Post-test probability calculator for musculoskeletal examination tests

Where the starting number comes from

Your estimate before testing comes from how common the condition is in your setting, plus the history. The same test means different things in a sports clinic and on a surgical waiting list. Many published figures come from surgical populations, where the condition is more common than in a first-contact clinic.

Use one test at a time

In principle the probability after one test can become the starting point for the next, but only if the tests are independent, and tests for the same problem rarely are. Lachman and the anterior drawer both measure the same forward movement of the tibia, so a second positive adds much less than its own figure suggests. Where a combination has been tested as a cluster or a decision rule, use that published result instead.

How to calculate a likelihood ratio from sensitivity and specificity

LR+ = sensitivity ÷ (1 − specificity)
LR− = (1 − sensitivity) ÷ specificity

Example: the Matles test for Achilles rupture has a sensitivity of 88% and a specificity of 85%. LR+ = 0.88 ÷ 0.15 = 5.87. LR− = 0.12 ÷ 0.85 = 0.14. A positive is a moderate rule-in; a negative is a moderate rule-out.

Some studies publish their own likelihood ratios, which can differ slightly from the ratio of the rounded sensitivity and specificity. Each test page says where its figures come from.

From likelihood ratio to probability

Turn the probability into odds, multiply by the likelihood ratio, and turn the odds back into a probability: odds = p ÷ (1 − p); post-test odds = pre-test odds × LR; probability = odds ÷ (1 + odds).

Worked example: you think a supraspinatus tear is 30% likely. The odds are 0.30 ÷ 0.70 = 0.43. A positive drop arm test (LR+ 6.45) gives odds of 0.43 × 6.45 = 2.77, which is a probability of about 73%. A negative (LR− 0.79) gives odds of 0.34, about 25%. That is why a negative drop arm test is not reassuring.

The shortcut: the 15-30-45 rule

LR	Change in probability (roughly)
2	+15 percentage points
5	+30
10	+45
0.5	−15
0.2	−30
0.1	−45

Accurate to within about 10 points for starting probabilities between 10% and 90%.

How big is big?

An LR+ of 10 or more is a strong rule-in and 5 to under 10 a moderate one; 2 to under 5 nudges the diagnosis up; 1 to under 2 barely moves it; under 1 points the wrong way. An LR− of 0.1 or less is a strong rule-out and above 0.1 but under 0.2 a moderate one; 0.2 to 0.5 nudges it down; above 0.5 up to 1 barely moves it; over 1 points the wrong way.

Sources

McGee S. Simplifying likelihood ratios. J Gen Intern Med. 2002;17(8):646–649.
Jaeschke R, Guyatt GH, Sackett DL. Users' guides to the medical literature. III. How to use an article about a diagnostic test. B. What are the results and will they help me in caring for my patients? JAMA. 1994;271(9):703–707.

The calculator describes groups of patients in the cited studies, not the person in front of you. It is a teaching aid for registered health practitioners and students, not clinical advice.