Editor’s Spotlight/Take 5: What Is the Probability of Radial Nerve Recovery After Surgical Repair of Humerus Fractures Accounting for Time Since Injury?

Teun Teunis MD, PhDWe use the Editor’s Spotlight/Take 5 section of CORR® to highlight the article each month that we believe will appeal to the largest portion of our readership. Usually, this is a function of the article’s topic. Although this month’s article about serious nerve injuries after surgery for humerus fractures will be clinically relevant to anyone who takes general orthopaedic trauma call, that’s not the reason we’re highlighting it. Rather, this month’s Spotlight article, “What Is the Probability of Radial Nerve Recovery After Surgical Repair of Humerus Fractures Accounting for Time Since Injury?” 9, deserves your attention for its analytic approach: Bayesian inferential analysisF1. Please don’t turn the page. Even if your methodologic chops have atrophied to the point where long division requires a calculator app, you can do this. Most research articles in surgical journals engage in hypothesis testing using what are called frequentist statistical approaches to decide whether something worked, to look for differences, or to make predictions. Frequentist approaches are very familiar to you, whether or not it seemed that way as you finished reading that last sentence—they're the approaches that use p values. A few months ago in the Spotlight section here at CORR, I did a plain-language deep dive on why these approaches generally are not fit-to-task and to suggest a better solution for most use-cases: Bayesian analytic approaches 11. Stay with me, because you know what those are, too, even if you don’t realize it. You use Bayesian analytic approaches every day in your office. Imagine someone comes in with a fracture nonunion, an x-ray showing a sequestrum, spiking fevers, and a draining sinus that tracks right down to the fracture site. If someone ordered an erythrocyte sedimentation rate and a C-reactive protein on that patient and they were normal, those test results would not dissuade you from the diagnosis of osteomyelitis. That’s because your confidence in that diagnosis was so high before you saw the labs, and the diagnostic power of those tests is so middling, that no amount of normal bloodwork could knock you off your perch, and rightfully so. The confidence you had in your diagnosis before you saw the blood tests would be called a “Bayesian prior probability” (or a pretest probability). What we know from Bayesian reasoning is that the posttest probability in that scenario doesn’t move much based on a couple of iffy blood tests when one’s Bayesian priors are so compelling. As I mentioned earlier, the Bayesian approaches we use to answer questions in the clinic every day also have great applicability in clinical research. Nearly a decade ago 12 (and intermittently since 10, 11), I looked for reasons to promote these approaches, because I think they’re powerful, underutilized, and far, far better than the frequentist (p value–driven) alternatives. And from time to time, we get papers that use Bayesian statistics, though not nearly as often as I’d like. Most commonly, they’re used either to drive a network meta-analysis 4, 7—a robust way to compare the effects of multiple treatments that is worth learning more about if you’re unfamiliar with it 3, 5—or to make predictions about patients’ prognoses as in this month’s spotlight article 9, though sometimes they are put to use in research in other, innovative ways 15. We at CORR are as excited about Bayesian approaches now as we were the moment we first encountered them. For that reason, please consider this an invitation to send your work that uses them to us. Email me directly when you do so if you like. I would prioritize it. Now, back to this month’s spotlight article 9. An international, multicenter group led by Teun Teunis MD, PhD from the University of Pittsburgh used Bayesian network analysis to determine that patients with no recovery of radial nerve function 7 months after ORIF of humeral fractures still have a better than 50% chance of recovering in the year or so that follows. By contrast, those with no recovery by a year had a less-than 1-in-5 chance of recovering. That information is useful when talking to patients who have this anxiety-provoking problem, but the study authors' analytic approach is really what captured my attention here, and I think it deserves the attention of anyone who performs clinical research. Dr. Teunis’s insights in the Take 5 interview that follows will open minds about new, better ways to answer the important clinical questions we encounter every day. Take 5 Interview with Teun Teunis MD, PhD, senior author of “What Is the Probability of Radial Nerve Recovery After Surgical Repair of Humerus Fractures Accounting for Time Since Injury?” Seth S. Leopold MD:Congratulations on this thought-provoking study 9. What attracted you to Bayesian approaches in general, and why did you think they would be especially helpful to answer questions about nerve recovery after humerus fracture surgery? Teun Teunis MD, PhD: Think about your everyday interaction with patients. A patient describes his or her symptoms. Based on this, you establish a differential and intuitively assign probabilities to each diagnosis. You perform a physical examination and update your differential. This step is repeated if you decide to obtain additional tests. You might finish the interaction by discussing treatments and the probability of adverse events and benefits, adjusting for the patient’s age and comorbidities. This is Bayesian reasoning at work. In essence, Bayesian statistics involve estimating a probability and updating this probability when additional information becomes available. This resembles actual, everyday clinical practice much more closely than the p values of regular (frequentist) statistics. Once I realized this, it was difficult not to get excited. The situation of a closed nerve injury lends itself exceptionally well to this line of thinking. At the outset, there is an initial probability estimate that a nerve won’t recover. And as time goes on, and recovery doesn’t happen, this probability increases (updating probability over time with new information). Dr. Leopold:Why do you think these approaches to answering questions aren’t more widely used? Dr. Teunis: That’s a good question, especially when you consider these approaches are named after Thomas Bayes, someone who died more than 250 years ago, and so whose approaches long predate most of our “usual” (p value–driven) statistical approaches. I suspect that the problem lies with the difficulty of calculating updated probabilities. In most instances, this cannot be done without a computer, and even with one, it is computationally intensive. I first tried to apply Bayesian statistics in 2013 during my PhD research and was unable to get them to work. In contrast, conventional statistical approaches provided methods to answer similar questions using pen and paper, so those approaches took hold in the medical sciences. Popular statistical packages have only recently started offering more accessible methods to apply Bayesian statistics, likely because of their applications in artificial intelligence projects. The next step is to make people more familiar with these kinds of analyses. Dr. Leopold:To get readers thinking in a more concrete way, can you give an example of a hypothetical study about treatment efficacy where a Bayesian approach involving a prior belief (prestudy probability, Bayesian prior, whatever you’d like to call it) about that treatment’s efficacy could be used to answer a clinically relevant question? Dr. Teunis: I’ll do better. I’ll give you an actual study, because the Bayesian framework is great for effectively and efficiently comparing treatments. My colleagues and I performed a trial that assessed whether adding lidocaine to steroid injection reduces pain intensity 14. First, we had to phrase our study questions to include probabilities. We used the following question to guide our work: “Is there a greater than 95% probability of a 1-point difference in pain intensity between steroid injection with and without lidocaine?” Because one of the underlying assumptions of Bayesian statistics is that there is no “true” answer—there is only a probability that can be taken to the next experiment—we can continuously analyze the data as new participants are enrolled. Therefore, the trial can be terminated when the question is answered. And indeed, after including 39 patients, we were 95% confident of the 1-point difference and stopped the study. Compare this to a trial 2 completed around the same time using regular statistics: The authors reported a statistically significant difference after 76 patients but couldn’t determine if this difference was clinically relevant. Another advantage to the Bayesian approach is that we can include information from prior studies. Assume there has been a trial on discomfort with injection, and it showed a 2-point decrease of pain intensity with lidocaine. Bayesian analysis allows us to consider the reasonable suspicion that difference is 2 points, which allows for earlier trial termination if our data are in line with this belief 13. Lastly, if we study more than two treatments, we can adapt the randomization process to randomize more patients to the more effective treatment group, which would save time and money in the performance of clinical trials by allowing the potential for earlier trial termination 1. Dr. Leopold:One apprehension people have about these approaches focuses on the fact that Bayesian priors often are imprecise. People believe that an imprecise estimate of, let’s say, whether a treatment is or isn’t likely to work that one has before an experiment cannot possibly deliver an accurate answer about the treatment’s effectiveness after the experiment is done. My sense is that this usually isn’t a problem, since most of the time our prior beliefs about a treatment’s efficacy are in the mid-range (rather than in the extreme, as in the clinical example about infection that I gave), which is why we wanted to do the study in the first place, and so good experimental data will move the needle nicely. This is similar to what we all know about diagnostic tests: They’re most helpful when we’re least certain about the presence or absence of a disease. How would you reassure readers on the topic of imprecise Bayesian priors, and when do you think Bayesian approaches should be avoided? Dr. Teunis: It’s a valid concern. If we stick with the study above 14, there are several possibilities of impreciseness. For example, we could get by with only a 0.5-point difference between the treatments; we could choose an 80% probability of this difference instead of 95%; we could specify a very strong conviction in an expected large difference; we could start analysis after only few patients in the study. As you can imagine, you don’t need much to “accidently” reach a result of your liking after such an approach. But since we are forced to specify these assumptions as part of any Bayesian experiment’s design, it should be obvious to the reader, reviewer, and editors. Consider the alternative: We perform a power analysis, we include lots of patients, and we find a small difference with p < 0.05 between our treatments. I still don’t know if this difference is clinically relevant, and I might have had to enroll many more patients than I needed. Dr. Leopold:This one is for the trauma surgeons among us. It’s my sense that watchful waiting has long been a part of the management of the problem you studied. What are you doing differently based on your discoveries? Specifically, you said at the top of your study that “a subgroup of patients does not recover” 9; to what degree do your discoveries help you to identify who those people might be? Dr. Teunis: I have noticed the potential for substantial distress in patients with closed nerve injuries about the timing of recovery. They’ve lost movement or feeling in part of their arm or leg, after all, and that is stressful and upsetting. In times of distress, we tend to prepare for the worst, which might result in overly focusing on the probability that the nerve will not recover. This, in turn, might result in too much emphasis on surgery “just to be sure,” which carries risks that may be greater than the potential rewards. The modeling of the probabilities over time in a study like ours facilitates a more honest discussion about treatment options and how these preferences might change. Early on, I found it helpful to show patients that their probability of recovery is high. This seems to reduce some of the distress. As time goes on, it also allows for personalization. One patient might be fine with waiting longer to consider surgery if the probability of recovery is still 50%, but others might not be. Additionally, in a large cohort of nerve surgeons 8, we noticed a discrepancy between the expected recovery (natural history) and the probability of offering surgery. This suggests our findings might also be helpful for surgeons to determine if and when they want to offer nerve surgery. This is why Bayesian-powered experiments are so exciting to me. We now are repeating the current study design for other closed nerve injuries. We are also looking into personalizing probability estimates based on nerve conduction studies. I would love to perform more Bayesian randomized controlled trials, and I am eager to apply Bayesian reasoning to diagnostic tests as others have done 6.