How useful is the Likelihood Ratio (LR) really?
"How much can I trust this test?"
That is when Likelihood Ratio (LR) comes into play.
However,
"If the positive likelihood ratio is 5, how reliable is it really?"
"If the negative likelihood ratio is 0.2, how much can I rule it out?"
It is often hard to get a feel for these things, isn't it?
Conclusion: You can remember it roughly like this!
This is a rule of thumb for clinicians introduced in McGee's 2002 paper.
Positive Likelihood Ratio (+LR)
+LR 2 → Diagnostic probability increases by about 15%
+LR 5 → Diagnostic probability increases by about 30%
+LR 10 → Diagnostic probability increases by about 45%Negative Likelihood Ratio (−LR)
−LR 0.5 → Decreases by about 15%
−LR 0.2 → Decreases by about 30%
−LR 0.1 → Decreases by about 45%
* You can consider this as "roughly this much." It is very useful as a guide when performing clinical reasoning using mental math.
How do you use it?
For example, if the pre-test probability of a certain disease is 30%,
What if you test positive with a +LR 5 test? → Add about 30% to 30% → You can say there is about a 60% probability
What if you test negative with a −LR 0.2 test? → Subtract 30% from 30% → It drops to roughly the 0–5% range
Of course, strictly speaking, you should calculate it using Bayes' theorem, but this "rough sense" is important in clinical practice.
Summary:
The Likelihood Ratio (LR) is a tool that can numerically express "how much does this test result contribute to the diagnosis?"
It is useful to keep the rough values of "2, 5, 10" and "0.5, 0.2, 0.1" in your head.
It will significantly improve the accuracy and speed of your diagnostic reasoning.
📚 Source:
McGee S. Simplifying Likelihood Ratios. J Gen Intern Med. 2002;17(8):646–649.
PMID: 12133161
Note: A common misconception about negative likelihood ratios
“If the -LR is 0.2, does that mean a negative result increases the probability of ‘not having the disease’ by 30%?”
📛 → Actually, this is slightly incorrect.
Correctly stated:
A “small -LR” means that when the result is negative, the “probability of having the disease” decreases by ○%.
Therefore,
❌ “The probability of not having the disease increases”
✅ “The probability of having the disease decreases”
This distinction is important!
Quick check with an example:
For a patient with a pre-test probability of 30%, if a test with a -LR of 0.2 is negative:
→ The probability of disease drops by about 30%, and
→ the post-test probability drops to roughly 0 to a few percent. That is the idea.
In a nutshell:
“A small negative likelihood ratio = the probability of ‘having the disease’ decreases!”
This is a point that is easy to misstate, so it is reassuring to double-check it.