Bayesian Calculator for MSK Diagnosis

Michael L. Richardson, M.D.

Lauren K. Toney, M.S., M.D.

University of Washington Department of Radiology

Version 1.0


Let's look at how to use Bayes' Theorem in everyday practice. First, a few principles:

  1. Odds are a common way of expressing likelihood, and common in sporting events.

    The odds of an event are related to its probability, and these two entities can be easily computed from each other thusly:

    Odds = Prob / (1-Prob)

  2. When we express the likelihood in terms of odds, we can simplify Bayes' theorem to the following equation:

    pre-test odds × Likelihood Ratio = post-test odds

    Thus all we need to estimate the post-test odds of a disease are its pre-test odds and the likelihood ratio (LR) for that test.

  3. The pre-test odds come from the clinician.
  4. The likelihood ratio (LR) for a positive or negative test can easily be computed from its sensitivity and specificity:

    LRpositive test = Sensitivity / (1-Specificity)

    LRnegative test = (1 - Sensitivity) / Specificity

  5. We like Likelihood Ratios, because they allow us to reconcile multiple different test results, or (as we'll see) multiple different findings within a single test, because LR's are multiplicative!

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Visual Bayes

Input the following information about your test (refresh page before trying a second set of numbers):

Pretest probability

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Example 1: MRI of Meniscal Tear

We will use the following table to estimate the likelihood of a meniscal tear, based on which of the following MR imaging features are present or absent.

In the following table, click in the box under LRpos if the feature is present, and click the box under LRneg if the feature is absent. Only click on the features you wish to consider. By doing this, we are collecting the likelihood ratios (LRpos, LRneg) that we will be using to determine post-test probability.

The conglomerate likelihood ratio is

Pretest Odds


Likelihood Ratio


Posttest Odds


Enter prob (%) here

Prob (%)







Prob (%)

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