Welcome back to another instalment of our Critical Appraisal Nugget series with Rick Body and Greg Yates here at St Emlyn’s. In our previous podcast, we delved into the concepts of sensitivity and specificity, laying a strong foundation for understanding diagnostic tests. Today, we’re building on that knowledge by exploring positive predictive value (PPV) and negative predictive value (NPV).
Listening time – 11:16
Revisiting sensitivity and specificity
Before we dive into positive and negative predictive values, let’s briefly revisit sensitivity and specificity. Sensitivity is the ability of a test to correctly identify those with the disease (true positives), while specificity is the ability of a test to correctly identify those without the disease (true negatives). Both metrics are intrinsic properties of the test, meaning they don’t change regardless of the prevalence of the disease in the population.
Positive predictive value (PPV)
Positive Predictive Value (PPV) is the probability that a person has the disease given that they have tested positive. It answers the question, “If the test result is positive, what are the chances that the patient actually has the disease?” We can calculate the PPV as follows: true positives / (true positives + false positives)
Negative predictive value (NPV)
Negative Predictive Value (NPV) is subtly different: it is the probability that a person does not have the disease given that they have tested negative. It answers the question, “If the test result is negative, what are the chances that the patient does not have the disease?” We can calculate the NPV as follows: true negatives / (true negatives + false negatives)
The importance of prevalence
One of the key differences between sensitivity/specificity and PPV/NPV is that positive and negative predictive values are heavily influenced by the prevalence of the disease in the population being tested. As prevalence increases, PPV increases and NPV decreases, and vice versa. This dependency on prevalence makes PPV and NPV highly relevant in clinical practice, where the pre-test probability (or prevalence) can vary significantly across different populations and settings. However, it also gives us reason for caution: if the prevalence is very low then we would expect to see a high NPV even if the test is not very good. That being so, while the NPV and PPV help to give us a practical idea of the post-test probability of disease in a given cohort, we also need to interpret them alongside the sensitivity and specificity, which are less dependent on prevalence and more dependent on the ability of the diagnostic test to differentiate between those who have the disease (or condition) and those who don’t.
Practical Example
Let’s consider a diagnostic test for a disease with a prevalence of 10% in a given population. Suppose the test has a sensitivity of 90% and a specificity of 90%. The 2×2 table below illustrates this:
| Disease present | Disease absent | |
| Test positive | 90 | 90 |
| Test negative | 10 | 810 |
In this example, the PPV is equal to 90 / (90 + 90) = 50%. The NPV is equal to 810 / (10 + 810) = 98.8%. So we have a pretty good rule-out test but not such a good rule-in test. Let’s now change the prevalence to 70% – a really high-risk cohort – but let’s keep the sensitivity and specificity of the test the same, at 90% each. Let’s see how the 2×2 table looks:
| Disease present (n=100) | Disease absent (n=42) | |
| Test positive | 90 | 4 |
| Test negative | 10 | 38 |
From this table, you can work out that the sensitivity and specificity are still both equal to 90% – so the test is working just as well. However, the PPV and NPV have changed drastically. The PPV = 90 / (90 + 4) = 95.7%, whereas the NPV = 38 / (10 + 38) = 79.2%. Suddenly, we have a pretty good rule-in test but not such a good rule-out test! So, you can see why we need to take account of both sensitivity and specificity, and the PPV and NPV.
Why PPV and NPV matter
In clinical practice, PPV and NPV are crucial because they provide direct information about the test’s performance in a real-world setting. They help clinicians make more informed decisions about patient care based on the likelihood of disease presence or absence after testing.
Summary
Understanding PPV and NPV is a really important skill for emergency physicians, whether it be for critical appraisal of a paper to decide if you should use a new test in practice, to guide your own research or to inform your daily practice as you apply diagnostic tests in everyday patient care. Remember to consider the prevalence of disease when interpreting PPV and NPV, and be sure to also look at the sensitivity and specificity too. While the PPV and NPV give us a practical idea of the post-test probability of disease, the sensitivity and specificity will also help to reassure us that the test is doing something more than just rolling a dice! We hope you find this CAN podcast helpful. Stay tuned for more critical appraisal nuggets at St Emlyn’s.
Podcast Transcript
Hello and welcome to the St. Emlyn’s podcast. I’m Rick Body. And I’m Greg Yates. It’s been a little while since we did our last critical appraisal nugget podcast, but here we are going to talk about positive predictive value and negative predictive value. This continues the theme of diagnostic test accuracy. If you remember, last time we talked about sensitivity and specificity. Now, these two concepts, positive and negative predictive value, are related to sensitivity and specificity, but they’re different in an important way. It’s really vital that if you’re preparing for exams or if you’re just thinking about how you can best apply diagnostic tests in your practice, these are really important concepts to get your head around.
Positive predictive value and negative predictive value are arguably a more clinically helpful way of thinking about what our different tests can do. Although, as we’re going to talk about today, there are probably some caveats to that statement. So, Rick, what do we actually mean when we say positive predictive value and negative predictive value?
By positive predictive value, we are asking what is the probability that a patient with a positive test actually has the condition that we’re trying to diagnose? A negative predictive value is looking at the probability that a patient with a negative test doesn’t have the disease. If that’s not already boggled, it might be helpful to think about a clinical example. So, last time we did one of these critical appraisal nuggets, we thought about border force officer Rick Body. Now this time, it’s going to be ward cover FYI Rick Body.
So, cast your mind back into the past. You’re covering the wards at night. It’s midnight. You’ve just prescribed your 19th bag of maintenance dextrose and you’re fed up. Your bleep has gone off again and it’s the vascular ward calling. They want you to come and see a patient there who’s just developed some chest pain. Very helpfully, the nurses have already done an ECG and they’ve sent off a series of blood tests, including a high-sensitivity troponin. So far, so good. Unfortunately, before you can see this patient, you get caught up with a cardiac arrest. Sorting that out and documenting everything that happened takes a long while, as it does. By the time you finish and finally get to the vascular ward, most of those blood tests have come back.
This patient with chest pain has had their blood test resulted and the high-sensitivity troponin is positive. So, what’s going through your mind right now? You’ve got a positive troponin, chest pain, vascular ward. Okay, so, I mean, clearly, I’m going to want to know the clinical context of this particular patient as we always should. And then having got that, I’m going to want to know what’s the probability that a patient with a positive troponin is actually having a heart attack. That’s what I’m trying to diagnose here. The troponin isn’t the diagnosis. The diagnosis I’m trying to make is a myocardial infarction. I know that troponin will be perfect, but I want to know that probability because it’s going to affect what I do. I will want to prescribe some treatments for the patient that are having a myocardial infarction, which might include aspirin or other antiplatelet medications. I want to get the cardiologists involved. But I don’t want to do that if the patient is unlikely to be having a myocardial infarction. So, it’s really important now to know that probability.
And I’d add to that, even a negative test is very helpful, isn’t it? Because you might consider an alternate diagnosis. You might think about where you could best spend your time with another patient, for example. So, there’s lots of value to knowing how likely a negative test is to reflect somebody who doesn’t have the disease.
Exactly. And had the test been negative, I’d similarly want to know, well, what’s the chance now that the patient’s got a myocardial infarction? Because I have to appreciate not all tests are black and white. It’s not going to be a 0% chance of a myocardial infarction. So, I want to know what’s the chance of missing that diagnosis. What you’ve basically described there are the two facts, or best attempt at the facts, that we get from positive and negative predictive values. Positive predictive value, as a sort of recap, is going to tell us the proportion of people with a positive test result who truly have the disease.
So, applying to ward cover Rick, it’s if I have a troponin that’s come back elevated, what percentage of patients with this elevated result are actually having a heart attack? Now, if that troponin had come back negative, again, our question would be about negative predictive value. If I have a troponin that has come back normal, what percentage of patients with this result are truly disease-free, i.e., not having a heart attack? You can see how at least a rough understanding of the positive and negative predictive values of your diagnostic tests can be pretty helpful in practice, particularly if you’re a junior doctor and you’re still getting to grips with these tests.
So, I can assume positive predictive value, negative predictive value, perfect statistics, why would we ever use anything else? Podcast is over.
It would be tempting to think that’s really all we need to know when we are treating patients, positive and negative predictive value, because that’s the practical knowledge we need. You then might ask, well, why did I need to listen to your last podcast about sensitivity and specificity? Because actually, it only matters to me if I know whether the patient’s got the disease. On the ward, when I’m seeing a patient, I don’t actually know. I don’t know the test results. So, the PPV and NPV are the ones that are most meaningful for me. However, there is a really important caveat on this. You need both, and the reason you need both sensitivity and specificity and positive and negative predictive values is because the positive and negative predictive values are heavily affected by the prevalence of the condition that we’re trying to diagnose. If we have a really rare condition, let’s say only one percent of the patients we’re testing have the condition, the positive predictive value is going to tend to be lower.
So, our test is basically going to shift that probability up if it’s positive in a sort of fixed proportion. The higher the prevalence, the higher the positive predictive value; the lower the prevalence, the lower the positive predictive value. And that works the same for negative predictive values too. So, if you have a high prevalence, you tend to find it difficult to get a low negative predictive value. And if you start with a low prevalence, you can achieve a high negative predictive value quite easily, even with a test that isn’t doing any work. It might be a useless test of very poor sensitivity, but you still get a high negative predictive value because the prevalence of the condition is so low. So, we need to know both sensitivity, specificity, and positive and negative predictive values to make sense of how good a test is.
Okay, so that’s disappointing. So, they’re not perfect statistics. We actually still need to think. When we get a test result back and we’re thinking about our NPV and our PPV, we actually need to think, okay, these statistics have been calibrated to a particular population with a particular prevalence. We need to think about the risk profile of the patient in front of us. If we’re in an environment where that disease that we’re trying to test for is very prevalent, that’s going to affect our PPV and NPV. Whereas, if it’s not very prevalent, that’s also going to affect our PPV and NPV. Is there anything else that we actually need to think about when it comes to these statistics?
Yeah, a couple of things. Just give you a couple of practical examples about how we might interpret these values in practice. Let’s imagine that we’re trying to diagnose a myocardial infarction now, but we want to diagnose it in everybody who attends the emergency department, no matter what they’re coming with. It might be a stubbed toe, but we’re interested in making that diagnosis. Now, imagine that the test we are applying is actually useless. It doesn’t detect anyone with a myocardial infarction. Its sensitivity is zero percent. But we’re going to apply this in a population where the prevalence of myocardial infarction is really low because we’ve got so many people with other conditions. The negative predictive value of that test, which has zero percent sensitivity, could be really high, like 99.99 percent potentially, if we’ve got a population without many myocardial infarctions in there. It would sound like a really good test, which is actually perfectly useless as a test. So, that’s why we need to know both.
Let’s give you one more example to turn things around and show how we need both concepts. Let’s think about the ECG. Think about looking for an ST depression on an ECG. Now, ST depression is quite a specific change for myocardial infarction in someone with chest pain. The specificity might be, let’s say, 95 percent. Sounds really high. Now, from the last podcast, you’ll remember, snuff it out and spin it in. So, high sensitivity is what we need to rule out a condition, high specificity is what we need to rule in. With a specificity as high as 95 percent, you’d think, ah, I’ve ruled in a myocardial infarction. Sounds great, actually, doesn’t it? But if the prevalence is low, let’s say we have only five percent or ten percent of the people with a myocardial infarction, the positive predictive value could be as low as 20 percent, even with that high specificity. So, we absolutely need to know both. I hope we’ve hammered that home enough. Do you think we have?
I think we probably have hammered that home to death. You need to know the prevalence of the actual disease in the group of patients that you’re seeing to correctly use these statistics. Let’s maybe finish with one final tip. Negative predictive value, the probability of the patient not having the condition if they have a negative test. A bit complicated, right? Yeah. Let’s think about when you see a negative predictive value, do 100 minus the negative predictive value. So, instead of, let’s say you see a negative predictive value of 99 percent, turn that round to one percent. That’s the probability of having the disease if you have a negative test. That’s much more meaningful for us. It’s the post-test probability.
Okay, that makes sense. So, to wrap up then, quick recaps. Positive predictive value is the likelihood that if you have a positive test, you’re actually going to encounter a patient who has the disease. Whereas the negative predictive value is when you have a negative test, what’s the percentage likelihood of a patient who truly doesn’t have the disease? Think about the prevalence of the disease and how that affects these statistics. Still think about your sensitivity and specificity, and think about the population that the test was calibrated in.
“Sensitivity is the ability of a test to correctly identify those with the disease (true positives), while specificity is the ability of a test to correctly identify those without the disease (true negatives).”
Should these definitions be reversed?
Actually, that’s exactly right! You might wonder how that fits with SpIN (specificity rules in) and SnOUT (sensitivity rules out), when sensitivity is about patients *with* disease. The point is that if a test accurately identifies almost everyone *with* the disease then there are very few false negatives – patients who will be missed. And if we achieve that (a high sensitivity), then we often say it’s a ‘rule-out’. So the definitions are correct, even though it might seem counter-intuitive at first.