Improving Diagnostic Accuracy with Bayes’ Theorem and a Fagan’s Nomogram | The Sports Physiotherapist

Improving Diagnostic Accuracy with Bayes’ Theorem and a Fagan’s Nomogram

Improving Diagnostic Accuracy with Bayes’ Theorem and a Fagan’s Nomogram

Posted on 18. Jan, 2011 by in Assessment, Blog, Diagnosis, Sports Physiotherapy


How do you make a diagnosis? I assume that you perform a subjective examination and develop competing hypotheses, and then work to support or negate these via your objective examination. Can you, however, following your physical examination tell the patient the percentage chance of them having a particular diagnosis? Is that something you might be interested in? If your answer is a resounding yes, Bayes’ Theorem and a Fagan’s Nomogram can give you the ability to do so.

If you are an experienced sports physiotherapist it is likely that you use Bayes’ Theorem and a Fagan’s Nomogram, either directly or indirectly. More importantly, these tools are something that all (and less experienced) physiotherapists can utilise to increase the objectivity of their clinical reasoning. For all you non-mathematical sports physiotherapists, relax, this post will give you the easily implementable basics of using the Fagan’s Nomogram to improve your diagnostic accuracy.


In order to use this technique of clinical reasoning you need a few things. These are:

  • A Fagan’s Nomogram, you can find one here.
  • The Pre-Test Probability of A Condition, which can be estimated using epidemiological studies. For more information on this click here.
  • The Diagnostic Accuracy of the clinical tests you use (in particular positive and negative likelihood ratio, which may be calculated if you have sensitivity and specificity)
  • The results of your clinical examination!


Let’s use a clinical example to illustrate the use of Bayes’ Theorem and a Fagan’s Nomogram. A patient presents to you with a knee injury that, following your subjective examination, you suspect may be a medial meniscus tear. You perform your objective examination and find that the patient has medial joint line tenderness, a positive Apley’s grind, and a positive McMurray’s test.

What do you think that percentage chance of the patient having a medial meniscus tear is given the information? Guess now…

Now I will use Bayes’ Theorem and a Fagan’s Nomogram to work out the probability of the patient having a medial meniscus tear.

The additional information I require, as stated in the list above, is:


Fagan’s Nomogram

As you will see, on the left hand side of the nomogram is the pre-test probability (in this case 10.8%). The centre of the nomogram is the likelihood ratio (for joint line tenderness is 2.74). If you line these up using a ruler you will get the post-test probability of a medial meniscus tear.

Fagan’s Nomogram: Medial Joint Line Tenderness

As you can see, the line intersects post-test probability at approximately 25%. This means the positive result would suggest a 25% chance of the patient having a medial meniscus tear. However, we have further test results. When we use the results of the Apley’s Grind, the pre-test probability is now 25% (given the previous result).

Fagan’s Nomogram: Apley’s Grind

As you can see, the second result gives a post-test probability of approximately 40%. Thus following two positve results the percentage increased from 10.8% to approximately 40%. Now for the final result, the positive McMurray’s (positive LR of 2.49).

Fagan’s Nomogram: McMurray’s Test

The final result is approximately 65%. This means that after the 3 positive results of the ‘Meniscal Special Tests’ the post-test probability is approximately 65%. Now, you can be more precise through the use of mathematics, however, the Fagan’s Nomogram is much more clinically useful.


How does the final result compare to what you guessed before the exercise. Were you close or did you rely too strongly on the results of the ‘special tests’? Despite 3 positive tests there is still a 35% chance that it is something else?? Yeah, it can be a little scary. Using the nomogram and the diagnostic accuracy of clinical tests will make you a evidence based assessing machine.

What are your experiences with evidence based clinical reasoning? Be sure to let me know in the comments or catch me on Facebook or Twitter

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Majewskia M, Susanneb H, Klaus S. Epidemiology of athletic knee injuries: A 10-year study. 2006;13(3):184-188.

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