Choosing and Interpreting Diagnostic Tests
Likelihood Ratios
Here we try to understand some of the concepts behind why we use test the way we do
Likelihood ratios help us determine how a test (this can be anything like clinical finding, a feature in a history or a laboratory test) changes the probability of a disease.
A likelihood ratio of <1 decreases the probability of a diagnosis (ie the LR for chest wall tenderness in MI is 0.3)
A LR of >1 increases the probability of the diagnosis (ie the LR for diaphoresis with chest pain for MI is 2.3)
LRs are closely related to sensitivity and specificity. However, Sensitivity and Specificity are not sufficient alone to change the probability of a disease – this is the role of the LR.
If we take a test with a sensitivity of 20% and a specificity of 85% we can calculate the LR from that test, in relation to the disease we are testing for.
With the LR in this example being close to 1 (1.33), this test, despite being highly specific, does little to increase the probability of the disease.
If you want to play around with this I have linked a calculator for PE and the relevant LRs for different features below, reading through you can start to see how the Wells Score helps risk stratify patients. Remember that the LR is determinant to your outcome, so it will be different for a D-dimer for PE to DVT for example.
http://getthediagnosis.org/diagnosis/Pulmonary_Embolism.htm?mode=calculator&id=1&sort=0&lr=1
How does an LR effect what I do clinically?
Essentially this is asking how does it change my probability of the disease being present when compared to my pre-test probability.
Borrowed from this: https://www.amazon.com/Evidence-Based-Physical-Diagnosis-Steven-McGee/dp/0323392768/ref=sr_1_1?keywords=evidence+based+physical+diagnosis&qid=1568661890&s=gateway&sr=8-1
From this conversion table (the maths makes me feel sick so im sticking to just cheating and using the this table). We can see that a LR of 2 increases the probability by 15% and 10 by 45%, likewise, an LR of 0.5 reduces the probability by 15%.
Unfortunately the stats and the LR doesn’t deal with real world people – just because its 45% less likely then we initially thought doest mean we can just ignore the morbidity of the disease or what the patient wants. Essentially it doesn’t account for the consequences of the minimal chance (think catastrophic like a missed dissection, which is why we end up scanning for a lot of them).
Some examples of LR in Clinical Practice
Cardiac Syncope? https://pubmed.ncbi.nlm.nih.gov/31237649/
Functional Weakness? Hoover’s sign has an LR of 42 for functional weakness https://jnnp.bmj.com/content/73/3/241.long
GI Bleed? Patient reported melaena has a LR of 6 https://pubmed.ncbi.nlm.nih.gov/22416103/
When we start plotting LR into our pre-test probabilities we create a Fagan’s normogram. As we can see from following the plots from our pre-test probability (that in clinical practice isn’t numerical remember) our LR changes what the post-test probability needs to be.
