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[Instructor] Dear students,
today we are going to

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go over practice problem
12 from chapter three.

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First I'm going to read the problem

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and understand what
information is provided.

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Then we will go over the
questions and answer them.

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Problem 12 states, "A clinical trial

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is run to assess the
efficacy of a new drug

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to reduce high blood pressure.

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Patients with a diagnosis of hypertension,

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high blood pressure, are
recruited to participate

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in the trial and randomized

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to receive either the new drug or placebo.

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Participants take the
assigned drug for 12 weeks

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and their blood pressure
status is recorded.

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At the end of the trial,
participants are classified

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as still having hypertension or not.

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The data are shown in table 3.15."

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As you can see, table 3.15 provides us

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with the hypertension status by treatment.

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The first column are the two
groups, placebo and new drug.

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The second column is
the number randomized,

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which is 50 each.

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And the third column is the
number free of hypertension

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at 12 weeks, which is six and 14.

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So part A is asking us
what is the prevalence

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of hypertension at the start of the trial?

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For this part, we actually don't need

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to perform any calculations.

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The answer here is a
hundred percent or one,

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because hypertension is an
inclusion criteria for the trial.

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However, if we do want to calculate it,

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then we need to use the
formula for point prevalence

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which is abbreviated as PP.

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So PP is equal to

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number of persons with the disease

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as the numerator,

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and then, number of persons
examined at baseline.

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So this will be 100 divided by 100,

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because number of persons with the disease

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is 50 plus 50, 100.

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And number of persons examined at baseline

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is also 50 plus 50, 100.

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So the answer will be
one or hundred percent.

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Now this was quite
straightforward, but the next one,

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part B, will require a
little bit more thinking

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and calculation.

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So part B is asking us
what is the prevalence

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of hypertension at the end of the trial?

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To answer this question,

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we have to again look at the information

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provided us in the table,

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use the point prevalence formula

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and determine how many are
still with the disease.

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Now the table tells us how many people

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are free of the disease
at the end of the trial.

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So from that, we,

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to calculate the number

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of people with the disease
at the end of the trial.

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So let's first start with
the formula, which is again

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PP, number of persons with the disease

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divided by number of persons
examined at baseline.

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So for the numerator this will be

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50 minus six for the placebo

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plus 50 minus 14 for the new drug.

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And then our denominator
will still be the same

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which is 100, which is 50 plus 50.

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Now as we do the subtraction,

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we see that for the first one we get 44.

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The second one we get 36.

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And we have to divide that by 100.

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So now,

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we have 80 as our
numerator divided by 100.

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Which gives us our answer,
which is 0.8 or 80%.

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So what does that mean?

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That means that the
prevalence of hypertension

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at the end of the trial is 80%.

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So as you may recall from part A,

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the prevalence of hypertension
at the beginning of trial

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was actually a hundred percent.

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Now we will go to part C.

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Part C is asking us to
estimate the relative risk

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comparing the proportion
of patients who are

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free of hypertension at
12 weeks between groups.

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So to calculate the relative risk,

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or as it is abbreviated as RR,

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we need to first find out the formula.

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So the formula for relative risk is

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point prevalence exposed

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divided by

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point prevalence unexposed.

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So what is our exposure?

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Our exposure is the new drug.

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So now we will calculate the numerator.

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So the numerator here will be

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point prevalence exposed,

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14 divided by 50,

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which is 0.28.

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And here will be the
point prevalence unexposed

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which will be six divided by 50 or 0.12.

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So our RR will be

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0.28 divided by 0.12

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equal to 2.33.

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So now the question is
what does this mean?

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So the best way to understand this RR

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is to compare it to one.

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So if RR is equal to one,
then the groups are similar.

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However, anytime RR is different from one

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we need to understand the dissimilar.

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So one way to interpret
the dissimilarity here

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is to state that the patients
receiving the new drug

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were 2.33 times more likely
to be free of hypertension

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at the end of the trial compared

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to patients receiving the placebo.

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So patients receiving the new drug

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were 2.33 times more likely

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to be free of hypertension

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at the end of the trial

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compared to the placebo,

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or patients receiving the placebo.