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Clinical Reasoning Corner: Likelihood Ratios

By Jack Penner

Welcome back, Clinical Problem Solvers!

Thank you for reading the latest post in our “Clinical Reasoning Corner”, where we discuss key clinical reasoning principles that shape how we think through cases.

We hope it serves as a resource for when you need a quick refresher or want to prepare your own materials for teaching clinical reasoning!

Today, we’re going to talk about likelihood ratios – let’s dive in!

Objectives

    1. Define likelihood ratios and their utility in diagnostic reasoning
    2. Identify how likelihood ratios alter the probability of a diagnosis
    3. Apply likelihood ratios in clinical reasoning 

What are likelihood ratios and how do they work?

Likelihood ratios (LRs), which help us determine how a test changes the probability of a disease, are defined as:

 

For example, say 60% of patients with aortic stenosis have a systolic ejection murmur best heard over the aortic valve area, and only 10% of patients without aortic stenosis have that same murmur.

We can calculate the LR by:

Or, let’s say 20% of patients who come to the ED with chest pain from acute coronary syndrome have a pleuritic component, whereas 60% of patients with chest pain who do not have ACS have a pleuritic component.

The LR would be:

As you can see, LRs can be greater or less than 1.

    • A LR > 1 increases the probability of a specific diagnosis.
    • A LR < 1 decreases the probability of a specific diagnosis.
    • A LR = 1 does not alter the probability at all

Applying this to the above scenarios, the presence of a systolic ejection murmur over the aortic valve area increases the probability of aortic stenosis. A pleuritic component to a patient’s chest pain decreases the probability of ACS.

Likelihood ratios, sensitivity, & specificity

LRs are also closely related to sensitivity and specificity, which we often think of as helpful test characteristics for ruling a disease in or out. However, a highly sensitive or specific test, alone, is not enough to meaningfully alter the probability of a disease. To do that, we need to rely on LRs.

For example, take a test with a sensitivity of 20% and a specificity of 85%. In theory, it should be a test that, when positive, helps us make a diagnosis.

However, when we calculate the LR:

A LR of 1.33 is quite close to 1, which means this highly specific test, when positive, does little to increase the probability of the disease. By relying on LRs, we can more accurately capture how much certain tests shift the probability of a specific disease.

For more, check out Josh Farkas’ deep dive into this key topic.

How Can I Use Likelihood Ratios in My Own Practice?

Recall from our first article in the “Clinical Reasoning Corner” that pretest probability represents the relative probability we attribute to a certain disease before we gather further diagnostic data.

A patient’s clinical presentation, risk factors, and the base rate of disease, in addition to our own clinical experience, all factor into the pretest probability we assign to any diagnosis. Further studies then reframe these probabilities and give us a posttest probability.

This reframing of diagnostic probability is driven by LRs.

Translating LRs into probabilities requires a nomogram and a lot of statistics. Unless you’re Rabih “The Mathematician” Geha, it might make your head spin.

Luckily, Dr. Steven McGee simplified the process down to simple principles and a fantastic graphic.

Image From: Evidence Based Physical Diagnosis by Dr. Steven McGee

An easy way to remember LR’s is to remember the numbers 2/5/10, and 15/30/45

    • An LR of 2 increases the probability by 15%
    • An LR of 5 increases the probability by 30%
    • An LR of 10 increases the probability by 45%.

The inverse also holds true

    • An LR of 0.5 decreases the probability by 15%
    • An LR of 0.2 decreases the probability by 30%
    • An LR of 0.1 decreases the probability by 45%

Layering this onto the “3 T’s” (“Toss, Test, Treat”) of pre and posttest probabilities, we get something that looks like this:

Remember, the exact thresholds for “Toss, Test, and Treat” (the “3 T’s”) change based on factors beyond probability alone, such as the morbidity of the disease, the morbidity of treatment, and patient preferences.

Thus, there is no single LR that leads us to make a certain clinical decision.

Rather, we layer LRs onto our own diagnostic and therapeutic thresholds that we continue to refine with time, experience, and practice in the pursuit of diagnostic excellence.

Importantly, LRs are just one tool in our clinical reasoning toolbox. As this article explains, using LRs can be time consuming, making it impractical to apply them to every clinical decision. The key is using this tool when it’s most likely to be handy.

I still struggle to know when it is the right time to use LRs, and often find myself reaching for them in times of diagnostic ambiguity or when I am considering unfamiliar diagnoses. 

Furthermore, creating a list of the LRs for useful diagnostic tests in common diseases (e.g., heart failure, pneumonia, or cirrhosis) has been a useful way to efficiently integrate them into my own practice. With the help of the #MedTwitter community, we have started a list of helpful LRs at the bottom of this article that we hope serves as a foundation for you to build on!

We’d love to know what makes you pause and apply LRs in your clinical reasoning. Let us know on Twitter or via email at theclinicalproblemsolvers@gmail.com, and please share some of your favorite LRs with us!

Let’s Practice With a Case

A 52 year-old-woman with cirrhosis secondary to chronic hepatitis C infection presents with three weeks of progressive abdominal distension and two days of abdominal pain and fevers.

On exam, her vitals are T 38.6°C, HR 102 bpm, BP 107/68, RR 16, and normal oxygenation on ambient air.

She has scleral icterus and a diffusely tender, distended abdomen with shifting dullness to percussion. A fluid wave is absent. She has scattered spider angiomas across her chest and mild pitting lower extremity edema.

Initial labs show a WBC count of 8.3 x 109 cells/L, Hgb 9.7 g/dL, and platelet count of 89 x 109/L. Her creatinine is 0.82 mg/dL, total bilirubin 5.6 mg/dL, and INR 1.6.

Your colleague asks, “Do you think she has ascites?” 

There are multiple physical exam findings associated with ascites including:

    • Bulging flanks (LR = 1.9)
    • Shifting dullness to percussion (LR = 2.3)
    • Fluid wave (LR = 5.0)

Q: How do these LRs alter the probability that she has ascites?

A: Based on the diagram from Dr. McGee, if she were to have a fluid wave, the probability of ascites would go up by ~30%.  The presence of shifting dullness increases the probability by only ~15%, which is enough to warrant more formal evaluation and not enough to definitively confirm she has it.

A bedside ultrasound, demonstrates significant peritoneal fluid.

As a quick refresher, here is a schema on Ascites:

Our ascites episode highlighted two important questions to ask whenever you encounter a patient with ascites:

    1. Is there portal hypertension?
    2. Is the ascitic fluid infected?

Answering both of these questions requires a diagnostic paracentesis.

A diagnostic paracentesis is performed with drainage of cloudy ascitic fluid.

Ascitic fluid studies show an albumin of 1.4 g/dL (serum 3.6), a total protein of 0.7 g/dl, a glucose of 78 mg/dL, and an LDH of 153 U/L (normal range for serum is 140-280 U/L). The total WBC count is 830 cells/mm3 with 290 neutrophils/mm3.

Q: Is there portal hypertension?

A: The presence of a high SAAG (> 1.1) is consistent with her ascites being secondary to portal hypertension. The most common cause of portal HTN is cirrhosis, a diagnosis supported by her labs.

Q: Is the ascitic fluid infected?

A: Ascitic fluid infections most commonly arise from spontaneous bacterial peritonitis (SBP).

A diagnosis of SBP is made when:

    • The neutrophil count in the ascitic fluid is ≥ 250 cells/mm3
    • Ascitic fluid cultures are positive
    • Secondary bacterial peritonitis has been excluded.

In this case, the ascitic fluid glucose being > 50 mg/dL, the protein being < 1mg/dL, and the LDH level being normal suggest against secondary bacterial peritonitis.

Because the diagnosis of SBP requires, in addition to a neutrophil count > 250 cells/mm3, a positive peritoneal fluid culture (which can take days to turn positive), we often decide whether or not to start antibiotics based solely on the neutrophil count.

We can use LRs to determine how much the ascitic fluid neutrophil count alters the probability of the bacterial culture turning positive.

    • Ascitic fluid neutrophil count > 500 cells/mm3: LR 10.6 (increases probability of positive culture by ~45%)
    • Ascitic fluid neutrophil count > 250 cells/mm3: LR 6.4 (increases probability by ~30%)
    • Ascitic fluid neutrophil count < 250 cells/mm3: LR 0.20 (decreases probability by ~30%)

In this case, the neutrophil count of 290 cells/mm3 increases the probability of a positive ascitic fluid culture (and thus a diagnosis of SBP) by ~30%, as represented below.

There are two things to highlight in the diagram:

    1. The neutrophil count > 250 cells/mm3 pushes the probability of bacterial peritonitis into the “Treat” category.
    2. The “Treat” section in this case is quite large

Because of the high mortality rates of SBP (up to 30%), we have a relatively low threshold to treat for SBP. Thus, we empirically treat patients with ascitic fluid that has > 250 neutrophils/mm3. 

A portion of patients with ascitic fluid neutrophil counts > 250 cells/mm3 will not have positive cultures, and thus, may not have SBP. 

The clinical finding of ascitic fluid neutrophil counts > 250 cells/mm3 + a negative ascitic fluid culture is known as culture-negative neutrocytic ascites. Bacterial infection isn’t the only cause of an ascitic fluid neutrophil count > 250 cells/mm3, so this brings other disease into the picture, such as peritoneal tuberculosis, malignancy, and chemical peritonitis (e.g. pancreatitis).

However, it may also represent SBP, with the negative culture being attributed to:

    1. The patient receiving antibiotics before the diagnostic paracentesis
    2. Sub-optimal ascitic fluid culture technique
    3. Spontaneous improvement in SBP

She was empirically started on Ceftriaxone. On hospital day #2, peritoneal fluid cultures returned positive for E. coli, confirming a diagnosis of SBP. She completed a 5 day course of antibiotics and recovered well. Because of this episode of SBP, she was discharged on lifelong SBP prophylaxis.

Summary

That covers it, Clinical Problem Solvers! To summarize:

    1. LRs are tools that help determine how much a clinical finding increases (LR >1) or decreases (LR < 1) the probability of a disease.
    2. The numbers 2/5/10, and 15/30/45 are an easy way to remember how much different LRs alter the pretest probability of a specific diagnosis.
    3. We can use LRs, in combination with patient preferences and our own diagnostic and therapeutic thresholds, to guide treatment and testing decisions.

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Further Reading:

Favorite Likelihood Ratios from the #MedTwitter Community:

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