Sensitivity; Specificity; Positive Predictive Value and Negative Predictive Value Video Lecture | Mastering R Programming: For Data Science and Analytics - Database Management

hi I'm Mike Marin and in this video
we'll discuss screening and diagnostic
tests and the relevance of concepts such
as sensitivity specificity positive
predictive value and negative predictive
value in particular we will compare and
contrast screening and diagnostic tests
define sensitivity specificity positive
predictive value and negative predictive
value we'll talk a bit about why we care
about these we'll look at how to
calculate them using two by two tables
and finally we'll talk about when using
a two by two table will lead us to an
incorrect calculation of the positive
predictive value and negative predictive
value screening tests are used exactly
as the name suggests to screen
individuals they are given to
individuals who are not yet
demonstrating any symptoms but are
considered to be at risk the intention
is to identify individuals early on
before they start to show symptoms
diagnostic tests are administered with
the intention of confirming the disease
or confirming that the person does not
have the disease
they are generally given to individuals
who are showing symptoms or who have
tested positive in a screening test
screening tests are intended to identify
early on those who may have the disease
while diagnostic tests are intended to
confirm the presence or absence of the
disease screening tests are administered
on asymptomatic individuals who are at
risk while diagnostic tests are
administered on those who are
symptomatic or those who have tested
positive in a screening test screening
tests tend to be cheaper and
non-invasive while diagnostic tests tend
to be more expensive and often are more
invasive although necessary to confirm
or refute a positive screening result
screening tests tend to have higher
sensitivity and higher false positive
rates so as to not potentially miss out
on an individual with the disease
diagnostic tests should have high
sensitivity as well as high specificity
and yes these are terms that we have not
formally defined yet soon we'll provide
a definition for sensitivity and
specificity a positive test result on a
screening
generally leads to a more invasive
diagnostic test while a positive test
result on a diagnostic test usually
leads to treatment of the disease
screening tests are usually cheap but
the cost should still be justified
while diagnostic tests tend to be more
expensive but are necessary
now some notation and definitions will
use the letter D to indicate the
presence of disease and the letters nd
to indicate not disease will use a plus
sign to indicate a positive test result
and a negative sign to indicate a
negative test result we define the
prevalence as the probability of the
disease or as the percentage of the
population with the disease the
sensitivity is the probability of
getting a positive test result given
that the individual actually has the
disease that is what is the likelihood
of a diseased individual getting a
positive test result in other words how
often will our test correctly diagnose a
diseased individual this also gets
called a true positive the complement of
this is a false negative testing
negative when one actually has the
disease these two should sum up to one
or a hundred percent that is given that
an individual has the disease they will
test positive or they will test negative
the probability of an individual who has
the disease testing positive plus the
probability of an individual has of the
disease testing negative will have to
add to one or a hundred percent the
specificity is the probability of
getting a negative test result given
that the individual does not have the
disease that is it tells us the
likelihood of a non diseased individual
testing negative in other words how
often will our test correctly identify a
non diseased individual as being
negative this also gets called a true
negative and again its complement is a
false positive testing positive when one
actually does not have the disease and
as before these two should sum up to one
or a hundred percent given that an
individual does not have the disease
they will either test positive or
they'll test negative the sensitivity
lets us know
how often we correctly diagnose a
disease individual and the specificity
lets us know how often we correctly
diagnose a non disease individual as not
having the disease
these are nice to know but they don't
tell us the whole story suppose that I
were to be given this test and I got a
positive test result how likely is it
that I actually have the disease the
positive predictive value can help us
with this the positive predictive value
tells us given that an individual has
tested positive how likely is it that
they actually have the disease similarly
the negative predictive value tells us
given that an individual has tested
negative how likely is it that they
actually do not have the disease they
help us know something about how
reliable or how accurate a positive and
negative test result are now consider
developing a screening test our goal is
to be able to classify an individual as
diseased or not diseased before the
onset of any symptoms suppose that the
development of our tests will work as
follows we will take a blood sample and
we will look at the level of something
in the blood let's call it blood level
of a if the blood level of a is high and
above some threshold which we'll call X
we'll screen them as being positive for
the disease
if the blood level of a is low and below
the threshold X we'll screen them as
negative for the disease to repeat that
again a blood level above X means they
test positive for the disease a blood
level below X means they test negative
for the disease after taking these
measurements we'll wait for many years
to pass and we'll examine these same
individuals to see who has developed and
who has not developed the disease of
interest nope that this will help us to
develop a test that can be used to
identify individuals who are likely to
develop the disease before they show any
symptoms also note that this design is
prospective in nature and follows a
cohort of individuals forward in time
suppose that the data ended up looking
as follows 160 confirmed cases of the
disease 1340 confirmed non cases of the
disease we also see that
175 individuals were screened as
positive based on their blood level of a
being greater than that threshold X and
we see that 1325 were screened as
negative out of the 1500 total
individuals now let's use this table to
calculate the sensitivity specificity
positive predictive value and negative
predictive value first we can calculate
the prevalence we can see that we have
1500 total individuals in our sample and
we also see that 160 are confirmed cases
this would lead us to an estimate of 160
out of the 1500 or 10.7%
prevalence we can consider this to be an
unbiased estimate of the population
prevalence as we followed a random
cohort of individuals forward in time
the sensitivity is the probability of
testing positive given that they have
the disease we can see that 160
individuals have the disease and of
those 140 tested positive and so the
sensitivity is 140 out of 160 or 80 7.5%
the specificity is the probability of
testing negative given that they do not
have the disease we can see that 1340
people did not have the disease and of
those 1305 tested negative and so the
specificity is 1305 Oh to the 1340 or
97.4% the positive predictive value is
the probability of having the disease
given that they tested positive for it
we can see that 175 people tested
positive for the disease and out of
those 140 actually developed the disease
and so the positive predictive value is
140 out of 175 or 80% we can think of
this as being an unbiased estimate as
the individuals were followed forward in
time and the development or non
development of the disease was not
manipulated an example where the disease
rate would be controlled or manipulated
is in a case control type study design
the negative predictive value is the
probability of not having the disease
given
they tested negative for it we can see
that 1325 people tested negative and out
of those 1305 did not have the disease
and so the negative predictive value is
one thousand three hundred and five out
of the one thousand three hundred and
twenty-five or 98.5 percent it's
important to note here that we could
fine tune this test by playing around
with that threshold value of x that we
use to screen as positive or negative
for example if we wanted to increase the
sensitivity of this test we could
decrease that threshold value of X
that's used to define a positive test
result in other words we could lower the
blood level of a that is required to get
a positive test result this would lead
to more positive test results in general
more true positives as well as more
false positives increasingly sensitivity
of our test would also lead to
decreasing the specificity of the test
take some time to think about why this
is and reconcile these in your head it's
worth having a short note here that the
use of a two by two table to calculate
positive predictive value and negative
predictive value will not always work if
the data were not collected in a
prospective manner but instead were
collected through a case-control type
design calculation of the positive
predictive value and the negative
predictive value directly from a two by
two table will be biased when the
prevalence of the disease in our sample
does not represent the prevalence of the
disease in the population calculating
PPV and NPV this way will be biased when
the prevalence of a disease is low in a
population we may need to use methods
other than following a cohort over time
instead we may decide to take confirmed
cases and Nan cases of a disease and
administer our screening tests on them
for example we may take 500 confirmed
cases and 500 confirmed non cases and
administer the screening test on them
and see who tests positive and negative
doing this will ensure that we end up
with enough cases in our sample for it
to be useful but it also means that our
proportion of individuals in our sample
with the disease will not be
representative of the population in
to calculate the PPV and the NPV for
such data we would require the use of
Bayes theorem this is a topic that's
beyond the scope of this intro video
although it was important and necessary
to acknowledge and mention this I hope
this video helped you better understand
the concepts of sensitivity specificity
positive predictive value negative
predictive value how they differ and how
they're useful thanks for watching this
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