00:00
Now let's talk about
relative risk. Relative risk is the granddaddy
of them all, it's what we always care about the
most, it's what would public health officials
really rely upon a lot to make decisions about
what kinds of behaviors to tackle. So back
to our contingency table again, the relative
risk is going to be the proportion of our
absolute risk in the exposed group over our
absolute risk in the unexposed group. Again
these terms sound very similar, that's
why I want you to be very careful and always
refer back to the contingency table because
that will help keep it straight in your mind.
So again, the cumulative incidence rate in
the exposed group, again the incidence of
getting lung cancer or the outcome if you
do the deed, if you do the exposure, if you
smoke, that's a over a + b. The cumulative
incidence rate in the unexposed group, again
the probability of getting the outcome of
lung cancer if you don't smoke, is c over
c + d, we've covered that already, those are
absolute risks in both categories. If I divide
those two I get a relative risk. The incidence
rate in the first group divided by the incidence
rate in the second group. Now you may recall
when we talked about cohort designs versus
case-control designs, that we can only compute
incidence rate in a cohort design. We can
also compute incidence rates in a randomized
controlled trial. But in the world of observational
study, only in cohort studies can we compute
incidence rates. So when I'm talking about
relative risks and absolute risks, I'm only
talking about cohort studies. Case-control
studies we cannot compute relative risks,
because we cannot compute incidence rates.
To do so, to give a sense of risk in a case-control
scenario, we're going to compute something
different called an odds ratio and we will
tackle that in another lecture.
01:51
Now let’s talk about an example, let's say
we have a cohort study, and again a cohort
study allows us to compute incidence, because
a cohort study is, you may recall, begins
by ascertaining exposure status and waiting
to see if the outcome manifests. Do you remember
that? If you don't, I hope you review it.
I'll say it again, a cohort study begins by
ascertaining exposure status and waiting until
the outcome manifests. So this particular
cohort study follows 100 smokers and 100 non-smokers
over a ten year period to see which group
end up with more lung cancer, straight forward,
classic observational cohort study. Let's
look at their data. So let's set up a contingency
table again, exactly the way that we were
doing it every step of the way with our exposure
status horizontally and our outcome status
vertically. So 75 individuals smoked and got
lung cancer, 25 individuals smoked but did
not get lung cancer that constitutes 100 of
my smokers. Amongst my non-smokers now, 10
people did not smoke and they still got lung
cancer, that's an important consideration,
something that the lay person often forgets,
it's possible to ge the disease, to get the
outcome even if you did everything right,
because that's the nature of the world. But
in this case, in our hypothetical sample,
10 people didn't smoke and they still got
lung cancer. That means that 90 of my 100
non-smokers didn't smoke and did not get lung
cancer, okay. So I add up all my totals and
my marginals and I get these numbers.
03:28
Now my relative risk is going to be the incidence
rate in my exposed group divided by the incidence
rate in my unexposed group, in other words,
the absolute risk in my exposed group divided
by the absolute risk in my unexposed group
and I get this numbers, 7.5. Is that big?
That's a big number, 7.5 we consider to be
a very large relative risk, it means that
your risk of getting lung cancer if you smoked
is 7.5 times more so than if you didn't smoke.
04:00
If it had been one, if the number had been
one, that would mean that the risk is equivalent
and there is nothing to be said for that,
maybe we conclude then that smoking has no
relationship with lung cancer, but 7.5 is
extraordinarily high. My absolute risk reduction
you may recall, is the difference in those
two incidence rates. That's exactly when I
get 0.65. What does that tell me? It tells
me that if I didn't smoke, I can reduce my
rate of getting lung cancer by 65%, which
is extraordinary. So those two ideas, relative
risk and absolute risk reduction give me two
separate nuances of information that together,
form a comprehensive whole about the power
of smoking and causing lung cancer or being
associated with lung cancer. Now there is
something called relative risk reduction,
this is the proportion of baseline risk that
is reduced through non-exposure, what does
that mean? It means if I don't smoke how much
less lung cancer can I expect in the population?
It's given by this formula. A relative
risk reduction is the absolute risk reduction
divided by the incidence rate in the unexposed
group. Let's look at an example again. Here
is my contingency table and here we have the
same example again. We have 100 smokers, 100
non-smokers being followed for 10 years and
we see again an absolute incidence rate or
absolute risk in the exposed group and absolute
risk in the unexposed group. Here are my numbers,
same as the previous example, now let's compute
my relative risk reduction, that's going to
be the absolute risk reduction divided by
the incidence rate in the unexposed group,
we've done that math already, it's 6.5. What
does that mean? It means, by avoiding smoking,
reduce the relative risk of lung cancer by
650%.