far and away the worst health outcomes in the country, as well as the highest rate of obesity and smoking. If you assume that black migrants from the south brought the same cultural habits, that may explain some of it. Over time assimilation to New York culture and the influx of immigrants from elsewhere (of all races) fades out the effect in the city.

      I’d say compare NYC to a southern city, but I’d bet those outcomes are part of a city/rural divide also. People in the little town I grew up in (not in the south) are just not as healthy (or slender/fit, whatever) and smoke more than people in cities.

    • How confident are you that life expectancy data is consistent across the whole time series? Not saying that it is a cause, but I’m curious if life expectancy is measured the same and with the same level of quality.

    • Many of your comparisons are rendered meaningless by category errors. For example, the fact that the Bronx is the poorest urban county is a snapshot in static claim. This is incomparable to the fact that its life expectancy has increased as fast as Manhattan’s. The two changes surely have the same cause.

      Ben is correct that your arithmetic about young deaths is completely wrong. Yes, to increase life expectancy in a population of 1 million by 1 year, you have to save 20k youths from dying. But that’s 20k deaths per life-span, not per year. To convert it to years, one could divide by the life-span. Better would be to divide by proportion of the population that are youths. Anyhow, Ben gave you a very simple reality check: look up actual death rates and expectancies.

      • Yes, it’s per life span. I didn’t claim otherwise. Even if there was a decline of death of 1000 per year in some category (and there’s not really, compared to other parts of the country), then over a lifetime we’re talking about still far fewer than the 48 million person years you’d need to get 8 million people to see their life expectancy go up 6 more years than the rest of the country.

        Moreover, I’ve been saying all along that there has to be a common cause for all of NYC. Where did you see otherwise?

    • How about survival of the fittest?

      NYC can only be survived if you are wealthy, or able to survive poor when you need to be wealthy.

      This drives out the poor and lures in the rich – the poor move to the South where the poor are favored – being lazy is a competitive advantage in heat and humidity.

      By driving out the poor and luring in the rich, NYC on average is rich, and being rich means being healthier and living longer.

      By luring the poor to the South, the South becomes less healthy means shorter lives.

    • You wrote:

      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.

      True, but New York City has accounted for 1/5 of all AIDs diagnoses for major metropolitan areas in the US, and the city’s population of AIDs sufferers is surely much higher as a percentage of the population than the rest of the US. The effect would not be equally dramatic. What would be interesting, if you were up to it, is to compare some other cities that had a similar profile of AIDs sufferers. I would wonder what San Francisco’s LE trend looked like.

    • Life expectancy isn’t calculated off the raw numbers though, it’s calculated off the age specific death rates (ideally single year age).
      So the value of saving a 25 year old is directly proportional to the number of 25 year olds in the population.
      That said, if you look at New York state (a larger population but it’s what I found quickly via google) age specific mortality (http://www.cdc.gov/nchs/nvss/mortality_tables.htm) and compare 1999 and 2007 you’ll see across the board drops in rates of mortality (between 12 and 25%) which suggests that it isn’t an age specific phemomena.

    • “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.”

      The overall population of New York City is 8 million people, as you point out. The death rate is roughly 6.3 deaths per 1,000 people, or around 50,000 deaths annually.

      That means that over the entire 20 year period of the study, we would have expected around 960,000 deaths *total* (and age at death would have averaged over 25 years.)

      And yet I believe you’re arguing in the above that if no one had died in New York City *at all* in the entire twenty year period, at any age, for any cause, then life expectancy would only have risen by six years over those twenty years. (Since the average age at death currently is greater than 25, the average number of years saved would have to have been less than saving 960,000 25 year olds.)

      That simply can’t be right.

      Something must be wrong with your math, or mine.

      It simply can’t be the case that New York City suddenly turning into a city of immortals and no one dying for twenty years would only raise life expectancy by less than 6 years.

      • You’re making this more complicated than it needs to be. Do you dispute that if all 8 million people live one extra year, then life expectancy goes up only one year? That’s 8 million person-years adding one year to life expectancy for NYC.

        • Yes, I dispute it. What I was trying to so is make it simpler, by pointing out that your logic implies something absurd. You’re doing the math wrong.

          The problem is that the life expectancy calculation is about rates, not a one time event. You’re treating it like a one time event.

          If the death rate goes down in one year, then when we calculate life expectancy, we actually assume that deaths will be lower in all years in the future as well. We take it as a sample. (Specifically, you figure out the death rates for each age, and then calculate life expectancy at birth by looking at death rates for each one year period.)

          To go back to my simplified example, imagine that absolutely none of the expected 50,000 people to die in a year died. There are two extreme possibilities:

          1) New York City has become a city of immortals. This is a change in probabilities. Therefore life expectancy immediately should go to infinity.

          2) This year was special. Everyone was really lucky. The overall probabilities have not changed. Life expectancy at birth is unchanged; this year was an outlier.

          The middle ground is really some kind of Bayesian updating of our probabilities.

          Measuring 8 million person-years being saved this year actually indicates that we expect than more than 8 million person-years will be saved in the future, unless we think it was a total freak occurrence (and our Bayesian reasoning shouldn’t let us think that.)

        • Let me try another way to make it simpler.

          Imagine that AIDS deaths decrease by 6000 deaths from 1999 to 2000, and then stay indefinitely at that lower rate. By your logic, that would mean that life expectancy would slowly increase each year. But how can life expectancy increase from, say, 2005 to 2006 if the death rates and number of deaths were the same in 2005 and 2006?

          Under my logic, when AIDS deaths decrease from 1999 to 2000, the life expectancy immediately increases to reflect not just the lives saved in 2000, but also the expectation of those 6000 deaths being prevented *every year thereafter.* So the initial jump in life expectancy is larger than you calculate, but unless the death rate plunges further, it would stay the same in each subsequent year.

    • “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.”

      Only about 50,000 people per year die in the City of New York, since the death rate is roughly 6.3 deaths per 1000 people, or 630 per 100,000 people (which is indeed a very good number from a national perspective.) The average age of death exceeds 25.

      From what I can tell, then, you’re arguing that if no one died in the city at all for a whole year, for any cause, at any age, then the life expectancy of the city would increase by less than a year. Can that be right?

    • Sorry I missed the kerfuffle yesterday. Any thoughts on whether improving environmental conditions has anything to do with it?

    • “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.”

      Again, when the total number of deaths expected for the whole city is 50,000, I actually would certainly think that reducing the number of overall city deaths by over 10 percent would raise the life expectancy of the whole city, particularly if those deaths skewed young.

      So something is off in your math somehow.

    • Public health measures can make large changes to life expectancy, but usually they require large lags. If everyone stopped smoking, the young people who haven’t yet done any damage would gain seven years, but that wouldn’t be visible for decades. The old people who’ve smoked all their lives wouldn’t gain as much, but the full effect would be visible within about ten years. And of course it didn’t go from everyone smoking to no one smoking.

    • The caveat that Bronx is the poorest urban county doesn’t count for much considering the size of that qualifier “urban”. You’re not comparing it to urban life expectancy. Median income in the Bronx ($34k) is more than trip the poorest county, and 1.5x the 100th poorest county.

      The biggest thing to strike me in that graph, is that most of the improvement seems to come in the time-frame of ’96 to 2001. LE seemed to be growing roughly inline with the national average prior to that, and only slightly better after. As pointed out in the earlier comment thread, for many interventions, there can be a significant lag in LE– smoking doesn’t kill you until 20-30 years down the road. As Megan pointed out, most of the public health initiatives in NYC are more recent than this trend.

      It is certainly a combination of things, but New York did undergo a major revolution during the Giuliani years (roughly coincident with the increase in LE). My guess that it is this combination– decreasing crime and drug use, better HIV treatment not just directly, but causing secondary changes in demographics–in wealth and migration to and out of the city. Bronx may be poor relative to the other boroughs, but it still sees these same effects. The middle class are priced out of Brooklyn and move to the Bronx, the poor there are pushed even further out.

      It would be interesting to see that graph overlayed with GDP per capita for the US and NYC.

      The bottom line is that the demographics for NYC are so atypical, I wonder how much of a lesson there really is for the rest of the country.

    • What if the change can be attributed to factors such as HIV/AIDS treatment, homicide rates, ect., but through another route? Similar to what ElamBend mentioned, what if the drop in these things attracted healthier immigrants. Thus, the cause in life expectancy would seem highly correlated with these things. This would not necessarily mean that they all come from a “healthy part of the country” as ElamBend suggests, but just that maybe healthy people saw the resulting lower crime rates, lower AIDS-death rates and other such statistics and chose to emigrate at far higher levels than other, less-healthy segments of the population, regardless of their original location. You might see traces of this in higher Asian or Latino emigration rates, but you also might have the healthier members of the white and African American segments of the population move as well (as opposed to the “average health” white or African American person).