Multi-Drug Poisonings Over Time

I’ve written several previous posts about multi-drug interactions. My write-ups of the 2014, 2015, and 2016 drug overdose data all show cross-tables as well as tables displaying the distribution of numbers of substances found in accidental drug overdoses.

I didn’t have the ability to see what this looked like over time until recently. If you want to see, for example, how many people died from a combination of benzodiazepines and prescription opioids, you can’t just go to the CDC’s Wonder database and pull that information. You have to go to the large file that lists all (roughly) two-and-a-half million deaths that happen each year along with each cause listed on the death certificate. Then you have to define your own counting logic. To see trends over time, you have to pull together the detailed files for several years. That is what I have done.

I’m looking to see which drugs are “associated” with each other. (Below I use the term "correlation" loosely; I am not using Pearson correlation or any other well-known statistic. I'm literally saying "These two things are co-related.")  Roughly speaking, this means they appear together more often than I would expect by chance. Here’s an example of what I mean. In 2016, there were 55,071 accidental drug poisoning deaths (presuming those are correctly labeled, which is an open question). 14,483 of these were prescription opioid overdose deaths (which, by my own definition, includes the “Other Opioid” drug category or methadone, ICD10 codes T40.2 and T40.3); 9,177 of these were benzodiazepines-related (the death record listed the benzodiazepine code T42.4); 4,873 of these listed both. Taking some ratios, 26.3% of accidental drug poisonings involved prescription opioids (14483/55071), 16.7% involved benzodiazepines, and 8.8% involved both. What might it mean for two drugs to be associated with each other? To show up together more often than “by chance?” Crudely we can think of the drugs listed on death records as being randomly distributed across those records, in other words they are “independent” observations. (Maybe there is a better way of specifying what independence means, but I think it works for my purposes.) We “expect” to see 0.263 x 0.167 = 4.4% of accidental poisoning deaths to include both substances if the independence assumption holds. Instead we observed that 8.8% included both. So these substances show up together 2.02 times as often as we’d expect given independence. We can say, crudely speaking, that these substances are positively associated. (You can enlarge the tables below by clicking directly on them.)

That is no surprise, and it’s no coincidence that I chose these substances to illustrate my point. It’s well known that benzos can exacerbate the respiratory suppression of opioids and vice versa. (Benzos have their own effect on respiration independent of other substances, just not quite as extreme. Someone I know recently suffered altitude sickness in Colorado. He told me (presumably he heard this while getting medical attention) that you can’t have benzos if you’re having a panic attack at altitude. I was perplexed for a minute then realized, “Oh, right, they suppress your breathing.” Possibly dangerous at high altitude.)

What about other substances? Heroin and benzodiazepines seem to be roughly “independent.” When I do the same exercise explained above, I get something that’s close to 1.00. See the table below for details. (I'm counting deaths that involved either heroin or synthetic opioids as heroin deaths, unless I specify otherwise. The reason is that some of these people are intending to take heroin and end up taking fentanyl or something stronger instead due to black market uncertainties about drug quality. These deaths could be marked with either or both substances. There are technically codes to differentiate these: T40.1 for heroin and T40.4 for "other synthetic narcotics." But in practice I don't think medical examiners are scrupulously checking to see which substance was involved.)

Cocaine and heroin were slightly “dissociated” from each other in 1999, but the correlation seems to have grown over time. Joint cocaine/heroin overdoses appear 1.2 times as often as expected by chance in 2016. It's interesting that this jumped from ~1.0 to ~1.2 in 2011, the first year of heroin's very recent dramatic increase. (You can see the slope change dramatically in the charts in this post.) Notice that cocaine deaths peaked in 2006, then came back down. But their dramatic recent rise, as in the past couple of years, is largely being driven by heroin. If someone were just tracking cocaine deaths and reported some kind of cocaine epidemic, they would be mistaken. This phenomenon of multi-substance poisoning is important. It would be misleading to look at trends in any one substance in isolation.

Taking a look at many possible combinations, I see the following table. (Other Opioids means specifically code T40.2; as stated above methodone has its own code T40.3. For anti-depressants, I'm looking at code T43.2, "other and unspecified antidepressants." Heroin in this table refers specifically to T40.1 and not T40.4. The last column shows how these two codes are correlated.)

I found the very last column interesting. Heroin and other synthetic narcotics were significantly dissociated from each other until 2014, when deaths listing T40.4 began to rise dramatically. That suggests these were very different phenomenon until 2013. There were some people dying of fentanyl and similar substances, but these were probably pain patients with legitimate prescriptions to the fentanyl patch or something like it. It looks like there is a sudden "regime switch." I would have expected the number to be bigger. A lot of the heroin deaths in the years 2014-2016 were actually taking heroin adulterated with fentanyl, but then again maybe there is a tendency for medical examiners to only write one substance on the death certificate. Like I had said, I don't think they are scrupulously checking to see if it's really heroin or if it's something else.

Take a look at the heroin and antidepressants column. It looks like these are dissociated, occurring together less frequently than we'd expect by chance. Other Opioids (code T40.2, not including methadone like the first table in this post) seems to overlap significantly with benzodiazepines and antidepressants. I'd summarize this table by saying that pharmaceuticals tend to go together, and tend not to go with heroin. I might be tempted to say something like, "There are street drug users, and then there are pharmaceutical drug users. These are distinct categories, even if they overlap." That's not quite right, because we're looking at just the population of users who died and not the full population. That's a pretty strong "filter" for our data, and presumably some kind of selection bias creeps in here. But I'd be surprised if you didn't see the same kind of pattern on SAMHSA drug survey data. Once again there is overlap on any given pair of substances, but we're trying to see if there is more or less than we'd expect by chance.

Here are some more substance correlations. Again "heroin" means just heroin (code T40.1) and Other Opioids means just code T40.2. "Cocaine Or Heroin" means just that, one or the other substance is present. So in the third column I'm roughly speaking looking for the correlation between prescription opioid deaths and street drugs. "Stimulants" refers to code T43.6, usually called "Psychostimulants with abuse potential", which includes things like methamphetamine and prescription ADHD medications. (Yes, the government counts them in the same category, because they are chemically similar and have very similar effects at similar doses. Insert stock comment about the hypocrisy of American drug policy here.) The second and third column sort of corroborate the story that "There are street drug users, and then there are prescription drug users." Methadone has interesting correlations with other substances. I wasn't sure what to expect, but I would have thought a lot of methadone poisonings were heroin users in rehab who maybe fell off the wagon. If that were true, I would have expected a number substantially higher than 1.00, but instead it's substantially below. Similar with Other Opioids and Methadone. (Does this mean methadone is often the sole drug found in an overdose death? Not particularly; see the tables in any of the three links at the top. Most methadone deaths involve multiple substances; the distribution of "number of substances involved" is similar to other things on the list.)

I wrote this post thinking the analysis is a good way of tracking this sort of question: Are deaths due to X being driven up by an increase in deaths from Y? If "Yes" I would expect some kind of change in this number. I don't exactly see any smoking gun here. It definitely looks like "other synthetic narcotics" went from being a pharmaceutical-type drug to a street-drug in the past three years, no surprise there. And it looks like heroin is driving up cocaine-related deaths; my "correlation" statistic jumps from ~1 to ~1.2 in 2011, which is when heroin-related deaths started really trending upward.

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Something about this analysis bothers me, regarding how I've defined "independence." I have a certain number of bodies, say 55,071 in 2016. Then I'm effectively saying, "I have 14,483 'prescription opioid' tokens, 9,177 'benzodiazepine' tokens, 27,035 'heroin' tokens, 9,979 'cocaine' tokens. 'Independence' means I'm going to randomly distribute these tokens to the 55,071 bodies. 'Dependence' means having one kind of token makes it more likely that you'll get certain kinds of tokens and less likely that you'll get other kinds of tokens." I think this is right, but something about it feels weird. Like I should be fully specifying a rigorous statistical model. Someone more familiar with the tools of social science can pick up the torch from here if they like. If anyone knows, does this "correlation" statistic I've cooked up correspond to an existing concept? If so, please share and I'll try to tighten this analysis up with a more familiar set of tools and concepts.