A recent article in the Journal of Bone and Joint Surgery, Bayesian Thinking in Orthopaedics Principles, Practice, and Pitfalls, caught my eye. Basically, it's the idea that we we continually update the understanding we had previously (the "prior") with newly observed information to create a revised undertanding (the "posterior").
Bayesian reasoning naturally aligns with how experienced surgeons think. When evaluating a patient, we don't start with a blank slate - we begin with prior knowledge from previous cases, published literature, and clinical experience. As we gather history, examine the patient, and review imaging, we continuously update our diagnostic and therapeutic probabilities. Formalizing this intuitive process through Bayesian statistical methods can enhance both clinical decision-making and research interpretation.
Bear with me as we go through this a bit formally.
In Bayes' theorem,
A = the hypothesis or condition you're interested in (e.g. the patient has a cuff tear)
and B = the evidence or observation you have (e.g. patient has a positive drop arm test)
P(A|B) = posterior probability of A given that B is true (e.g. probability patient has a tear given positive drop arm test (positive predictive value))
P(B|A) = probability of B given that A is true (e.g. probability of positive drop arm test given patient has a tear (sensitivity of test))
P(A) = prior probability of A (before considering B) (e.g. baseline prevalence of tears in your patient population)
P(B) = probability of B occurring (e.g. overall probability of a positive drop arm test)(P(B) = true positives + false positives. When specificity is poor, false positives inflate P(B), diluting your posterior probability even with good sensitivity.
P(A|B) = [P(B|A) × P(A)] / P(B)
Example
Prior: 65-year-old with night pain, weakness → P(tear) = 0.60Test: Positive drop arm test → Posterior P(tear) = 0.85This 0.85 becomes the new prior if you order an MRINext test: MRI shows full-thickness tear → New posterior ≈ 0.98So Bayes' theorem tells you: the probability your patient actually has a tear given their positive test depends not just on the test's sensitivity (P(B|A), but also on how common tears are in your population and how often the test is positive overall (P(B).
This is why the same test result means different things in different populations - the prior probability P(A) matters enormously:
- High P(A) → high posterior probability
- Low P(A) → low posterior probability
- Same test, different priors, different conclusions
P(B) = probability of B occurring (e.g. overall probability of a positive drop arm test). Importantly, P(B) represents true positives + false positives—when specificity is poor, false positives inflate P(B), diluting the posterior probability even with good sensitivity.
Clinical example:
Scenario 1: High prior
- 70-year-old, chronic pain, night pain, weakness, atrophy
- P(A) = 0.80 (high pretest probability)
- Positive drop arm → Posterior ≈ 0.95
- The test confirms what you already suspected
Scenario 2: Low prior
- 25-year-old, first-time anterior dislocation, full range of motion
- P(A) = 0.05 (low pretest probability)
- Positive drop arm → Posterior ≈ 0.20
- The test is probably a false positive
How does this relate to clinical decision making?
Diagnostic Reasoning
Consider a 65-year-old patient presenting with shoulder pain and weakness. Before examining them, we already have prior probabilities based on age and presentation:
• Rotator cuff tear: ~40% probability (high prevalence in this age group)
• Glenohumeral arthritis: ~15% probability
• Cervical radiculopathy: ~10% probability
• Frozen shoulder: ~5% probability
A positive drop arm test increases the probability of a full-thickness rotator cuff tear to approximately 70%. An MRI showing a 3cm retracted supraspinatus tear with fatty infiltration further updates our posterior probability to >95%. This sequential updating of probabilities reflects Bayesian inference.
Treatment Selection
Bayesian thinking becomes particularly valuable when choosing between treatment options. For a patient with a chronic, massive rotator cuff tear, we might frame the decision as:
Prior belief: Based on literature and experience, there's approximately 60% probability that reverse shoulder arthroplasty will provide superior pain relief and function compared to debridement alone.
Patient-specific factors update this probability:
• Age >70 years increases probability to 75%
• Pseudoparalysis increases probability to 85%
• Minimal arthritis maintains probability around 85%
• Patient engaged in heavy labor decreases expected satisfaction to 70%
This probabilistic framework facilitates shared decision-making by explicitly quantifying uncertainty and incorporating patient-specific factors.
Research Applications
Rotator Cuff Repair: Structural Healing vs. Functional Outcomes
Our 25-year systematic review showed persistent weak correlation between structural healing and functional outcomes (r ≈ 0.3-0.4) despite improved retear rates with modern techniques. A Bayesian analysis could answer:
Question: "Given 25 years of accumulated evidence, what is the probability that achieving structural healing produces a clinically meaningful improvement in functional outcomes?"
Prior: Weakly informative, centered on moderate correlation (r = 0.5)
Data: 25 years of studies showing consistent r ≈ 0.3-0.4
Posterior probability:
• >95% probability that some correlation exists (r > 0)
• ~60% probability that correlation is weak to moderate (r = 0.2-0.5)
• <5% probability that correlation is strong enough (r > 0.7) to justify prioritizing structural healing as primary outcome
This probabilistic statement is far more clinically useful than "p < 0.05 for correlation." It tells us that while structural healing probably matters somewhat, the evidence strongly suggests we should focus on functional outcomes and pain relief rather than obsessing over retear rates.
Reverse Shoulder Arthroplasty: Technology Assessment
Question: "What is the probability that robotic assistance in RSA improves clinically meaningful outcomes compared to standard instrumentation?"
Prior: Start with neutral prior (50% probability of benefit), though skeptics might argue for pessimistic prior given lack of evidence
Available evidence:
• No randomized trials showing outcome differences
• Observational studies showing improved component positioning (1-2° accuracy)
• No clinical studies showing positioning accuracy translates to reduced failure rates
• Known failure modes (infection, instability) minimally or unaffected by positioning precision
Posterior probability:
• ~15% probability of any clinically meaningful benefit
• ~3% probability of benefit exceeding minimal clinically important difference
• ~85% probability that cost ($3,000-5,000 per case) exceeds value
This analysis forces robotics proponents to justify their optimistic priors with evidence, which seems to be lacking at present. If more negative or neutral studies accumulate, even strongly optimistic priors wash out (as Figure 2 in the article illustrates).
Illustration of the diminishing influence of the prior on the posterior distribution as more data are accumulated. In this example, they began with a pessimistic prior (the control group may perform better). As more data were accumulated, we see a decreased influence of the prior belief on the posterior probability of the treatment effect.
Acromial Fracture Prediction
Prior probabilities based on known risk factors:
• Baseline fracture risk: 2-3%
• Osteoporosis increases risk by factor of 3-4
• Deltoid tension (measured by geometric parameters) increases risk
Bayesian prediction model could provide individualized fracture probability:
• 70-year-old woman with T-score -2.5, high deltoid tension: 15-18% probability
• 65-year-old man with normal bone density, moderate tension: 3% probability
This probabilistic risk stratification could guide surgical approach selection and postoperative rehabilitation protocols.
Perioperative Optimization
Nutrition optimization protocols exemplify Bayesian updating in real-time:
Initial assessment (prior): Patient with albumin 3.2 g/dL has ~40% probability of wound complications
Intervention: Nutritional supplementation for 4 weeks
Reassessment (posterior): Albumin now 3.8 g/dL, probability of wound complications updated to ~15%
Decision: Proceed with surgery versus continue optimization
This iterative assessment and updating based on accumulating evidence is Bayesian reasoning applied clinically.
Bayesian probabilities enhance informed consent by providing intuitive risk communication:
Traditional approach: "Rotator cuff repair has a retear rate of 20-40%"
Bayesian approach: "Based on your specific situation - a 2cm tear with minimal retraction and good tissue quality - there's approximately 75% probability of structural healing at 2 years. However, even if the repair doesn't heal completely, there's still an 80% probability you'll have significant pain relief and functional improvement."
This probabilistic framing acknowledges uncertainty while providing actionable information. It also naturally incorporates your finding that structural and functional outcomes are only weakly correlated.
Critical Evaluation of Literature
When reading research using Bayesian methods, we can apply the two key questions from the paper:
1. Was the prior appropriate?
Acceptable priors:
• Neutral (non-informative) prior centered on null hypothesis - appropriate when little prior evidence exists
• Prior based on high-quality systematic reviews or meta-analyses
• Prior explicitly justified and sensitivity analysis showing results robust to prior selection
Problematic priors:
• Optimistic prior favoring new technology without evidence justification
• Prior based on weak observational data when better evidence exists
• Prior selected to achieve desired conclusion (evident when sensitivity analysis not provided)
2. Was sample size adequate?
Just as underpowered frequentist studies (looking at p values from standard statistical tests such as t-test, Chi Square, Mann-Whitney) produce inconclusive results, Bayesian studies with insufficient data yield wide posterior distributions with high uncertainty. Look for:
• Narrow posterior credible intervals
• High probability (>90%) for clinically meaningful effects
• Sensitivity analyses showing stable conclusions
Practical Example: Stemless vs. Stemmed RSA
Research question: Does stemless design provide equivalent fixation to stemmed implants in osteoporotic bone?
Bayesian framework:
Prior belief: Neutral prior (50% probability of equivalence), though biomechanical principles might suggest pessimistic prior since osteoporotic bone provides less surface area for fixation
Evidence accumulation:
• Early case series: Small samples, mixed results, wide uncertainty
• Biomechanical studies: Reduced contact area in poor bone, updates probability of equivalence down to ~40%
• Medium-term clinical studies: Similar reoperation rates in general population, probability returns toward 50%
• Subset analysis in osteoporotic bone: Higher early loosening rates, probability of equivalence drops to ~25%
Posterior probability:
• ~25% probability that stemless provides equivalent fixation in osteoporotic bone
• ~60% probability that stemless shows higher failure rates
• ~15% probability of equivalence or superiority
Clinical interpretation: In patients with good bone quality, stemless may be equivalent. In osteoporotic bone, evidence suggests higher risk with stemless designs. This nuanced conclusion better serves clinical decision-making than binary "significant/not significant. This demonstrates how evidence accumulates to overcome initial priors (see figure)—even if you started neutral or optimistic about stemless, the osteoporotic bone data updates you toward ~25% probability of equivalence.
Avoiding Common Pitfalls
Pitfall 1: Assuming Bayesian methods rescue poor study design
As the paper emphasizes, Bayesian analysis doesn't overcome fundamental design flaws. Insistence on rigorous methodology applies equally to Bayesian and frequentist approaches. Poor measurement, inadequate follow-up, and confounding bias compromise Bayesian results just as they do traditional statistics.
Pitfall 2: Using priors to reach predetermined conclusions
Critics sometimes accuse Bayesian methods of allowing researchers to "choose their answer" by selecting favorable priors. This concern is addressed by:
• Using neutral priors when limited evidence exists
• Explicitly justifying informative priors with high-quality evidence
• Conducting sensitivity analyses showing conclusions robust across reasonable prior specifications
• Recognizing that with adequate data, even strongly biased priors wash out (Figure above)
Pitfall 3: Confusing statistical probability with clinical certainty
A 95% posterior probability that Treatment A provides some benefit doesn't mean:
• Treatment A definitely works
• The magnitude of benefit is clinically meaningful
• Treatment A is appropriate for all patients
Always consider the full posterior distribution, clinical context, and patient preferences.
Integration with Evidence-Based Medicine
Bayesian methods complement rather than replace traditional evidence hierarchy:
• Systematic reviews inform priors
• Well-designed RCTs provide likelihood data
• Patient values and circumstances personalize posterior probabilities
• Clinical expertise integrates probabilistic evidence into individualized recommendations
Conclusion
Bayesian thinking formalizes how experienced clinicians already reason - starting with prior knowledge and updating beliefs as evidence accumulates. In shoulder surgery research, Bayesian methods offer particular advantages:
• Direct probability statements about treatment benefits
• Nuanced interpretation of effect magnitudes
• Natural framework for incorporating prior evidence
• Intuitive communication for shared decision-making
• Explicit quantification of uncertainty
However, Bayesian methods require the same rigorous study design, adequate sample sizes, and appropriate outcome measures that characterize all good research. They are a powerful tool for analysis and interpretation, but not a substitute for methodological excellence.
For work challenging expensive technologies and promoting evidence-based practice, Bayesian frameworks provide compelling arguments. When proponents of robotics or patient-specific instrumentation claim benefits, ask: "What's your prior probability and how do you justify it? What's the posterior probability given accumulated evidence? What's the probability that benefits exceed costs?" These questions force explicit evidence-based reasoning rather than allowing claims based on theoretical advantages or marketing assertions.
The future of orthopedic research will likely include more Bayesian analyses. Understanding these methods - their strengths, appropriate applications, and limitations - will enhance our ability to critically evaluate literature and contribute to evidence-based advancement of shoulder surgery.
It's Elegant
Here are some videos that are of shoulder interest
Shoulder arthritis - what you need to know (see this link).
How to x-ray the shoulder (see this link).
The ream and run procedure (see this link)
The total shoulder arthroplasty (see this link)
The cuff tear arthropathy arthroplasty (see this link).
The reverse total shoulder arthroplasty (see this link).
The smooth and move procedure for irreparable rotator cuff tears (see this link)
Shoulder rehabilitation exercises (see this link).
