Instructor: Hello students and welcome
to Biostat ER chapter eight, example four.
In this example, we will learn how to calculate sample size
for two-independent samples, continuous outcome
to perform hypothesis testing.
This example is from our textbook.
So as always, I'm first going to read the problem.
So it's problem 10.
Recently it has been observed that HIV infected patients
develop peripheral lipoatrophy
while on potent antiretroviral therapy.
A clinical trial is planned
to determine if a new chemical will improve this condition.
In the trial, participants will be randomized
to receive the new chemical or a placebo
and changes from baseline
in subcutaneous adipose cross-sectional area
as measured by CT scan will be calculated
after 24 weeks of treatment.
Investigators hope to show
that the increases in patients receiving the chemical
are greater than the increases in patients
receiving the placebo.
They hypothesize that the participants
assigned to the clinical arm will exhibit
a mean change of 30% and the participants
assigned to the placebo arm will exhibit
a mean change of 0%.
Prior literature suggests that the standard deviation
of the changes will be 57% in both arms.
So how many participants are needed to ensure 80% power?
We will assume that alpha is equal
to 0.05 equal numbers in each group
and that 20% of the participants will drop out
over the course of follow-up.
So first here I have provided you with the formula,
and as part of the formula, we will first proceed
with calculating the denominator, which is ES, the effect size.
Now for the effect size here, the mu one minus mu two,
the differences here is directly provided to us
in the problem and I have highlighted it in yellow
for your convenience.
And that is what I have inserted here, 0.30.
And for the sigma, again,
that is provided to us in the problem.
And that is 57%, which again,
I have inserted here as 0.57.
So when we do the division, we get 0.53.
So now for the next step, we will have to obtain that value
for Z one minus alpha divided by two,
which is again the Z 97 point fifth percentile.
And that is going to be 1.96.
Again, that is the Z value for which the 97.5%
of probability lies below.
The Z value one minus beta is the Z of the 80th percentile
because one minus beta is the power of the study,
and that is going to be 0.84.
And of course we are going to obtain these values
from the Z table.
So once we insert all these values
and perform the algebra, we get 55.8.
Again, as always, we are going to round up
because it is sample size calculation.
So the sample size of N one is going to be 56
and N two is going to be 56.
And that will ensure that the test
of hypothesis will have an 80% power
to detect a 0.30-unit difference
in change flow between groups.
Now we have to also account for the loss to follow-up.
So to account for 20% loss to follow up,
the investigators need to recruit 140 participants.
And how do we know that?
We know that because we have this formula
and we are going to insert the values in the formula.
So it's going to be N, which is the number
to enroll, multiplied by percent retained.
And that is going to be equal to our desired sample size.
And here we know that there's going to be a 20% drop,
so it's going to be 0.80,
and then it's going to be 112,
Because when we add 56
and 56 together, we are going to get 112.
So once we insert that,
and again, when we perform the algebra, we get 140.