Understanding and Applying Positive and Negative Likelihood Ratios (LRs) in Practice
We rely on the diagnostic accuracy of tests (history, physical exam maneuvers, labs, diagnostic imaging, etc.) to help us reach a diagnosis.
If a patient presents to us with a concern, we generate a list of possibilities (differential diagnoses), then we test the possibilities. When we perform or order tests, we think about their diagnostic accuracy. We can do this with sensitivity and specificity, negative and positive predictive values, and with likelihood ratios (LRs). Today, we will focus on LRs. These can be difficult to conceptualize, but they are important, nonetheless.
Case: You’re seeing a 7-year-old female with a 4-day history of fever, purulent cough, and general malaise. You generate a list of initial possibilities: infectious (upper respiratory tract infection, pneumonia), allergic (asthma), foreign body aspiration. You then note that she does not have any wheeze, stridor, or shortness of breath (less likely asthma or foreign body). Her vitals are stable and her temperature is 38.5C (101.3F). You now want to rule out pneumonia. What is your pre-test probability for pneumonia?
Estimating your pre-test probability for an illness or disease is a combination of information that is readily available, experience, and clinical gestalt. If we had 10 clinicians evaluating this 7-year-old they would all have a slightly different pre-test probability for pneumonia.
If your pre-test probability is low or high, you might not need to conduct further testing, but if it’s in the middle (the “diagnostic uncertainty range”), further testing is required to rule in, or rule out a disease.
Back to the case: Let’s say your pre-test probability for pneumonia is 50% with the history and vital signs alone (that is, it is equally likely the patient has or does not have pneumonia). You need to conduct more testing to increase your pre-test probability before treating for suspected pneumonia (to get out of the diagnostic uncertainty range). You listen to her lungs and note crackles in her left lung base. Now your post-test probability is higher, let’s say 70%. This becomes your new pre-test probability before you perform another test, for example, lung ultrasound.
You can see from this example that the diagnostic reasoning process is a non-linear maze that goes back and forth between pre and-post-test probabilities every time you incorporate a new test.
What is a likelihood ratio? Likelihood ratios are alternative statistics used to summarise diagnostic accuracy (1), and represent the direction and strength of evidence provided by a test result (2). Your pretest probability, multiplied by the test LR gives you your post-test probability. Sensitivity and specificity of a test are used to generate LRs.
There are positive and negative LRs.
Positive LR: A LR greater than 1 is associated with a positive test result and an increased probability of a patient having a disease (3).
Negative LR: A LR of less than 1 is associated with a negative test result and a decreased probability of a patient having a disease (3).
Back to the case: the positive LR for lung ultrasound for a diagnosis of pneumonia in children has been reported as 13.4 (4).
For suspected pneumonia, your pre-test probability from the history and physical is 70%, the positive LR is 13.4, which gives you a post-test probability of 96.8%.
Where do we find LRs? LRs are derived from research studies, which means we use LRs with a grain of salt – they are not perfect, just as research studies are not perfect. You can use LRs from individual studies (e.g. RCTs, meta-analyses, etc.), or thennt.com has a dynamic calculator tool you can use to assess your pre and post-test probability for specific tests. It has LRs for different tests/diseases on the site. I used thennt.com for the case example above. You can also incorporate LRs into Fagan’s Nomogram (stay tuned for a future post).
Clinical applicability: let’s be clear – we aren’t looking up LRs and calculating pre and post-test probability for every test that we conduct. Nor are we expected to memorize LRs from specific studies to apply to every test. Having a general understanding of LRs can help us recognize test accuracy, test limitations, and whether a test will change management based on our pre-test probability.
Keep the following points in mind to quickly estimate post-test probabilities using LRs:
Positive LRs of >10 and negative LRs of <0.1 generate large and often conclusive changes from pre to post-test probability – meaning, the test will help rule in or rule out a diagnosis and change management.
Positive LRs of 1-2 and negative LRs of 0.5-1 will minimally change your post-test probability – meaning, the test will not help rule in or rule out a diagnosis so may not be worth ordering.
An LR of 1 does not change your post-test probability.
Some clinicians find specificity and sensitivity most helpful to assess test appropriateness, others find negative and positive predictive value most helpful, and others like to use LRs. Many use a combination of all three concepts.
Key Take Home Points:
The pre-test probability of a disease multiplied by the LR gives the post-test probability of a disease.
We can use LRs prior to ordering a test. LRs help determine whether a test will change our post-test probability.
Positive LRs >1 increase our post-test odds of a patient having a disease (rules it in), negative LRs <1 will decrease our post-test odds of a patient having a disease (rules it out).
If a test has an LR of 1, it won’t change our post-test probability.
References/Readings
The NNT. Lung Ultrasound for Diagnosis of Pneumonia in Children. [Interne] [cited 2023 October 15]. Available from https://thennt.com/lr/lung-ultrasound-diagnosis-pneumonia-children/