False Positives, False Negatives, and Prescription Opioids

There is a fundamental trade-off between making fewer false positives and making fewer false negatives. Always be aware that both kinds of errors exist, that you can't decrease one without increasing the other, and be clear about which one you are favoring and why.

I am often annoyed by the way the media and politicians talk about social problems. Usually a social problem is discussed as if the solution were obvious and as if the only question was how hard to crank on the “Solve Problem” lever. Any discussion of trade-offs goes out the window, as do any problems with data quality, and questions about the flawed administration of the proposed solution.

Take prescription opioids. (Please.) News reports and demagoguing politicians often start with scary statistics about the number of overdose deaths. Or perhaps they completely dispense with the statistics, assuming that somebody else has already done the math and other boring stuff, and jump straight into their narrative. The problem here is supposedly that doctors are prescribing too many opioids, leading to too many overdose deaths and causing unwitting patients to become hopelessly addicted.

There are two kinds of errors relevant to this discussion. Prescribing someone opioids that they don’t actually need is one kind of error. Perhaps the person has an addictive personality, or has had a previous addiction to opioids or other drugs. Perhaps the person is a heavy drinker, or is on benzodiazepines or something else that could interact fatally with prescription opioids. Perhaps the person suffers sleep apnea, such that the respiratory suppression caused by high-dose opioids could be dangerous. Such people probably shouldn’t be prescribed opioids lightly, or should only get them with special counseling about the dangers, or should only get them if their pain is above a certain threshold. Giving such a person opioids that are unnecessary or potentially dangerous is an “error”, but it’s only one kind of error. This is a false positive: you think the person needs the medicine, but they really don’t.

The other kind of error is a “false negative”: the person needs the medicine but doesn’t get it. I hope we can all agree this is a very costly error. Some people have chronic pain that doesn't respond to anything else, so it would be unbelievably costly (I would even say cruel) to deny such a person their prescription. There is a fundamental trade-off here. If you set the threshold for treatment higher, you will get fewer false positives but more false negatives. There will always be errors of both kinds. An intelligent discussion acknowledges this at the outset and tries to optimize based on the relative costs of those kinds of errors.

“Make fewer mistakes” isn’t always an option. It would be glib to say, “We just need to do a better job of separating the patients who truly need prescription painkillers from those who don’t.” Sometimes we’re already doing the best we can do, and all the relevant information is already being collected. It won’t do much good to throw more resources at the problem. What, should we get multiple doctors to sign off on every prescription? Should we try to collect more information about the patient? The doctors usually already have the patient’s medical history. Should they be conducting in-depth interviews with the patient's family members about potential risk factors? We could try to go down these roads, but it quickly becomes very costly to acquire information of no more than dubious value.

This is not one of my “I’m just articulating the trade-off, not venturing an opinion” posts, although it probably could be if I stopped here. I have a very strong opinion on this topic. I think that a false positive is not very expensive, but a false negative is incredibly costly. I think that people who are in pain and think they would benefit from opioids should get them. I think they shouldn’t require permission. Even if some of them are misinformed, even if most of them are misinformed, to place restrictions on them runs the risk of cutting off a true pain sufferer from their only source of relief.

I also think that if people want to consume drugs recreationally, they should be able to do so. This will come to no surprise to anyone who has read a sampling of my blog posts.  From this perspective a “false positive” isn’t even a mistake, or not a costly mistake at any rate. Someone “mistakenly” acquires the drug that they enjoy using. So what? You can start bringing in the scary overdose statistics here, but this is a risk that the recreational opioid user takes on voluntarily. Certainly there are things that we might do to mitigate this risk: informing users of overdose risk factors, insisting that someone be present in the event of an overdose, etc. But at the end of the day adults need to be able to make those kinds of decisions for themselves.  You might not agree with my civil libertarian idea that adults should be able to make decisions for themselves. Perhaps you are a leftist paternalist who thinks that corporations foist products on unwary consumers who don’t actually want them, or perhaps you are a right wing paternalist who thinks that (certain) recreational drug use represents the abandonment of civilization. You don’t have to buy my drug libertarianism to recognize that there is a cost here. You have to acknowledge that restricting opioid prescriptions will mean that some people who really need them won’t get them. The net you build to catch recreational opioid users will ensnare a few chronic pain sufferers. It is worth reflecting on the relative costs of false positives and false negatives. Suppose you tighten the net on opioid prescriptions and wrongly snare one real chronic pain sufferer, whose only escape from hell-on-earth was his legal supply of opioid pain relievers. How many recreational opioid abusers would you have to deter to make this worth it? I say there is no number that will justify cutting off even a single chronic pain patient. (Am I jettisoning the concept of trade-offs I tried to instill above? Not really. It's just that I see a "false positive" as having almost zero cost, and a false negative as being unbelievably costly. Perhaps this makes me a demagogue, but anyway there you have it.) But whatever number you have in mind, you’d damn sure better be willing to justify it. There is no escaping the trade-off, but you can at least argue that some point on the false positive/false negative curve is optimal.