If Prison Were a Disease, How Bad Would It Be?

Cross-posting a comment from Sarah's blog:

Comparing life expectancies of people who have and have not gone to prison, as if “prison” were a disability, they compute that white males lose 19,665 person-years of life to prison per 100,000, black males lose 139,507 person-years, and Hispanic males lose 45,766 person-years. For comparison purposes, here is a table of person-years of life lost to the most common diseases in the US. Cancer, the top killer, only appears to cost 2882 person-years of life per 100,000. All causes together only cost 38,211 person-years of life per 100,000.

The prison YLL estimates were pretty hard to interpret, but I think the reason the numbers are so big is because it’s in different units than the NIH disease mortality numbers. From the paper you linked:

To provide context, rates of imprisonment and person-years of life lost to imprisonment were first calculated. Rates were calculated for each year, 2000 through 2004, for the age group 18 to 44 years. Rates of imprisonment in this age group were the average of the number of persons in prison per 100,000 population. Person-years of life lost to imprisonment were calculated by multiplying the number of persons imprisoned in a specific age group by years left to 45 years. Person years were then totaled for each gender and racial group and expressed as person years lost per 100,000 population.

As far as I can tell, here’s what they did. They assumed that everyone in prison is released at the age of 45. (This seems like a weird assumption but maybe it gives you numbers close to the true ones?) To repeat, since this was apparently unclear: Their calculation is assuming nobody incarcerated in a given year gets out before the age of 45, at which point they’re released with certainty.

So they limited their analysis to people age 18-44. For each calendar year reported, they counted the total number of people in prison in each group, and divided this by 100,000, to get the “Rate of imprisonment.” Then, to calculate “Person-years of life lost to Prison”, they multiplied this by the difference between the average inmate’s age and 45. Another way of putting this is that they summed the difference between each inmate’s age and 45, and divided by 100,000. (I backed out the multipliers and they’re all in the range 10-15, implying average ages in the range 30-35, about what you’d expect.)

This means that there’s substantial carry-over from year to year. For instance, the paper reports 141,108 “Person-years of life lost to Prison” per 100,000 African American men in 2000, out of 9,885 incarcerated per 100,000. The way they calculated it, if no one were imprisoned after 2000, the number reported in 2001 would be 141,108 – 9,885 = 131,223. In 2002 it would be 121,338, and so on.

By contrast, the NIH table is counting years of life lost due to disease-related deaths each year:

Person-Years of Life Lost is measured as the difference between the actual age stemming from the disease/cause and the expected age of death due to a particular disease or cause. Specifically, this measure is estimated by linking life table data to each death of a person of a given age and sex. The life table permits a determination of the number of additional years an average person of that age, race, and sex would have been expected to live.

These don’t carry over. Each year, a certain number of people die from a disease. For each person who dies, the NIH calculates the difference between the person’s age, and the life expectancy at birth of someone with their demographic characteristics. This is their estimate of that person’s years of life lost due to their cause of death. They then sum these estimates, and divide by 100,000. So, if I have terminal cancer this year, and die next year, this year I have 0 years of life lost, but next year my cancer is responsible for lost decades. This is an imperfect measure but at least measures a rate of some kind.

Comparing these two rates is comparing a stock and a flow. To get the “flow” numbers for years lost to prison, you would want to count total expected years incarcerated for people newly imprisoned each year. You can do this by taking “Person-years of life lost to Prison” in one year, and subtracting the number you’d expect if there were no new incarcerations (i.e. the reported “Person-years of life lost to Prison” for the previous year, less the reported “Rate of imprisonment” to account for each existing prisoner being a year closer to getting out.) For example, in 2001, the reported “Person-years of life lost to Prison” for African American men is 141,602. As calculated above, the expected number with no new incarcerations is 131,223. Therefore, new incarcerations between the 2000 and 2001 reporting dates account for 10,379 “Person-years of life lost to Prison” per 100,000 African American men. This is only half an order of magnitude more than cancer – by this estimate the average African American man spends 3x as many years in prison, as the average American’s lifespan is shortened by cancer. A bit of an odd comparison, but at least we’re not mixing stocks and flows.

Note that this backing-out method doesn’t give very accurate estimates. Some year the number is negative, presumably because the rule “prisoners are released at age 45” isn’t a perfect fit for the data, and some years many more people were released than that model expected, driving down the estimate of # of years left.

I put together a spreadsheet to illustrate the above calculations.

I feel like the appropriate comparison here isn't between prison and disease, but between prison and alcoholism or obesity. Like, prison isn't just some scourge that manifests wherever the wrong microorganisms gather. It is a consequence of certain behavior. It falls upon those who sin. It is punishment, and not tragedy.

If you let the bad guys take themselves hostage you have already lost. You can never rescue someone from themselves. When the sufferer and the sinner are one and the same you must close up your ears to the sufferer's wails, or you will soon find yourself wailing.

This wasn't intentionally misleading -- I deliberately just wanted to look at costs and not benefits, and it didn't occur to me that people would interpret that as a claim that prisons only had costs and no benefits. In retrospect, I've noticed that some people are reading this as a way stronger claim of the terribleness of prisons than I meant it (including quoting the numbers that I myself don't believe because the study is super dodgy.)

How did the cited studies try to argue causality?

In other words, it is expected that certain behaviour (drug use, "criminal lifestyle") both causes time spent in prison and lowered life expectancy. Just correlating time spent in prison and life expectancy does not cut the cake.

You would need some kind of randomized control group. For example: Suppose the judges responsible for granting parole were assigned on a last-name basis. Different judges have different statistics on granting parole. Then you compare life-expectancy vs last name of delinquents.

I like the article but agree with this. I also agree with a comment I saw on facebook that "victimless" crime would be a much better metric than "nonviolent" crime.

The list of controls in the "prison reduces lifespan" study seems a little on the short side--race, age, gender, education, and the crime. It's fine if that's all that was available, but if you had some other data as well, I would expect to see the life span reduction reduced as well. Particularly if the major causes of death are homicide and drug overdose right after getting, a strong linear relationship between time spent in prison and life expectancy seems weird. I'm not sure how that would work, causally.

But mostly I agree with chron--you can't just completely ignore the possibility that the existence of prisons reduces crime.

I saw an article last month about prisoners being released, and having AIDS, HepC, and other transmissible disease treatment cut. They showed that the re-infection rates from just these released, and untreated inmates was infecting more folks than any other reservoir. Another community cost that is rarely mentioned

I didn't get that impression. Sarah wasn't stating: Here is a cost vs. benefit of Prisons. She was instead writing about how we could measure the costs of prison. If she doesn't write at all about benefits, there is no reason to infer that she is deliberately leaving them out to be misleading. Actually, I think this sort of inference towards what she is actually trying to say based on what you think she left out is misleading.

Gwern doesn't say anything interesting. He points out that you do, in fact, need to measure benefit for cost vs. benefit. I guess that would be an interesting point if there was any reason to suspect Sarah wasn't aware of this idea. Also, as far as what 'surprises' him as being a metric for reasonableness is useless. It's no secret to anyone who reads about this stuff that the incarceration system in the US has a rich history of being incredibly disturbing.

Evidently Gwern thinks that so long as it registers as 'bad', that's okay, because hey, bad is a deterrent! Whereas Sarah is taking the more methodical approach of actually measuring how bad it might be.

I don't think someone writing about only costs, or only benefits, is necessarily bad. I never go the impression the article was advocating for widespread release and abolition of the prison system. It was instead quantifying the measured cost. You can stop there, that's all the article intended to do.

"Prisons are supposed to be terrible" just sounds like a cartoon villain statement when you think about the actual ways in which prisons are terrible, though, tbh. I'm inclined to trust my instinct to just go NOPE YOUR OPINION IS NOT MY PROBLEM when I see someone who responds that way.