Instructor: Hello students.
Welcome to Biostats ER example 8 chapter 6.
In this example, we are going to learn how
to calculate the 95% confidence interval for odds ratio.
We are going to use the same problem
that we used, for example 6 and 7,
which is from our textbook problem 7.
I'll first read the problem, which states 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 a hundred participants
who received the experimental medication,
38 report reduction in symptoms as compared
to 21 participants of 100 assigned to placebo.
For your convenience, I have presented the information
in a tabular format here,
and then I have stated the formula.
However, before we start solving the problem,
I want to let you know that for this Biostats ER example,
the solution is typed
because once I heard from a student that
all of my Biostats ER examples are solved by hand.
Hence, I have again typed the solution here,
but I am going to go through it step by step.
So as you can see from this formula, the first thing we need
to calculate here is the OR hat.
And the formula to calculate the OR hat is presented here.
So to calculate the OR hat, we need to know the p1 hat
and the p2 hat and one minus p1 hat
and one minus p2 hat.
So I have provided you with formulas
in terms of how to obtain those values.
And once we obtain those values, we insert it here.
So as you can see here in the numerator, we have 0.38,
which we obtained from here,
and 0.62, which we obtained from here.
And then for the denominator we have 0.21,
which is obtained from here.
And then we have 0.79, which is obtained from here.
And after that, when we perform the division
and then again to the final division,
which is dividing 0.61 by 0.27,
we get 2.26.
Then we take this value 2.26 and insert it here
and obtain the natural log of 2.26
by using our calculator
and we get 0.815.
Now we have to look at the other parts of this equation,
which requires us to obtain the 95% Z value,
which is 1.96 and we insert it here.
Then it requires us to subsequently insert the values
for x1, which is 38,
n1 minus x1, which is 62,
x2, which is 21 and n2 minus x2, which is 79.
So after we insert all these values, what we have to do is
one at a time perform these divisions
and then add them all up.
So once we perform the division and add them all up,
we need to take the square root
of that number and that is 0.321.
Then we have to multiply 0.321 by 1.96,
which will give us 0.628.
Then we have to subtract and add 0.628 to 0.815.
So when we subtract 0.628 from 0.815,
we get 0.187.
And then when we add it, we get 1.443.
So the 95% confidence interval for the natural log of OR
is 0.187, 1.443.
Now to generate the confidence interval for the odds ratio,
we take the anti-log
of the upper and lower limits.
And when we do that, we get 1.21 and 4.23.
So the confidence interval here, as you can see,
does not include a one.
Therefore, we can state with 95% confidence
that there is a difference in the odds of symptom relief
between the two groups,
which is the exposed experimental group
and the unexposed placebo group.
Thank you very much for your time and attention
and I'll see you in the next video.