Hi, Terry Shainefeld here from UAB School of Medicine. In this video we're going to discuss how we use likelihood ratios in choosing a diagnostic test and in determining post-test probability. So likelihood ratios express how many times more or less likely a test result is to be found in people that are diseased compared to people that are not diseased.
And the likelihood ratio is a ratio, so it has a numerator and a denominator, and it's a ratio of probabilities. In the numerator is the probability an individual with the condition has a given test result divided by the probability of the individual without the condition having that same test result. And as we'll see in a minute, it's a measure that incorporates both sensitivity and specificity into a single number.
So there are two likelihood ratios. There's positive likelihood ratios and negative likelihood ratios. A positive likelihood ratio is used when the test result is positive.
and it's the probability of a positive test in persons with disease divided by the probability of a positive test in persons without disease and we've seen this probability of a positive test in people with disease before that's called sensitivity so sensitivity is in the numerator of a positive likelihood ratio and one minus specificity is in the denominator now the higher the positive likelihood ratio the greater will be that test in increasing our post-test probability. So if you want to rule in disease and you have multiple tests that you can choose you want to choose the one with the largest positive likelihood ratio because it'll change the post-test probability of disease the most as we'll see in a couple slides. Now a negative likelihood ratio is used when the test result is negative and it's the probability of a negative test in persons with disease divided by the probability of a negative test in persons without disease. Now we've seen this denominator before, the probability of a negative test in people without disease. That's specificity.
And the numerator of a negative likelihood ratio is 1 minus sensitivity. And if we want to rule out disease, if we need to reduce our probability as much as possible and we have multiple tests, we want to pick the test that has the smallest negative likelihood ratio. That will reduce our post-test probability the most.
So there are two things we can use likelihood ratios for. One is upfront to choose a diagnostic test and number two to calculate post-test probability. So let's talk about choosing a diagnostic test. This is a table from a study that looked at a variety of lab tests to try to figure out how good they were at determining if a child had infection.
In this particular example, there are three different tests that were looked at, C-reactive protein, procalcitonin, and white blood cell counts. And this slide demonstrates, or this table demonstrates, two important components about likelihood ratios. The first is that every test has both a positive and a negative likelihood ratio.
So all tests have positive and negative likelihood ratios. And I'm going to talk about the second point after we answer two questions. So I want you to look at this table and figure out which test should you choose if you want to rule in the infection.
And which test should you choose if you're trying to rule out infection? And we'll pause the video for a minute and let you think about that and then restart it and see what my answer is. So which one did you choose to rule in infection?
Well, to rule in infection, we want to choose the test that has the highest positive likelihood ratio. So procalcitonin has the highest positive likelihood ratio and will increase our post-test probability the most. So if our role... After we determine pretest probability was to rule in an infection, we should choose procalcitonin if we're only going to do one test.
To rule out infection, we want to choose the test that has the lowest negative likelihood ratio, and that's the C-reactive protein. So if we determine our pretest probability was low and our goal was to rule out infection and we could only choose one of these tests, we should choose the C-reactive protein. Now, the second point that this table shows is that different tests often have different roles. So you can see here to rule in our best test is going to be procalcitonin, but to rule out C-reactive protein was going to be our best test. So it's uncommon to find one test that is both great at ruling in and ruling out disease.
You often have this trade-off where one test is better to rule in, one test is better to rule out, and that's why it's really important to determine the role of testing in your patient. Just like we talked about previously with sensitivity and specificity, we use sensitive tests. to rule out disease we use specific tests to rule in disease same thing here for trying to rule in and rule out we're going to choose a different test based on their likelihood ratios now the second thing that likelihood ratios are good for is deter Determining post-test probability.
So let's focus over here on the left. This is Fagan's nomogram. And Fagan's nomogram is sort of a paper-based version of determined post-test probability.
So it has three components. It has the pre-test probability on this axis. In the middle, you have your likelihood ratio. And if your test is positive, you use this upper part of the Fagan's nomogram.
If your test result is negative, you use the lower part. And then over here on the far right axis is the post-test probability. Now this next This window, B here, shows that this patient started out with about a 20% pretest probability. And the way you use Fagan's Nomogram is you put a dot here on your pretest probability, you put a dot at the likelihood ratio, you draw a straight line through these connecting over to the far axis, and where your line hits the far axis is your post-test probability. So this is an example of a positive test.
You go from about 20% probability with this test when it's positive up to about 80%. You expect that. The test should increase probability. This C window shows a negative test.
You start out with about the same probability. Your test is negative. You lower your probability from 20% to 2%. And finally, this last window shows the same pretest probability, but two different tests. And one test is much better at ruling in disease than the other test.
It takes it from 20% up to about 96% or from 20% to about 70%. So you can see different tests affect your probability. your post-test probability depending on how good the test is how sensitive and specific it is now if you were to use a EBM calculator to determine post-test probability what it does is actually uses likelihood ratios and multiplies the likelihood ratio whether it's positive or negative by the pretest odds and multiplying pretest odds by your likelihood ratio results in the post-test odds now you can't use probabilities here you have to convert probabilities to odds And the way you do that is using this formula right here, that in odds is the probability divided by 1 minus the probability. And when you run this formula and you get your post-test odds, you now have to convert this odds back to probability, and you would do it using this formula down here, that probability is odds over 1 plus odds. Now, most people aren't going to do this sort of calculation, trying to remember the relationship between odds and probabilities, but this is how an online calculator or a calculator in an app would do it.
It uses a likelihood ratio and multiplies it by the odds. Now, Steven McGee developed a little way to try to estimate the change in probability based on the result of the likelihood ratio. And so that's what this table tries to show. Now an important thing is that likelihood ratio of 1 doesn't change probability at all. So with tests which have likelihood ratios close to 1 are useless tests.
They don't change your post-test probability. And the reason is, if you remember, a likelihood ratio is a ratio. And a ratio of 1 means the numerator and the denominator are exactly the same. So what that means is your test result is just as likely to be seen in somebody who's diseased or not diseased and that's a useless test. And so one thing that this demonstrates is that positive likelihood ratios increase probability, negative likelihood ratios reduce probability.
So remember that. And that makes sense. A negative test should reduce the probability, a positive test should increase the probability.
Now let's focus on the top part here first. And in McGee's estimation. Each change in your likelihood ratio increased probability by 15%.
So when you went from a likelihood ratio of 1 to a likelihood ratio of 2, the probability went up by 15%. So if you start out with let's say a 10% pretest probability, you had a positive test and that test likelihood ratio is 2, you went from 10% now plus 15 equals 25%. So remember the likelihood ratios of 2, 5, and 10. Each one increases from the previous one by 15%.
And you can see that if you had a pretty good diagnostic test that has a likelihood ratio of 10, your pretest probability goes up by a total of 45%. Now, to remember these numbers at the bottom, if you take 1 divided by 2, you get 0.5. If you take 1 divided by 5, you get 0.2.
If you take 1 divided by 10, you get 0.1. So that's an easier way to try to remember the lower part of this table. And each decrement... Our lowering of the likelihood ratio reduces your pre-test probability by 15%. So I think one of the things you can take away from this is the greatest changes in probability are with the highest likelihood ratios, especially 10 or greater really increase your post-test probability.
And likelihood ratios of 0.1 or less really reduce your post-test probability. So again, you want to Pick tests when you have multiple-level tests that have the highest positive likelihood ratios if you want to rule in disease, and ones that have the absolute lowest negative likelihood ratios if you want to rule out disease. I hope this video has helped you understand more about likelihood ratios.
Remember, if you have any questions, you can contact me through the course website or through the Contact Me section of my blog. Have a great day.