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All right, so turning now from the Vioxx story.
I went over rate ratios and risk ratios. I now want to turn to hazard ratios which
again are directly related to rate ratios.
We're going to see these later in the course, so you don't have to worry about
all the details now. The hazard ratio can be interpreted just
like a rate ratio. I'm just going to walk you through it a
little bit, so that you'll be familiar with it if you see it in the literature.
Again we'll, we'll talk in more detail. Later in the course.
So hazard ratios are calculated using, a type of regression technique called ***
regression. This is a complimentary regression.
They are usually multivariant adjusted. And I'll just show you an example of a
hazard ratio in the literature. This was a study comparing a drug,
Ranolazine to a placebo. And they were looking at the outcome.
It was a composite outcome. They were looking at death, myocardial
infarction, heart attack, or recurrent ischemia, they wanted to know if they
could reduce that composite outcome with this drug.
Here is the hazard ratio I have circled it for you for the primary endpoint,
turned out to be 0.92, so we would interpret that as an 8% reduction in the
rate. Of this primary end point.
In the drug and the active drug group compared with the placebo group.
Now that wasn't statistically significant.
You can see that the confidence interval ranges from 0.83 to 1.02.
So we're not completely sure that the true value isn't 1.0.
Right, that the null value falls within that window.
So it's not statistically significant. It's a small reduction.
But that's how you would interpret the hazard ratio.
Now we're going to move to the odds ratio.
We're going to spend the rest of this module and all of next month.
The next module on the odds ratio. Odds ratios are just another measure of
relative risk. You're going to see in a minute that
they're kind of funny and you're going to wonder why they even exist.
But there's two reasons that they exist. First of all, they're they only valid
measure of relative risk for case-control studies, so why is that?
So remember, for a case-control study, you cannot calculate the risk of disease
or the rate of disease. Because, at the investigator goes out and
finds cases. So the proportion of cases in the study
just reflects the study design. It does not say anything about the
prevalence or risk of disease in the general population.
Therefore we can't estimate the risk or prevalence of disease in the general
population. Since we can't estimate disease
frequency, we can't estimate risk ratios or weight ratios.
It turns out that the odds ratio, for mathematical reasons, is valid though.
The more important reason that you're going to see odds ratios all over the
medical literature is because of logistic regression.
So even when you're doing cohort studies and cross-sectional studies.
Author's may choose to run a statistical technique called logistic regression.
When you have a binary outcome and you want to adjust for confounders the
typical statistical test that people use is logistic regression.
It happens that logistic regression gives you out odds ratios.
So that's what you get out of the logistic regression, that's what people
usually report. And this means there's a lot of logistic
regression is run in the literature, there's a lot of odds ratios in the, in
the literature. To understand odds ratios, first of all
you have to understand, what is an odds. An odds is just the probability of an
event happening divided by the probability of it not happening.
And that's a really funny measure to get your head around unless you're a somebody
who does horse betting or gambling or sports betting, you probably don't think
in odds. I certainly don't think in odds.
I think in probabilities. What's the chance of something happening?
I don't think about, what's the chance of it happening divided by the chance of it
not happening. But it turns out that odds have some nice
mathematical properties, and that's why they come up.
So let's just walk through a couple of examples.
So if the risk is 50%. If the risk of something happening is
50%. That means there is one chance that it'll
happen, and one chance that it won't. The, if the risk of it happening is 50%.
Then the risk of it not happening is 50%. So that would make the rip, the odds 1 to
1. If the risk of something happening is
75%, reach it times of 4 it's going to happen.
So 1 times out of 4 it's not going to happen.
So the odds would be 3 to 1. If the risk of something happening is
10%, 1 out of 10, that means 1 out of 10 times it will happen, and 9 out of the 10
times it won't, so the odds would be 1 to 9.
If the risk is 1%, 1 out of 100, the odds would be 1 to 99.
Now notice that if you think of an odds as a fraction, so we're, I could rewrite
this as 1 over 1, 3 over 1, 1 over 9, I could rewrite this as fractions.
If you think of the odds as fractions, notice that the odds is always higher
than the corresponding risk. Alright, one is higher than a half, 1 out
of 99 is higher than 1 out of 100. So the odds is always higher than its
corresponding probability. But, if you're talking about small risks,
so like 1 out of 100, and 1 out of 10, the odds and the risk are very close in
magnitude; 1 out of 100 isn't that different from 1 out of 99.
So if you're talking about rare events, the odds and the risks are similar.
However, if you're talking about common events, like when the risk is 50% or 75%.
Then the odds and the risk look very different.
So keep that in mind. Because that's going to be true of the
odds ratio. When you have a common event, the odds
ratio and the risks ratio are going to diverge.
When you have a very rare event, however, the risk ratio and the odds ratio are
going to look a lot alike.