Instructor: Hello students and welcome to
Biostat ER, example seven.
In this example, we are going to learn how to calculate
the 95% confidence interval for relative risk.
We are using the same problem we used before.
Nevertheless, I will read the problem to you.
We used this problem for example six.
"A clinical trial is conducted
"to compare an experimental medication to placebo
"to reduce the symptoms of asthma.
"200 participants are enrolled to the study
"and randomized to receive
"either the experimental medication or the placebo.
"The primary outcome is self-reported reduction of symptoms.
"Among 100 participants who received
"the experimental medication, 38 report reduction
"in symptoms as compared to 21 participants of 100
"assigned to placebo."
First here, I have presented the information
in a tabular format.
And before we get started, in terms of solving the problem,
I want to draw your attention to our textbook Chapter Six,
page 114 and here it states clearly why we need to use
the natural log and subsequently the anti-log
to determine the relative risk.
I have copied and pasted the information here
from our textbook and I am not reading it
in the interest of time,
but I'm hoping that you will read it.
Also, I will like to mention that for this
Biostats ER example, the solution is typed
because as I mentioned previously,
once I heard from a student that all of my Biostats ER examples
are solved by hand.
Hence, I have decided to type some of the solutions
and this is one of those that I typed.
Nevertheless, I will go over the solution step by step.
So first here, as you can see, this is the formula
we are going to use to solve the problem.
The Ln here stands for the natural log.
The first thing we have to do is calculate the RR hat
and the formula for that is p1 divided by p2
And to determine p1, we need to divide x1
divided by n1 and then to determine p2,
we have to divide x2 by n2.
So once we do these divisions, we get 1.81
and that will be inserted here,
and we will subsequently obtain the natural log of 1.81
and for which we have to use our calculator.
Now we will insert the Z value here, which is going
to be 1.96, and then under the square root
we are going to insert the values.
For n1 minus x1, the value is 62 and x1 is 38,
and n1 is 100.
Then here we have for n2 minus x2,
the value is going to be 79
and for x2, the value is going to be 21
and then we are going to divide that by 100.
So once we do the divisions and then we do the addition
and then once we get the square root,
our final answer here is 0.232.
Now we have to take this answer and now multiply it by 1.96.
And once we do that, we get 0.455.
Now 0.455 is going to be subtracted and added
to the natural log of 1.81 and that is 0.59.
So first we are going to take 0.455 and deduct it from 0.59
and then we are going to add 0.455 to 0.59.
Once we do the subtraction and addition,
we get 0.135 and 1.045.
The 95% confidence interval for the natural log
of RR is 0.135 and 1.045.
To generate the confidence interval for the RR,
we take the anti-log of the lower and the upper limits.
And when we do that, again, by using our calculator,
we get 1.14 and 2.84.
So as you can see, the confidence interval here
does not include a one.
Therefore, we can state with 95% confidence
that a statistically significant difference exists
between the two groups.
Thank you for your attention
and I will see you in the next video.