Likelihood Ratios

Podcast – Likelihood Ratios: Critical Appraisal Nugget 12

Diagnostic tests are an essential part of our work as healthcare professionals. But to truly understand their value, we must go beyond sensitivity and specificity to a concept that’s both more nuanced and practical: likelihood ratios (LRs). Whether you’re a seasoned emergency physician or just starting out, mastering likelihood ratios can transform your diagnostic skills, improve patient care, and make your decision-making more robust. In this podcast, we’ll break down what likelihood ratios are, why they’re essential, and how you can use them effectively in your clinical practice.

This is our latest podcast in the Critical Appraisal Nugget series. You can find all our previous episodes here.

Listening Time – 11.30

What Is a Likelihood Ratio?

At its core, a likelihood ratio is a way to compare the performance of a diagnostic test. It answers the question: How much does a test result change the likelihood that a patient has a disease? Unlike sensitivity and specificity, which are intrinsic properties of a test, likelihood ratios help us apply test results to individual patients.

Here’s the formula for a positive likelihood ratio (LR+):

LR+ = Sensitivity / (1 - Specificity)

For a negative likelihood ratio (LR-), the formula is:

LR- = (1 - Sensitivity) / Specificity

To put it simply:

  • LR+ tells us how much more likely a positive test result is in someone with the disease than in someone without it.
  • LR- tells us how much less likely a negative test result is in someone with the disease than in someone without it.

Why Likelihood Ratios Matter

So, why bother with likelihood ratios when we have sensitivity, specificity, or predictive values? The answer lies in their flexibility and applicability to real-world scenarios:

  1. Account for Disease Prevalence: Sensitivity and specificity don’t change with prevalence, but predictive values do. Likelihood ratios allow us to adjust for prevalence by working with pretest probabilities specific to our patient population.
  2. Move from Probabilities to Actions: By combining pretest probabilities with likelihood ratios, we can calculate post-test probabilities—the chance a patient has (or doesn’t have) a disease after a test result. This can directly influence clinical decisions, from ruling in a myocardial infarction (MI) to ruling out pulmonary embolism (PE).
  3. Make Individualized Decisions: Unlike broad population-level metrics, likelihood ratios allow us to tailor decision-making to the individual patient sitting in front of us.

How to Use Likelihood Ratios in Practice

Let’s make this tangible with an example.

Case: The Chest Pain Conundrum

It’s 2 a.m., your third night shift in a row, and you’re called to review the ECG of a 25-year-old presenting with chest pain. The ECG shows anterior ST elevation, but is this a STEMI or benign early repolarization?

You decide to use the Smith Calculator for Anterior ST Elevation, a tool that predicts the likelihood of an occlusive myocardial infarction. Here’s what you know:

  • Sensitivity: 86%
  • Specificity: 91%

From this, the positive likelihood ratio (LR+) is calculated as:

LR+ = Sensitivity / (1 - Specificity)
    = 0.86 / (1 - 0.91)
    = 0.86 / 0.09 ≈ 9.2

This means a patient with a Smith Calculator score above the threshold is roughly 9 times more likely to have a STEMI than someone below the threshold. But how does this translate into real-world decision-making?


The Power of Bayesian Reasoning

Likelihood ratios work hand-in-hand with Bayesian reasoning, which uses prior probabilities to predict outcomes. In this context:

  • Pretest Probability: Your estimated chance of disease before performing the test.
  • Post-Test Probability: The revised chance of disease after considering the test result.

Let’s calculate.

Example 1: A Low-Risk Patient

Imagine you assess the patient as low-risk (pretest probability = 5%). Using odds, this translates to:

Pretest Odds = Pretest Probability / (1 - Pretest Probability)
             = 0.05 / (1 - 0.05)
             = 0.05 / 0.95 ≈ 0.0526

Now apply the positive likelihood ratio:

Post-Test Odds = Pretest Odds × LR+
               = 0.0526 × 9.2 ≈ 0.4839

Convert back to probability:

Post-Test Probability = Post-Test Odds / (1 + Post-Test Odds)
                      ≈ 0.4839 / (1 + 0.4839)
                      ≈ 32.6%

For a low-risk patient, a positive Smith Calculator result raises the probability of STEMI to about 33%—enough to warrant further investigation, if not immediate intervention.

Example 2: A Moderate-Risk Patient

Now, let’s say the patient has risk factors or symptoms that make you estimate a 50% pretest probability. The pretest odds are:

Pretest Odds = 0.5 / (1 - 0.5) = 1

Applying the same LR+:

Post-Test Odds = Pretest Odds × LR+ = 1 × 9.2 = 9.2
Post-Test Probability = Post-Test Odds / (1 + Post-Test Odds)
                      = 9.2 / (1 + 9.2)
                      ≈ 90.2%

In this case, the test result significantly increases your confidence in diagnosing STEMI, likely prompting immediate intervention.


The Real-World Impact

The beauty of likelihood ratios lies in their practicality:

  • For ruling in disease: A high LR+ (e.g., >10) strongly supports the diagnosis.
  • For ruling out disease: A low LR- (e.g., <0.1) strongly argues against it.

Tests with likelihood ratios closer to 1 are less useful, as they don’t significantly change pretest probabilities.


Challenges and Limitations

Using likelihood ratios isn’t without its challenges:

  1. Estimating Pretest Probability: This often relies on clinical judgment, which can introduce variability.
  2. Complexity: The math can feel daunting, especially during a busy shift.
  3. Dependence on Study Quality: Likelihood ratios are only as good as the data behind them, so always evaluate the study population and methods.

Despite these challenges, likelihood ratios provide a structured way to handle diagnostic uncertainty.


Key Takeaways

  1. Likelihood ratios bridge the gap between test performance (sensitivity/specificity) and patient-centred decisions.
  2. They allow you to personalize care, applying diagnostic tests meaningfully in diverse populations and clinical settings.
  3. Mastering likelihood ratios can enhance your confidence, ensuring you make decisions grounded in evidence, not guesswork.

Final Thoughts

Likelihood ratios might feel abstract at first, but they are a vital tool in every healthcare professional’s arsenal. By embracing them, you can improve diagnostic precision and patient outcomes. Whether you’re deciding on reperfusion for a STEMI or ruling out PE, likelihood ratios guide you through the murky waters of diagnostic uncertainty.

We’d love to hear your thoughts! How do you use likelihood ratios in your practice? Share your experiences and tips in the comments below.


Podcast Transcription


Cite this article as: Iain Beardsell, "Podcast – Likelihood Ratios: Critical Appraisal Nugget 12," in St.Emlyn's, January 8, 2025, https://www.stemlynsblog.org/podcast-likelihood-ratios-critical-appraisal-nugget-12/.

Thanks so much for following. Viva la #FOAMed

Scroll to Top