okay so welcome to another MedCram lecture we're going to talk about what
may be considered a dry subject but I think it's actually very important it's
the topic of sensitivity and specificity in relation to statistics now sometimes
we see this appear on test and we've got to know what sensitivity and specificity
means I think it's also very helpful in interpreting some of the data that we
see in medical journals and it's actually very helpful in our everyday
life in terms of understanding the test that we're ordering on patients so I
think it deserves a little bit of a an introduction and an analysis and how to
actually do the questions that you need to do for tests so imagine if you will
with me that you've got a nice car and you want to protect your car so you
install a car alarm okay he's got a little blinking light there and you've
got a knob in that car that allows you to change the sensitivity on that car
alarm well you've got a couple of choices you can either have the
sensitivity high and what does that mean that means that well if a thief tries to
break in the car alarm is probably going to go off but it also means that since
you're parked on a on a busy street if a motorcycle goes by that could also set
it off so if you have a thief and the car alarm went off then that would be a
true positive result you would hear that car alarm go off and sure enough there's
a thief trying to break into your car that would be a true positive so the
disease here is is your car being broken into or is it not being broken into and
the test is is the car alarm going off or is the car alarm not going off and
you can actually break this up into a square and have the four possibility so
you could in terms of our disease you could have a positive disease or
negative disease and in terms of a test you can either have the alarm going off
or the alarm not going off so in this box here this would be if there was a
thief trying to steal your car and the car alarm was going off that would be a
true positive okay if there wasn't a thief trying to steal your car but your
car alarm went off that would be a false positive that would be like a motorcycle
going by or somebody touching the car as it as it went by and the car alarm goes
off you go out there the alarms going off that no one's tried to break in and
obviously that's not an optimal result you don't want to have false positives
because every single time the alarm goes off you've got to go out there I've got
to check the car you got to make sure no one's getting into it
also the more times this car alarm goes off the less likely you are of taking it
seriously so not good the other possibility is which is also
not a good possibility is that your car is being broken into but the alarm
doesn't go off that would be a false negative that's probably the worst
result that you could have you go out to your parking lot the car's gone okay the
alarm never went off it didn't disengage the engine that's a problem and then
finally the thing that happens you know all the time is a true negative
car alarm is not going off and your car is not being broken into that's that's a
good result so we like true positives we like true negatives we want to minimize
these as much as possible and you can see how that would happen
depending on how you sent the sensitivity of your car alarm if you
sent the sensitivity of the car alarm up very high what you would see is you
would start to have a lot of these false positives but the chances of having
false negatives would go down okay conversely if you set the sensitivity of
your car alarm very low you probably wouldn't be getting motorcycles setting
off the car alarm but on the other hand it might be easier for a thief to break
into your car and to steal it without the car alarm going off so the point
here is I want to show you that there's a trade-off in terms of where you set
the sensitivity for a test it's very important because depending on where you
set the sensitivity for a test you're either going to get more false positives
or false negatives and depending on what you're testing for and what kind of
situation you're in you know you may want to set the sensitivity of that
alarm to different areas for instance if you're living in it
high-crime area where you know cars are getting stolen every day and there's not
a lot of motorcycles sure set that sensitivity up pretty high
if on the other hand you're parking your car in the area where there's not a lot
of thieves and and there's really been no reported thieves but there's a lot of
motorcycles going by you may want to set that sensitivity low so it just sort of
depends on where you're living and the same thing applies to medicine now we're
going to talk a little bit about these false positive true positives false
negatives in this box a little bit but I wanted to introduce to you the concept
of what sensitivity is and what specificity is sensitivity
mathematically speaking okay is the true positives divided by the true positives
plus the false negatives and you can see here that sensitivity is the true
positives divided by the true positives plus the false negatives and so the
sensitivity as you can see mathematically will be very high if the
false negative rate was very low in fact if something is very sensitive and it's
negative you can practically rule out that disease okay on the flip side
specificity which takes of this column specificity is the true negative rate
down here divided by the true negative plus the false positive and clearly you
can see there that if the specificity is very high this false positive has to be
very low and so if something is very specific and it's positive the chances
of it being falsely positive are extremely low we'll get into that more
another way they'll sometimes test you is they'll look at all of the different
populations of things okay so this is what we're dealing with if we can go
back to the car example here is a population of all the things that could
falsely set off an alarm and here is the population of things
that could truly set off alarm so this is what thieves could do okay and so
what we're trying to do is we're trying to devise a test that would separate
these things out so what I mean to say here is that this would be the disease
negative state okay so this is the disease here is your car being stolen
and here this is all the stuff that could set off a car alarm but it's not
really your car being stolen so this would be like motorcycles boomboxes
things of that nature and this is all of the things that thieves could do to
steal your car so this would be the disease positive state the problem here
is that there's some overlap and so no matter where you set your threshold for
your sensitivity you're going to have a problem in that you're going to be
including one or the other so there's there's a couple of areas here where you
could set the sensitivity you could set the sensitivity right here at point a
you could set the sensitivity here at point B or you could set the sensitivity
here at Point C or any of these points and now I want you to notice here what
what's going on so if we were to set set it here then everything to the right
would be positive and everything to the left would be negative everything to the
right of B would be positive to the left would be negative everything to the
right of C would be positive and to the left to C would be negative so the
question is and this is the question that you'll sometimes get on tests is
which of the following points represents the most sensitive test and which of the
following points represents the most specific test so specificity is the
opposite of sensitivity in this case so of course if you are anything that is on
the right side of a test is going to be a positive test anything that is on the
left side of this point is going to be a negative test depending on which
population they belong to will tell you whether it's a true or a false negative
or positive let's take for example this point here at C okay so here at C if we
were to set the alarm at C in terms of specificity and sensitivity then all of
this area right here would be a positive now because it
belongs to the actual disease it would be a true positive but all of this back
here would be a negative now some of these would be false negatives because
they still belong to the disease but then some of these would be true
negatives because they don't belong to the disease and so what you notice here
is that if something is positive it is definitely part of the disease but
you're missing out on a lot of falsely negative but notice here that we've
moved this C all the way out here so that there is no more false positives if
you have a very low false positive rate that means you're very specific okay
just for review remember that the sensitivity is the true positive rate
through positive rate divided by the true positive rate plus the false
negative rate and the specificity is the true negative rate divided by the true
negative rate plus the false positive false positive rate so because of that
if we were to look at this point here a notice what we have here at a at a there
is no more false negatives and because there is no false negatives negative
would be on this side of the line okay so negative there are no disease or
robbers of the car if you will that are showing up on this line because we've
moved it so far to this side so this is the most sensitive setting that we could
set it to so imagine that imagine this in terms of our car if we turn the
sensitivity of the car alarm up very very high we're going to catch every
single thief that's going to try to steal our car which is represented by
this curve but we're also going to catch a lot of false positives here which
represent motorcycles and you know very loud cars or loudspeakers that are
driving by on the converse if we set a very specific test at right
here notice here that we're no longer going to pick up it'll be negative now
because negative is to the left of the line all of these things that could make
the car alarm go off will be treated appropriately as a true negative but
we've made it so specific now for the car alarm to go off that there's things
that thieves can do to break into your car okay so so long as you set this up
with the negative disease on the left and the positive disease on the right
always remember that this direction is the most sensitive and this direction is
the most specific which actually is going to help us later that to remember
that sensitivity is on the left and specificity is on the right
I hope this clears things up in terms of sensitivity and specificity the next
lecture is going to talk about the actual mathematics in this lecture I
want to talk about concepts let's talk next about the actual mathematics and
how to calculate things so you can calculate things quickly on it test
exams thanks for joining us
you