Instructor: Hello, students, and welcome to Biostat ER,
chapter eight, example three.
In this example, we will learn how to calculate sample size
for two-matched samples, continuous outcome,
to determine confidence interval.
This example is from our textbook.
So first, I'm going to read the problem statement,
which is problem five.
"A crossover trial is planned to evaluate the impact
of an educational intervention program
to reduce alcohol consumption
in patients determined to be at risk for alcohol problems.
The plan is to measure alcohol consumption,
the number of drinks on a typical drinking day,
before the intervention, and then again after participants
complete the educational intervention program.
How many participants would be required to ensure
that a 95% confidence interval
for the mean difference in the number of drinks
is within two drinks of the true mean difference?
Assume that the standard deviation of the difference
in the mean number of drinks is 6.7 drinks
and that 20% of the participants will drop out
over the course of follow-up."
So for the answer here,
I have first inserted the formula here,
and it is, as you can see, Z times sigma D,
because it's a difference,
we have paired samples, and then it is divided by E.
So the Z value here is, again, going to be 1.96,
as you have seen in the previous example.
The sigma sub D is going to be 6.7,
because that is what has been provided to us,
and the E is going to be two,
which is, again, what has been provided to us.
So once we insert these values into the formula
and we perform the algebra, we get 43.1,
and we always round up for sample size calculation,
so a sample size of N equal to 44 is required.
Now, we are going to go to the next step,
and we are going to address the loss to follow-up.
So to account for 20% loss to follow-up,
we have to use this formula, which is N, number to enroll,
multiplied by the percent retained
is equal to the desired sample size.
So because we are losing 20% to follow-up,
then percent retained is, of course, 80%,
because we are subtracting it from 100.
And then, once we insert these values,
and again, we perform the algebra here, we get 55.
So the investigators here need to recruit 55 participants.