Assalamu alaikom, Hey everyone!
Welcome back to our 3rd and final part on our video series on how to evaluate a diagnostic
test It's our time to match our final match: likelihood
ratio Alright.
So, if you lookup its definition, you will probably will be more left because well, it
is a mouthful So, likelihood ratio is the likelihood that
a given test result would be expected in a patient with the target disorder, compared
to the likelihood that the same result would be expected in a patient without the target
disorder.
But, let's say that we have a particular test that detects iron deficiency anemia, and after
all the calculation, don't worry we will go over them soon in this video, we have a positive
likelihood ratio of 20 What does that 20 mean?
Well, that 20 means that this person that just got the positive, is 20 times more likely
to have iron deficiency that someone who does not have the disease.
Remember, we always are comparing to someone who does not have the disease.
If our negative likelihood ratio was 0.1, this means that person that just got the negative,
is 0.1 times likely to develop the disease.
So, this would make intuitive sense, getting a positive obviously ups your chances in getting
the disease, and vice versa, assuming the test sensitivity and
specificity are adequate.
So, with that theory in your mind, how do we calculate it?
What's the formula?
Well, here you are, and you just have to memorize them
But here are two tips to recall them if you are in an exam
1- sensitivity is always in the numerator and specificity is always in the denominator
2- to remember where the "1-" goes, just remember what's on top
If it's positive likelihood ratio, positive on top and the "1-" to the denominator
If it's negative likelihood ratio, negative goes on top, so the "1-" is in the numerator
Alright, with all of this, you should be able to calculate and understand the meaning of
likelihood ratio, but to take it few steps further, we need to have a quick talk about
probabilities and odds.
Let's show an example to understand each of them.
Suppose we toss a coin twice, what is the probabilities of getting two heads in a row?
What are the odds of getting two heads in a row?
And aren't they the same thing?
Well, no! they're distinct, and the best way to highlight that is by writing down all the
different possibilities that we can get.
In other words, our sample space.
So, here's it's gonna be heads heads, heads tails, tails heads, and tails tails.
So, the probability is the chance of getting a particular event when compared to the total
sample space, i.e., the denominator does include 2 heads in a row.
So, it should be 1/4.
But odds shows the likelihood of getting a particular event to happen when compared to
all other events, i.e., the denominator does not include 2 heads in a row.
So, it should be 1/3 But 1/3 is so awkward to say
and that's why I left this little note down here: we usually keep the numbers x/1 we want
this form of x:1, and x represents our odds, so 1/3:1 is the exact same as 1/3, we just
prefer to keep things :1.
Alright, so they do have a link between them, and here's how we can convert one to another.
So, for odds to probability: you can take the odds and put it over (1+odds) and now
you get the probability.
For probability to odds: you just take the probability, and put it over (1-probability),
and that way you gonna get the odds Alright, now let's put all of this together
to understand how they fit into likelihood ratio
So, let's take a really long example, and hopefully this will cement everything!
[Example shown on screen] So, this 10% it's going our prevalence,
now pretest probability is always going to equal prevalence, unless if there's any risk
factors or symptoms, because risk factors and symptoms up your pretest probability.
In this case just to keep it simple, our pretest probability is exactly equal to our prevalence.
Alright, so let's go over some calculations: Our LR+: SN/(1-SP)
SN: 80% = 0.80/0.05 = 16
What does this 16 mean, well it means if someone got a positive, he's 16 more likely to develop
the disease compared to someone who did not develop the disease.
What about our negative LR?
Well, it's going to be 1-sensitivity So the opposite of our 80%, which is going
to be 20%, 0.2 in this case over specificity, which is
in this case 95% and it's gonna be 0.95, yielding us a final
result of 0.211 Our pre-test odds, is the same as pretest
probability, you just have to convert it to odds
So it's gonna be 0.2/1-pretest probability 0.2/0.8 = 0.25
Now we can find post test odds, by multiplying the positive/negative LR to our pre-test odds
So our + pretest odds: 0.25 x 16 = 4 and this 4 means 4:1
Now we can convert this + post test odds to something that is easier and more palatable
for us to understand, which is + post test probability
We just take that odds 4 / 4+1 = 80% Final positive post test probability = 80%
And we can do the exact opposite with negative post test odds, is just we take the pretest
odds, 0.25 x 0.211 = 0.0527 Convert by taking that odds over 1+those odds
= 0.05 which is 5% So what does this 80% + post test probability
mean? and what does 5% post test probability mean
For + post test probability, they went from 20% to 80%
for - post test probability they we down, down from 20% to 5%, so they reduced their
chance of developing the disease.
So this is a pretty good test!
It's fairly important to mention, most tests for them to be considered pretty good, their
+LR has to be > 10 and - LR <0.1
Now ideally you'll be really good for them to satisfy those criteria, but if it's either
it still indicates a pretty good diagnostic test.
By now, you guys should be the masters of LR
But to give you the PhD, let's have a look at the diagram we call "LR Nomogram"
Remember all that calculations we did in the previous slide?
Well, this Nomogram eliminates any need for odds
Just plot your points based on pretest probability and + and - LR, then connect the pretest probability
for each LR's using lines And you'll get the same exact post test probability
So, let's apply our example: recall that + LR = 16
so that's gonna be right about here - LR = 0.211
and that's gonna be right here Our pre test probability was 20%
and that's gonna be right here Now if you plot these lines, you're gonna
see that we're going to get the same exact + and - post test probabilities of 80% and
5%, respectively.
Now, recall from our last video, that prevalence, aka pretest probability in this case, is directly
proportional to positive predictive value (PPV), but inversely proportional to negative
predictive value (NPV).
Moreover, sensitivity and specificity are stable and are never affected by prevalence.
So since LR is calculated using based on Sn and Sp, it makes since that it (LR) too is
stable measurement, and it's not affected by prevalence
But the reason I wanted to give this, is that we can tie in the PPV and the NPV yet again
Notice on the Nomogram, with and given + LR, a decreasing pretest probability corresponds
to a decrease in post test probability Moreover, if you make a 2x2 table and calculate
PPV and NPV in this example, you're gonna find that the PPV is exactly to our + post
test probability The NPV should be the exact opposite to our
- post test probability And this just further cements the idea, of
how prevalence just affects PPV and NPV, and does not affect Sn and Sp
Because as we move points on our pretest probability, we can move points on our post test probability,
but the points in the middle, never, ever, ever change
And with that, we hope you benefited from our 3-part video series on How to Evaluate
a Diagnostic Test!
Consider liking and subscribing.
And as always, thanks for watching!