[Instructor] Dear students, today we are going to
go over practice problem 12 from chapter three.
First I'm going to read the problem
and understand what information is provided.
Then we will go over the questions and answer them.
Problem 12 states, "A clinical trial
is run to assess the efficacy of a new drug
to reduce high blood pressure.
Patients with a diagnosis of hypertension,
high blood pressure, are recruited to participate
in the trial and randomized
to receive either the new drug or placebo.
Participants take the assigned drug for 12 weeks
and their blood pressure status is recorded.
At the end of the trial, participants are classified
as still having hypertension or not.
The data are shown in table 3.15."
As you can see, table 3.15 provides us
with the hypertension status by treatment.
The first column are the two groups, placebo and new drug.
The second column is the number randomized,
which is 50 each.
And the third column is the number free of hypertension
at 12 weeks, which is six and 14.
So part A is asking us what is the prevalence
of hypertension at the start of the trial?
For this part, we actually don't need
to perform any calculations.
The answer here is a hundred percent or one,
because hypertension is an inclusion criteria for the trial.
However, if we do want to calculate it,
then we need to use the formula for point prevalence
which is abbreviated as PP.
So PP is equal to
number of persons with the disease
as the numerator,
and then, number of persons examined at baseline.
So this will be 100 divided by 100,
because number of persons with the disease
is 50 plus 50, 100.
And number of persons examined at baseline
is also 50 plus 50, 100.
So the answer will be one or hundred percent.
Now this was quite straightforward, but the next one,
part B, will require a little bit more thinking
and calculation.
So part B is asking us what is the prevalence
of hypertension at the end of the trial?
To answer this question,
we have to again look at the information
provided us in the table,
use the point prevalence formula
and determine how many are still with the disease.
Now the table tells us how many people
are free of the disease at the end of the trial.
So from that, we,
to calculate the number
of people with the disease at the end of the trial.
So let's first start with the formula, which is again
PP, number of persons with the disease
divided by number of persons examined at baseline.
So for the numerator this will be
50 minus six for the placebo
plus 50 minus 14 for the new drug.
And then our denominator will still be the same
which is 100, which is 50 plus 50.
Now as we do the subtraction,
we see that for the first one we get 44.
The second one we get 36.
And we have to divide that by 100.
So now,
we have 80 as our numerator divided by 100.
Which gives us our answer, which is 0.8 or 80%.
So what does that mean?
That means that the prevalence of hypertension
at the end of the trial is 80%.
So as you may recall from part A,
the prevalence of hypertension at the beginning of trial
was actually a hundred percent.
Now we will go to part C.
Part C is asking us to estimate the relative risk
comparing the proportion of patients who are
free of hypertension at 12 weeks between groups.
So to calculate the relative risk,
or as it is abbreviated as RR,
we need to first find out the formula.
So the formula for relative risk is
point prevalence exposed
divided by
point prevalence unexposed.
So what is our exposure?
Our exposure is the new drug.
So now we will calculate the numerator.
So the numerator here will be
point prevalence exposed,
14 divided by 50,
which is 0.28.
And here will be the point prevalence unexposed
which will be six divided by 50 or 0.12.
So our RR will be
0.28 divided by 0.12
equal to 2.33.
So now the question is what does this mean?
So the best way to understand this RR
is to compare it to one.
So if RR is equal to one, then the groups are similar.
However, anytime RR is different from one
we need to understand the dissimilar.
So one way to interpret the dissimilarity here
is to state that the patients receiving the new drug
were 2.33 times more likely to be free of hypertension
at the end of the trial compared
to patients receiving the placebo.
So patients receiving the new drug
were 2.33 times more likely
to be free of hypertension
at the end of the trial
compared to the placebo,
or patients receiving the placebo.