00:01
Keep in mind now that at any given time, everybody
has a non zero probability of having a certain
disease. Think about the pregnancy example,
if you are a heterosexual sexually active
women of reproductive age, there is a non zero
chance you're probably pregnant. When you
take the pregnancy test, we change that probability
because the results of the test give us a
bit more wisdom about how likely it is that
you're probably pregnant or not pregnant.
00:30
In other words we're trying to measure the
likelihood that you're pregnant and that brings
up a whole new measurement, called the likelihood
ratio. The likelihood ratio tells us how much
additional information or wisdom a result
from a pregnancy test gives us, or screening
test gives us relative to not having taken
that test, keeping in mind there is always
going to be a baseline amount of risk. So
a likelihood ratio is a ratio, hence the name,
the thing about ratios is they are symmetrical
about the number one. If the ratio is one,
nothing is going on, if it's more than one,
we know that the test result is associated
with the presence of a disease. On the other
hand, it's less than one, it's associated
with the absence of a disease. So again, everything
is symmetrical around one, that's what ratios
are all about. So a high likelihood ratio
or LR+ or positive likelihood ratio, tells
us there's a strong suspicion that a positive
result from our test means the person has
the disease. On the other hand, a low, negative
likelihood ratio or LR- tells us we have a
strong suspicion that a negative test result
means that a person doesn't have a disease,
a lot of information there. I've told you
about the positive likelihood ratio and the negative
likelihood ratio. In reality we tend to only
compute the positive likelihood ratio.
01:49
So if you read about likelihood ratios, or LRs,
usually the person doing the writing was talking
about the positive case, very rarely have
I ever seen a negative likelihood ratio used
in real life, but I'm going to show you how
compute it anyway and we're going to interpret it
together. So likelihood ratios tell us how
much we should shift our suspicion of a particular
test result, or as a result of a test result.
We always have some suspicion that an individual
has a disease or not, the test result gives
us more information that allows us to shift
that suspicion one way or the other. So the
LR+, the positive likelihood ratio tells us
how much to increase our suspicion if they
have the disease if the test is positive.
02:34
The LR- or negative likelihood ratio tells
us how much to decrease our suspicion if the
test is negative. The LR+ is given by the
probability of true positives, remember what
that means, the people who test positive who
actually are positive, divided by the probability
of false positives. Remember what that means,
false positives are people who test positive,
but aren't positive. So in other words the
LR+ or positive likelihood ratio is a probability
of a positive test result for a person who
really has a disease divided by the probability
of a positive test result for someone who
doesn't really have the disease. It's a lot
of words, it's easier if you look up the contingency
table and work it out visually, at least I
find it that way. Trust me when I say when
you mess around with the variables and the
arithmetic, the LR+ can be given as a function
of sensitivity and specificity, specifically,
no pun intended, sensitivity divided by one
minus the specificity. Similarly the LR- or
the negative likelihood ratio is the probability
of false negatives divided by the probability
of true negatives. In other words, the probability
of a negative test result for a person who
really has the disease divided by the probability
of a negative test result for someone who
doesn't really have the disease. Again I understand
if it is confusing, but when we do an example,
it'll be clearer. And again, much like the LR+,
we can re-express the likelihood ratio as
a function of sensitivity and specificity.
The LR- is essentially one minus the sensitivity,
all divided by the specificity.
04:15
So back to our contingency table, we can use
the same table to compute likelihood ratio.
04:22
We have our true positives, our false positives,
our false negatives and our true negatives.
04:26
The LR+ given by the probability of true positives
divided by false positives. And as I mentioned
that can be expressed as a function of sensitivity
and specificity. So back to our example of
pregnant women. How much more likely is a
pregnant woman to test positive than a non-pregnant
woman? That is a question of likelihood ratio.
Our sensitivity remember, was 0, our specificity
was 0, our LR+ is given as a function of
sensitivity and specificity and we compute
it to be 12.329. Similarly our negative likelihood
ratio gives us a number of 0.108. How do we
interpret these numbers? It tells us that
there is a 12 fold greater likelihood that
a woman who tests positive truly is pregnant.
So anything over 10 is pretty extreme, some
people like to say five is the cutoff, that
tells us the test is useful, a positive test
result gives me some very useful information
that I can use in my clinical practice. Similarly
my LR- of 0.1 tells me that a negative test
result reduces the odds of being pregnant
by 90%. Again we tend not to use the negative
likely ratio, usually we're using just the
positive one and we tend to call it just the
likelihood ratio.
05:46
So let's go over our take home messages. Sensitivity
tells us how well a test can detect whether
a diseased person truly is diseased. Specificity,
similar, but in the reverse, it tells us how
well a test can detect whether or not a non-diseased
person truly is non-diseased. The positive
predictive value tells us how much confidence
to put into a test positive result, in other
words how precise is the test. And the NPV
or negative value tells us the opposite, how
much confidence to put into a test negative
result. Likelihood ratios tell us how much
to shift our suspicion of disease given the
test result. So the positive likelihood ratio
tells us how much more likely a person with
the disease is to have it positive test result,
whereas a negative likelihood tells us how
much more likely a person without the disease
is to have a negative test result.