Wednesday, September 6, 2017

The Costs of Drug Use: Overdose Risk

I wanted to do a little back-of-the-envelope calculation to show how much drug users are "paying" for their habit. One of the risks of drug use is that you will overdose and die. I want to quantify that, just to get a rough feel for the magnitudes.

To do this, I'll need to use a concept that makes some people squeamish: the statistical value of a human life. When making certain policy decisions, it is necessary to use this concept. Economists measure this by figuring out how much people are willing to pay for safety features that avoid, say, a 1 in a million chance of death. Or they figure out the pay differentials between risky jobs and similar jobs that are less risky. They come up with numbers such as, "People will pay $6 to avoid a 1 in one million chance of death, therefore the statistical value of a human life is $6 million, according to their own valuation." You can argue that the true number should be higher or lower, but you can't avoid putting some kind of reasonable number on the value of a human life. Carried to its logical limit, the "human life has infinite value" position would have us spending all of society's wealth on ridiculous safety features. I'm going to use the smallest value in the above link for the sake of my calculations below: a human life is worth roughly $6 million. If valuing a life is too hard a concept to get your head around, think of it as "It's worth about $60,000 to avoid a 1% chance of death" or "It's worth about $6,000 to avoid a 1/1,000 chance of death."

Cocaine

There were about 4.5 million users of cocaine in the past year, and there were about 5,000 deaths last year. This comes to a 0.11% death rate. Converted to a dollar figure, that's about $6,600 (= 0.11% * $6 million). So the average cocaine user is effectively willing to spend $6,600 on his habit on this consideration alone. Of course, you have to add to this the cost of acquiring the drug, the opportunity cost of whatever else the person would have done with his time, and health problems due to cocaine use that fall short of actual death. I'm not making the case that cocaine use is destructive so we have to stop these people. On the contrary, I'm making the case that it will be very hard to stop someone who is this motivated to indulge their habit.

Prescription Painkillers

There are about 85 million legal prescription pain medicine users in the past year. (I'm inducing this by subtraction; the SAMHSA survey asks about "any use" and "illicit use". Obviously the "any use" number is bigger. I am subtracting the "illicit use" number from it.) There were 13,000 deaths from prescription opioids like Oxycontin and hydrocodone (I'm adding methadone deaths to "other opioid" deaths from CDC death data, avoiding overcounting). This gets us about a 0.015% chance of death, or 1.5 deaths for every 10,000 legal users. The "value-of-a-human-life" calculation comes to roughly $900. That's what I'm paying in terms of "risk of death" by becoming an opioid patient. Have you ever suffered severe pain? That probably sounds like a bargain to avoid even a week of nagging pain, let alone months of severe pain. The $900 figure is likely too high, as I suspect most of the deaths come from particularly incautious people doing incredibly stupid things, such as taking way too much or mixing opioids with alcohol, benzodiazepines, and other medications. Avoiding these behaviors can drop the chance of overdose to essentially zero.

Heroin

There were roughly half a million heroin users last year. There were 12,345 heroin-related deaths, but that number is probably too low. Sometimes people who are buying "heroin" actually get fentanyl or something stronger. Sometimes the overdose is labeled a "heroin" death on the death certificate and sometimes it is labeled a "synthetic narcotics" death. If I count the total of heroin and synthetic narcotics deaths (avoiding double-counting those in both categories) I get 18,425. Taking these figures literally, a heroin user has a 3.69% chance of death. He is effectively paying $221,000 for his habit by this consideration alone. And once again, you have to add in the actual dollar costs, opportunity cost of time spend acquiring and using, other health issues, etc. Suppose there are actually a lot more heroin users than the SAMHSA survey picks up. After all, a lot of these people are homeless and won't be reachable by a household survey, and a lot of survey-takers might be hesitant to tell someone from the federal government that they used heroin in the past year. Fine, inflate the number of users by a factor of ten. You still get that a heroin user is effectively "spending" $22,100 on his habit, again on the "chance of death" consideration alone. Whatever we're doing to deter heroin users, it has to be on this order of magnitude or they won't even flinch at it. The chance of being arrested or imprisoned will have to be very large. Drug interdiction will have to push the cost of heroin to stratospheric levels (this has been a failure, as heroin is relatively cheap these days). Otherwise the deterrence imposed by drug prohibition will be a drop in the bucket compared to what they are willing to pay.

All of this reinforces a point I've made in previous posts: people have a very high willingness to pay for their drug habits. You have to threaten them with something comparable to their "willingness to pay" in order to get them to stop, otherwise they will simply laugh off your attempt. And "threatening" means occasionally carrying out the threat, otherwise it's no threat at all.

Feel free to quibble with these numbers, as they are back-of-the-envelope. I'll list some of my own reservations. Risk is heterogeneous. (Trust me, I'm an actuary.) You can't just divide the number of drug-related deaths by the number of users to calculate a generic "death risk." Some of these users are very foolish risk-takers and suffer a much higher chance of death-by-overdose. Some of these users are extremely cautious. People who use prescription painkillers as prescribed have nothing to worry about. People who use cocaine once and never develop a habit probably don't need to worry (although there's always the chance of a sudden cardiac arrhythmia). People who get injections of morphine in a hospital setting likewise have no need to worry. (It's a relevant comparison because morphine is chemically similar to heroin, it's just that the fat-solubility of heroin makes it cross the blood-brain barrier more quickly). In other words, most normal, casual users are easier to deter than my numbers above imply, but hard-core problematic drug users are going to be much harder to deter. But it's the problem users who we want to deter, and the casual users who we shouldn't so much worry about. The "risk is heterogeneous" quibble means drug prohibition makes even less sense.

You can come up with other quibbles, for sure. Maybe the $6 million figure is way too high for someone who is destroying their body with drugs. Maybe the SAMHSA figures are biased low because people are unwilling to confess to their drug use on a government survey. (Careful with this critique; this would mean that the risks of drug use calculated above are overstated. But if any drug warrior wants to argue that drug use is a lot less harmful than my calculation implies, I will listen with amusement.) Maybe the death totals collected by the CDC are overstated or understated. Determining a cause of death is a human decision, after all, and subject to a great deal of error. The definitive textbook on drug pathology is just riddled with warnings about how hard it is to actually diagnose a cause of death.

Drug use data from the SAMHSA survey is here (large pdf, ~3,500 pages of charts). You can look up deaths by drug type at the CDC website using their WONDER database. This take a little work, but it's not hard. I am excluding suicides from the death totals.

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