Likelihood Ratios in Clinical Practice

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:

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.
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).
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:

Estimating Pretest Probability: This often relies on clinical judgment, which can introduce variability.
Complexity: The math can feel daunting, especially during a busy shift.
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

Likelihood ratios bridge the gap between test performance (sensitivity/specificity) and patient-centred decisions.
They allow you to personalize care, applying diagnostic tests meaningfully in diverse populations and clinical settings.
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

Hello and welcome to the St. Emlyn’s podcast. I’m Rick Body.

I’m Greg Yates.

And today we’re going to go through another critical appraisal nugget podcast. In the last episode, we touched on positive and negative predictive values, talking about diagnostic accuracy.

And today we’re going to be talking about likelihood ratios, which is a more advanced concept, but one that’s really practical. when we’re treating patients on the shop floor. And we’re going to tell you how you might be able to use that in your day to day care in the emergency department. So Greg, what is a likelihood ratio and how do we calculate one?

All right. So put into simple terms a likelihood ratio is a comparison of the probability that a given test result would be seen in a patient with the disease to the probability that test result would be seen in a patient without the disease. So if you want to think back to our first critical appraisal nugget, it’s the ratio of the sensitivity to one minus specificity.

Now I know one minus specificity is a concept that’s given me a bit of a headache in the past. Essentially that is false positive rate. So how often the test is positive in somebody who does not have the condition. So if you think about a really sensitive test that gives you very few false positives, that is going to have a high positive likelihood ratio.

And a test that has absolutely rubbish sensitivity, that gives you false positives all the time, will have a really low positive likelihood ratio.

Yeah, and it’s really important to recognize that as well as the positive likelihood ratio, we have the negative likelihood ratio. And these are a little bit akin to the positive and negative predictive values.

So a positive likelihood ratio is really talking about ruling in a condition. How much more likely is it that the patient has the disease given a positive test? A negative likelihood ratio is the opposite. So that tells us about the rule out aspect. How good is this test at ruling out the disease? So let’s put this into practice.

Greg, let’s go through an example. from the shop floor. Let’s think about a patient who has chest pain.

Yep, that sounds about right. okay, Rick, it’s 2am, third night in a row. You’ve just been asked to review the ECG for a 25 year old young man who’s come in with some chest pain. This is your 50th ECG of the evening.

I’m going to make your heart sink. There’s anterior ST elevation, but it’s really unclear to you whether this is anterior occlusive MI,an acute heart attack, or is this benign early repolarization. I’m sure you’ve had this happen to you before.

I’m sure every emergency physician is familiar with this situation. It can be really difficult to differentiate benign early repolarization from a STEMI.

Yeah, absolute nightmare. We’ve all been through it. Fortunately, there does exist tools to help us with this. one of them that is really helpful, if you’ve never used it before, is the Smith Calculator for Anterior ST Elevation.

This was produced by Stephen Smith, who’s an emergency physician in Minnesota. and we encourage you to, look at lots of his research, which is really helpful with ECG interpretation. But you can essentially put some of the parameters from your ECG, enter the Smith calculator, and it will tell you the likelihood that this represents an anterior occlusive MI versus benign early repolarization.

Let’s say we’ve done this, and we’ve popped it through the calculator, and it’s told us this is above threshold, and that this is likely to represent an anterior STEMI, in this 25 year old guy with no medical history, but some chest pain. and I’m going to go back to the original study, and I can see here that our sensitivity of this test, the Smith calculator, is 86%, with a specificity value of 91%.

So surely at this point, job done, why would I need a likelihood ratio?

I guess they’re a little bit abstract, aren’t they? The sensitivity and, specificity, they’re 86 % and 91%. So if we were going to calculate the positive likelihood ratio of this, we’re going to take the sensitivity of 86%, we’re going to divide it by the false positive rate, so that’s 100 minus the specificity, which was 91, so it’s 86 divided by 9, and the authors have calculated that for us and tell us that the likelihood ratio, or positive likelihood ratio, is 9. 2. .

Okay.

So that means that a patient with a Smith Calculator score above the threshold is over nine times as likely to be having a STEMI as someone with a lower score.

Okay,are we able to get that in terms of percentile probabilities as well? Or are we stuck with odds? Because I always find, I don’t know about you, but I’ve not done much sort of horse betting or anything.

Odds I actually find really difficult to understand.

There’s an interesting relationship between them, and generally they’re often very similar. But as opposed to a, probability, we’re comparing the ratio of positive and negative cases, instead of dividing the total of one, divided by the total.

So it’s a little bit different. So let’s just say, for example, that this patient,is 25 years old, has come in with chest pain. There’s a low probability of a STEMI. We might say that the probability is, let’s say, 5%. Our odds in that case is going to be, different than 5%, which is five out of a hundred. Our odds is 5 to 95 So subtly different. And likelihood ratios work with odds. So we put in the pretest odds, we times it by the likelihood ratio, and it gives us a post-test probability of the patient having the disease. And that’s the crucial thing. And how this becomes practical for us on the shop floor, because the ratio by itself isn’t that helpful.

Okay. So what I don’t get, what always strikes me as a bit odd is why don’t we use positive predictive values in a patient like this? Like, why can’t I just say the test is positive or the calculated score in this case is positive and therefore this is, the likelihood that the patient truly is having an anterior MI.

Why do I need to think about the, the post test odds and things like this?

Yeah, so if we assume that prevalence in this population is the same as in the original study, then we really only need the positive predictive value and the negative predictive value. Where the likelihood ratios really come into their own are when we apply the findings to a population with a different prevalence.

So let’s say our individual patient is much lower risk, than in the original study, we might say you know what I think this patient has only a 5 percent probability of disease, whereas in the original study it was much higher and we can the likelihood ratios are technically independent of prevalence So we can now apply that new pretest odds Times it by the likelihood ratio and come up with a new posttest odds and convert that back to a probability So if our patients got a 5% probability of STEMI originally, with the Smith ECG calculator, if it’s positive, our post test probability goes up to 33%. However, if we’d applied this to a much higher risk patient, let’s say, it’s a 50:50 chance it’s a STEMI. We’re really not sure about this because the patient’s got some classical features, quite persistent pain, but they’re not sweaty.

You know, we’re kind of on the fence about it. And now we’ve got this ECG that appears to be on the fence too. We’ve applied the Smith ECG calculator. It’s positive. So our post test probability, in our opinion, was 50%. Now, the post test probability is going to be 90%. And that’s where this comes into its own.

We can apply it on a case by case basis, using Bayesian reasoning, based on what we think the pre test probability is. for our individual patient.

So just to recap that, you’ve got your first patient who’s low risk, 5 % pretest probability. You’ve applied this calculator to your ECG and now it’s actually given you a patient who’s got roughly a third of a chance of having something really significant on coronary angiography, an occlusive lesion, and that, that’s really going to change your decision making, isn’t it? You’ve gone from somebody you’d likely send home to somebody who you’re now thinking may well need reperfusion or at least need more advanced tests. And if you think about your second example, you’ve got somebody, which is another really common situation, some risk factors, some suggestive symptoms, pretest likelihood, 50: 50, whether it’s a serious, cardiac problem or not, and you’ve applied this test and it swayed you from being on the fence to really confident that this is somebody who needs, either immediate reperfusion or, at least further testing. So that’s really powerful. That’s a really good example of how the test is changing your actual practice with an actual patient. Now you use the term Bayesian. You You might need to explain that one for, some of the people listening.

Yes, very simply Bayesian,reasoning. takes account of the prior probability. So the probability before we applied any tests, that’s our pre test probability. And we know that, when we apply the test, it’s going to change the probability in a fixed way, and we come out with a post test probability.

So, it’s about taking account of prior knowledge when we apply the test. And in this case, that’s deciding whether this patient is low risk or high risk and estimating that probability.

And I suppose that’s the bit that some of our listeners are going to find a bit challenging. How did you come to the 5 % figure for the first patient.

And then how did you upgrade yourself to a 50 percent figure? Because a cynical listener could say that you just plucked that out of thin air, didn’t you?

Yeah, that’s right. And that is one of the limitations of applying this kind of approach. We have to acknowledge that those are estimations and we might not be totally accurate.

So we’re really just getting ballpark figures by doing this. We could have applied an analytical approach and searched the literature to get an idea of what that pretest probability might have been in the individual circumstances. But practically on the shop floor, We’re unlikely to be able to do that.

It’s just giving us a ballpark estimation and enabling us to embrace uncertainty and handle it a lot better, provide more personalized care to our patient.

And emergency medicine inevitably involves uncertainty, decision making and so on, doesn’t it? And I’d be very suspicious of somebody who’s looking up, the sort of odds ratios of their different diagnostic maneuvers and the different tests and so on.

So yeah, that makes sense. So let’s recap. So likelihood ratios compare the probability that a given test result would be expected in a patient with the disease to the probability that same test result would be expected in a patient without the disease. You can calculate them as sensitivity divided by the false positive rate, or one minus specificity, and a higher likelihood ratio signals a more effective diagnostic test.

And if you want to see how useful your diagnostic test is, you multiply your pretest probability of disease, which again, there’s different ways you can come up with that figure, by your positive likelihood ratio to get your post test probability. And the greater the increase between pre and post test probability, the more helpful that test is for making judgements about treatment, admission, and so on.

And it’s fair to say that if your test does not really significantly lead to a difference between your pre test and post test probability, might not be that great a test.

Yeah, absolutely. Great summary there, Greg. And remember, we’ve focused here mainly on positive likelihood ratios. Remember, you can also use the negative likelihood ratio when you’re seeking to rule out a disease as well and you can apply exactly the same principles when you’re handling that. hope this podcast has been helpful for you. Please do leave us any feedback if you have any. Be very helpful for us planning the next ones that we come up with. and, take care from me.

Thank you for listening.