Bayes’ Theorem: Increase the Chances of Doing Better Clinical Work

This article argues that the most important clinical factor in addiction treatment is accuracy. Without it, you risk making erroneous clinical evaluations, decisions, and treatment selections, one after another.

The cornerstone of this argument rests on something you may not want to hear: that all your clinical hunches, evaluations, assessments, and even prized educated theories you hold about your clients are simply accuracy probabilities. It is true—no matter how strongly you feel you nailed a clinical conclusion, it remains just a possibility. Some clinical inferences are undeniably a little more accurate, but admit it, some are flat out guesses.

You will never, and I mean never, come to a full, 100 percent accuracy rating of any one clinical factor or cluster of clinical factors. This holds true even as you collect more client information. Why never a full 100 percent accuracy rating? Because all clinical probabilities are based on other probabilities.

All this leads to the prospect that your clinical conclusions might be suspicious or flat out wrong. And you want to avoid being wrong in all facets of your work. You cannot conduct good, reliable, long-lasting treatment based on flawed probabilities.

Now, all that sets up some important questions. How do you improve the chances that your client assessments are accurate? How do you improve the chances your assessments are correct, not specious? How do you up your treatment selection choices so you can apply the best treatment methods for a particular client, not some off-the-mark treatment that is based on a blemished assessment? The answer to improving your clinical accuracy is to employ a thing called “Bayes’ theorem” or “Bayes’ rule.”

Bayes’ theorem is a statistical equation. Oh, please do not stop reading and turn the page because you saw the word “statistics.” All too often when viewing the word “statistics” (read: Bayes’ theorem) many addiction clinicians panic and put some sizable distance between themselves and that esoteric-sounding contraption. And yes, if you take a quick peek at the formula later in this article, it does indeed appear daunting. But this is important: Bayes’ theorem can be understood quite well with down-to-earth English. Let me repeat that. It can be understood in plain English, and has the potential to offer you the ability to do better, much better treatment for your clients.

So, how do we accomplish this feat? It will take a few small steps. First, we will need a quick history lesson, then translate the theorem into easy-to-understand language, then describe some minor technical language, then take a quick look at the equation itself (though you can skip that section if you wish), describe a clinical illustration, and finally encourage implementation of the theorem in the field. The big finish is for you to step into the twenty-first-century version of addiction treatment and begin to think with a Bayesian flare. Just begin to think with that twist; it is a modest shift in thought.

Who is This Bayes Guy?

Thomas Bayes was an eighteenth-century British Presbyterian minister who happened to be an amateur mathematician. He came up with a method to calculate the validity of beliefs, claims, and hypotheses. Essentially the formula, in English, states that if you have an initial belief about something and you obtain new evidence pertinent to that belief, you then need to readjust your initial belief and generate a new and improved belief (Horgan, 2016).

That can go one of two ways. First, it could indicate that your initial belief might be unreliable based on new evidence, and you now need to create an alternative explanation. Or, your new evidence might support your initial belief, which means you are on the right track. In this case, your initial belief is reinforced. Get this short paragraph and you get the core of Bayes’ theorem.

Bayes’ rule, or in our case Bayes thinking, helps you update your clinical beliefs via the new information you obtain, and that updated information then spawns a new and improved belief (Morris, 2016).

Now, if all this is not a major portrayal of conducting good treatment, then I do not know what is. And hopefully some of you said, “I do that all the time.” If that is the case, give yourself a pat on the back. But, now you have a suitable name for what you have been doing. However, if you do not do that, or never heard of it, the entreaty is to begin to use Bayes’ rule.

More Ways to Describe Bayes’ Rule

If all of this still does not make sense, then one method to deepen your understanding of Bayes’ rule is to hear it in different ways or applied differently. Here are a few other approaches to help you to understand Bayes.

Again, it is about the accuracy of some clinical belief or theory you hold about your clients. What are the odds that whatever you believe about them is spot on? What are the chances?

Keep in mind, none of your clinical beliefs are without flaws. What you really have are levels of confidence in them. And again, they are never 100 percent truthful. Your accuracy levels need to change as additional clinical data or evidence is gathered. The new clinical information will either reinforce or shrink your clinical confidence.

Said in a slightly different manner, new information about your clients ought to change the way you think about your clients. As new scraps of information come to your attention, that information has to alter your initial assumptions. Sometimes fragments of information press you to change your initial beliefs in an incremental manner. Sometimes the new information presses you to change your beliefs by orders of magnitude.

One more time: all your clinical beliefs about clients will fluctuate and vary as additional information comes to your attention. And all that information comes from a variety of sources (e.g., test results, daily observations, collateral information, and others). You just need to pay attention to all of it. That’s Bayes thinking. Everything is a probability. Consider it as a refining or polishing practice.

A Tiny Bit of Specialized Language

Since you understand Bayes’ rule in plain English, let us take up a notch. We are going to switch to some slightly technical language. Again, it is nothing you cannot handle.

If you have not figured it out by now, Bayes’ rule is about probabilities. In our case, Bayes’ rule relates to clinical probabilities. In particular, it is about a thing called a “conditional probability.” That simply means that whatever clinical probability you come up with in your daily work has other conditions or other probabilities that impact it (Westbury, 2010). Think of those conditions as stipulations associated with some clinical probability you hold in your head. Now, this is important: no clinical probability stands unaccompanied by other influences. Clinically everything interacts and is swayed and influenced by some other probability. Hence, the term “conditional probabilities.”

This takes us to the second slightly technical term. It is call a “prior,” which in our case refers to an opening clinical belief. This initial clinical view is based on the knowledge you have at a certain time. This next part is essential to understand: that prior is subject to change. Recall that a prior is just a probability, not some absolute belief.

As updated and reliable information comes to your attention, you need to make modifications in your initial belief and that resulting modification becomes a “posterior,” or another probability. But this should be a better belief, and will have added accuracy and confidence over the one with which you started (Westbury, 2010).

But, that is not the last of it! No, no, no. Once you factor in new evidence, you end up with a new probability. Then the next batch of information will promote yet another probability. Posteriors become priors waiting for new information to transform them yet again. And on it goes.

An Illustration

Let us consider a simple example. Say a new client arrives at your clinic. Let us make this is a residential clinic. You have been assigned the case. You observe the client in group therapy for three separate sessions. You note the individual does not talk much, keeps his or her head down, and avoids eye contact. You begin to assume this client may have guilt issues. This is based on your intake, during which the client mentioned feeling shame about coming to your program. The behavior in group and the mention of shame in the intake session lead you to believe this client has guilt issues associated with his or her problematic drinking. This is your prior belief. And this got you to think, “What is the probability I am right about this guilt thing?” So, you contact the immediate family to get some appropriate information. You mention your guilt idea and you look for confirming observations from the family. At first they are quiet, then they disclose that this client has always been painfully shy. They reveal that since childhood the client has had a difficult time talking to others, had few friends, and even avoids family eye contact. The family believes the excessive drinking was a lifelong response to shyness. This is new, updated information.

Given this new information, it would appear you need to modify your prior belief to a new belief: a posterior. Notice all your priors and posteriors are conditional or provisional based on any and new reliable information you come across.

What you just experienced in this illustration was that new and hopefully dependable information is going to have an impact on your initial belief. Under these circumstances, you will have to reevaluate how reliable your initial belief was and come up with something more reliable. That is Bayes’ theorem in action, and that leads to clinical impressions that are stronger and better, resulting in better treatment.

The Equation

Remember, you can skip this part. I told you that at the beginning of this article you would come face to face with the equation. Well here it is, in one of it more straightforward forms. And as intimidating as it might appear, it is not.

P(A|B) = P(B|A) P(A)/P(B)

Again, in plain English and using the terms you already learned, this is what the equation says:

• P(B) is the prior clinical probability or some initial client theory you formed in your head. (P is the probability or estimate of the belief [B]. Since we are not doing rigorous statistics, try to make a realistic estimate of its accuracy [e.g., 50 percent].)
• P(B|A) P(A) is the updated information, data, and evidence you uncover during the course of your clinical work. (“A” is the updated information and “|” is the likelihood.)
• P(A|B) is your posterior probability. This is what you get after you made some adjustments in your prior [P(B)] based on the new clinical information. Again, outside of using rigorous statistics, just make a realistic estimate of the posterior. In our example in the first bullet, the posterior is going to be smaller or larger than the 50 percent probability of the prior (e.g., 5 percent, 10 percent, 20 percent, or more). Make a realistic estimate.

Remember when your “prior” “clinical probability” is updated with new information, it produces a new probability called the “posterior” (Chambers, 2017). This is rather simplified version, but there you have it.

Infuse in the Field

Clinicians often create a set of baseline beliefs about clients. Often they pretty much stay glued to those beliefs. These are sticking points in addiction treatment. Yet, every now and then some new data or new evidence comes along that is hard to ignore, and if you are a good clinician you recognize the need to modify your clinical theories to account for the fresh client information.

Overall, the point is to begin to scrap the idea of certainty in your clinical estimations, and elect to think in probabilities from now on. Remember, any new evidence must be able to be explained by the good solid models or theories bouncing around in your head. If those models cannot explain the new information, then a rejuvenated clinical model is needed.

So, how do you spread the word? Here are a few suggestions:

• As you complete a counseling session and write your progress note, ask yourself what the probability is that this note is as accurate as you believe it to be. This compels you to rethink, recheck your work, and not merely write a note and ten seconds later not remember what you wrote. It is called reflection, which as a professional you often implore your clients to do.
• At the end of an intake, when you highlight the key clinical elements that need treatment focus, ask what the odds are that what you targeted with a certain treatment is accurate.
• After reading notes from a transferred case, ask what the odds are that these notes accurately reflect the case.
• For supervisors, ask your counselors, after they present a case in a staff meeting, what the chances are that their reports were accurate. If you like, take this up a notch and press your staff to substantiate their clinical assessments.
• Begin to talk to colleagues as to how they are adapting Bayes’ rule to their work.

Doing something akin to these suggestions would be a big step getting addiction professionals to think with Bayes’ rule. In addition, some of you might want to infuse Bayes’ rule in the workshops or in-services you conduct, or even in the college classes you teach. Finally, and this is bold big step, national certification boards ought to include Bayes’ theorem in their criteria.

Already addiction studies are being published using Bayes’ theorem—as in, using the application of the theorem—to estimate population prevalence from the alcohol use disorders identification test (AUDIT; Foxcroft, Kypri, & Simonite, 2009).

Last Thoughts

Nothing stays the same in treatment. Nothing. If you come across new information about your clients, be it from external sources, input from repeated client contact, or input for your supervisor or colleagues, it will pressure you to change your clinical judgments. The change might be major, minor, and all the points in between.

For those of you who do some version of Bayes’ theorem already, that is terrific. In that case, all this article does is provides you with a name for what you do and offers some structure. For the ones who do not do any version of Bayes’ theorem, this article is encouraging you to think deeply about your clinical work. Do not just make a first impression and run with it. It goes without saying that the more accurate your clinical data, the more confident you become about your client appraisals, and the better the treatment will be.

Bayes’ theorem helps you revise your clinical probability each time you obtain new evidence. The better the clinical revision, the better the conclusion. Rather than relying on speculation, consider Bayes’ theorem as providing enhanced direction and guidance.

Now, the statisticians are going to quibble about the way Bayes’ rule has been described here, but let them! You just need to understand the crux of Bayes’ rule and genuinely apply it. Then you should begin to see your daily work improve. Not bad for such a modest shift in thought!

References

• Chambers, C. (2017). The seven deadly sins of psychology: A manifesto for reforming the culture of scientific practice. Princeton, NJ: Princeton University Press.
• Foxcroft, D. R., Kypri, K., & Simonite, V. (2009). Bayes’ theorem to estimate population prevalence from alcohol use disorders identification test (AUDIT) scores. Addiction, 104(7), 1132–7.
• Horgan, J. (2016). Bayes’s theorem: What’s the big deal? Retrieved from https://blogs.scientificamerican.com/cross-check/bayes-s-theorem-what-s-the-big-deal/
• Morris, D. (2016). Bayes’ theorem: A visual introduction for beginners. Portsmouth, NH: Books Express.
• Westbury, C. F. (2010). Bayes’ rule for clinicians: An introduction. Frontiers in Psychology, 1, 192.

Michael Taleff

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Michael “Mike” Taleff, PhD, has been retired for several years after spending four decades in the addiction field as a clinician and academic. His latest book is A Journey of Deep Recovery: Using Your Best Thoughts (2017).

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