so we're going to talk a little bit about why it is okay to calculate an
odds ratio for a case control study design so you might recall that the odds
ratio is the odds of getting the disease given someone's exposed relative to the
odds of the disease given their not exposed okay we're going to work this
out using the following two-by-two table set
up in the conventional ABCD format and I generally have not a big fan of using
the ABCD z-- to work out odds ratios but it's going to we're going to present it
this way for the sake of working through the calculations a reminder that the
odds ratio again is the odds of disease given exposed over the odds of disease
keepers are not exposed and if you recall probabilities right the odds of
disease given exposed can be written as the probability of having the disease
given their exposed divided by the probability of not having the disease
given their exposed right so again odds are a ratio of occurrences to non
occurrences and the odds of having the disease given something's not exposed we
can write this as the probability of having the disease given they're not
exposed divided by the probability of not having the disease given they're not
exposed right so again the odds the ratio of the probability of occurence to
probably of non occurrence right so conditioned on having not been exposed
what's the problem of disease what's the problem of not disease and if we work
these out numerically the probability of disease given someone's exposed right so
given their exposed that's conditioning on this row here and
the probability of disease is a right over a plus B a over a plus B the
probability of not having the disease given their exposed and again we're
conditioning on the individual being exposed and probability of not having
the disease is B over a plus B the next few I'll move through a bit quicker and
we won't kind of label over all of these but the probability of having the
disease given someone's not exposed is C over C plus D
and they're probably not having the disease given they're not exposed it's D
over C plus D now I'll let you play around with the algebra but if you work
this out this is going to come out to a over B divided by C over D right or we
can express this as ad over BC okay so you may recall this formula the odds
ratio is ad over BC so first first note is why I don't like using the ABCD DS I
think it's a lot more intuitive rather than saying the odds ratios ad over BC
that the odds ratio is what are the odds of getting the disease for someone's
exposed relative to the odds of disease for someone who's not exposed okay so
think of the odds ratio this way tells you what it is ad BC doesn't actually
tell you what it is okay so let's get back to the idea of the case control
design and if you remember a case control we select people who have the
disease we select people who don't have the disease and then we asked about
their exposure so in that case when we've selected people based on disease
status we can't actually estimate these prevalence is here right we can't
estimate what's the probability of disease giving you're exposed when we've
selected people who are diseased right we've select them based on their disease
status same with these right so we actually can't estimate those right
what's the product disease for someone who's not exposed when we selected them
based on whether or not their disease we're in a look at this now if there's
some very convenient mathematics that happened for us so let's take a look at
that the odds ratio if we've selected people based on exposure status right we
can't estimate anything about disease cure prevalences but we can't estimate
both their exposures so we can estimate what's the odds that someone was exposed
given their disease relative to what are the odds that someone was exposed given
they're not diseased so the odds ratio we can get at is what are the odds of
exposure for someone that's diseased relative to not disease okay these are
fine test night for a case control design right we haven't done anything to
control exposures in that sort of design now
let's expand on this year the odds of exposure given someone's disease we can
write as the probability of being exposed given their disease divided by
the probability of not being exposed given their disease right so again the
odds is a ratio of occurrences to known occurrences and expanding this here this
is the probability of exposure given someone doesn't have the disease divided
by the probability of not being exposed given they don't have the disease again
that's right but these are in our table in terms of the ABCs DS so probability
of being exposed to given someone's disease and again that's conditioning on
this column here given that they're diseased what's the probability of
exposure a over a plus C and divided by what's the probability of not being
exposed given their disease again conditioning on the disease column right
the probability of not being exposed is C over a plus C and again awful on the
bottom here a little bit more quickly so probability of exposure given their not
disease is B over B plus D and their probability of not being exposed given
their not disease is D over B plus D
okay again if you play around with the algebra and cancel out some of the terms
you're going to find that this comes up to be a over C right these are going to
cancel each other out over B over D okay or ad over BC okay so you can notice
here well tech the pay for a case control design we cannot
estimate anything about prevalence we can't estimate the probability of
disease given exposure so we can't really estimate these here it happens
mathematically that the odds of disease given exposed divided by odds of disease
given they're not exposed mathematically happens to be equal to the odds of
exposure given disease odds of exposure given they're not disease right in a
case control design where we've selected people who are diseased and nuts and
then asked about exposures we can estimate these here we can estimate
prevalence of exposure for some of his disease or not okay so again just to
note that this is why we can estimate an odds ratio for a case control design and
one final kind of nice feature to talk about you've probably learned or you
will have learned that in certain cases a knowledge ratio while a bit more
difficult to interpret right for our brains it's approximately equal to the
rate ratio when is that and that's for rare disease so we've encountered that
rate ratios are a little bit nicer for our brain to interpret or a bit more
intuitive all the ratios are yeah but we've also learned for rare diseases and
guideline you know something with prevalence less than 5% or so was the
guideline for a rare disease in that case odds ratio and rate ratio are
approximately equal and let's think about case control designs what's the
most common use for those the most common use is when we're studying rare
diseases if we were to do a cohort and follow people over time we might not get
enough cases of the disease so we start by citing people with disease people
without and then look back for exposures okay so we got this really convenient
loop that the odds of exposure so the odds of disease given their exposed over
the odds of disease given their not exposed happens to be equal to odds of
exposure given disease over odds of exposure given up disease so we get in
this nice loop where we can estimate the odds ratio and we can interpret it this
way as these two are mathematically equivalent and also for case control
designs often the reason we're using them is because we're studying rare
diseases and in that case the odds ratio is
approximately equal to the rate ratio and we can interpret it that way thanks
for watching our video subscribe to my channel chill videos stick around guys
cause we are not more certificates almost as yummy as chocolate