1. A clinical trial was conducted to compare an experimental medication to a pla
ID: 3341021 • Letter: 1
Question
1. A clinical trial was conducted to compare an experimental medication to a placebo to reduce the symptoms of asthma. One hundred patients were randomized to receive either the experimental medication or a placebo. The outcome of interest was self-reported reduction of symptoms. Among the 50 patients who received the experimental medication, 17 reported a reduction of symptoms. Among the 50 patients who received the placebo, 10 reported a reduction of symptoms. The goal was to determine whether there is a significant difference in the proportion of patients who report a reduction of symptoms in the experimental versus the placebo group.
a) Is a one-sample or two-sample test more appropriate? Why?
b) State the null and alternative hypotheses.
c) What is the most appropriate test to use? Why?
d) Conduct the test and formulate a conclusion. In addition to indicating whether or not you reject the null hypothesis, also state clearly in words what conclusion you draw from the results.
e) When you try to publish the results, the journal asks for the 95% CI for the difference between the proportions of the two groups. What assumptions are required to compute this confidence interval?
f) Compute the 95% CI for the difference between the proportions of the two groups.
g) A larger clinical practice is interested in testing the experimental medication in their patients. They will randomize an equal number of patients to the experimental medication versus the placebo. How many patients are needed in each group to have 80% statistical power to detect an increase in the proportion reporting reduced symptoms in the experimental medication versus placebo groups? Assume an alpha level of 0.05.
Explanation / Answer
a) Is a one-sample or two-sample test more appropriate? Why?
Given that there are two groups experimental and placebo. So here we use two sample test.
b) State the null and alternative hypotheses.
Here we have to test the hypothesis that,
H0 : p1 = p2 Vs H1 : p1 not= p2
where p1 and p2 are two population proportion for experimental group and placebo group respectively.
Assume alpha = level of significance = 5% = 0.05
So here we have to test two proportions.
c) What is the most appropriate test to use? Why?
We can use here two proportion Z-test.
Given that,
sample sizes :
n1 = 50
n2 = 50
successes :
x1 = 17
x2 = 10
Test statistic follows Z-distribution.
d) Conduct the test and formulate a conclusion. In addition to indicating whether or not you reject the null hypothesis, also state clearly in words what conclusion you draw from the results.
We can do this test in MINITAB.
steps :
STAT --> Basic statistics --> two proportions --> click on summarized data --> Input all the values --> Options --> Confidence level : 95.0 --> Test difference : 0.0 --> Alternative : not equal --> click on use pooled estimate of p for test --> ok --> ok
Test statistic = 1.58
P-value = 0.115
P-value > alpha
Accept H0 at 5% level of significance.
Conclusion : There is not sufficient evidence to say that two proportions are differ.
e) When you try to publish the results, the journal asks for the 95% CI for the difference between the proportions of the two groups. What assumptions are required to compute this confidence interval?
Assumptions :
For given x1,x2,n1 and n2 :
p1^ = x1/n1 and p2^ = x2/ n2
p1^ and p2^ are sample proportions.
q1^ = 1- p1^
q2^ = 1 - p2^
n1p1^ > 5, n2p2^ > 5, n1q1^ > 5 and n2q2^ > 5
If all these conditions are satisfied then we can find confidence interval.
For our problem all these conditions are satisfied.
95% confidence interval for p1-p2 is (-0.0318, 0.3118).
Conclusion : We are 95% confident that the difference in proportion is lies between -0.0318 and 0.3118
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.