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 of 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 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 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 as 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 but 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 you'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 so 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 a very 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
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 ok 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 would 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 rates 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 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
do 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 gonna catch every single thief
that's gonna 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 gonna 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 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 now hope this clears things up in terms of
sensitivity and specificity the next lecture is going to talk about the
actual mathematics and 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