The results of a clinical trial in 592 HIV patents designed to demonstrate equiv
ID: 3223697 • Letter: T
Question
The results of a clinical trial in 592 HIV patents designed to demonstrate equivalence between an abacavir-lamivudine-zidovudine (ALZ) therapy and an indinavir-lamivudine-zidovudine (ILZ) therapy were reported. To compare the therapies, an HIV RNA level was measured. The results are: ALZ treatment: x^bar = 400 copies/ml s = 55 copies/ml ILZ treatment: x^bar = 500 copies/ml, s = 85 copies/ml Based on discussions with researchers, clinicians, and the FDA, the equivalence margin for the difference in means was set at delta = 75 copies/ml Are the results of ALZ and ILZ therapies equivalent (use alpha = 0.01)?Explanation / Answer
Solution:
For the given scenario, we have to use the two sample t test for the population mean.
The null and alternative hypothesis for this test is given as below:
H0: µ1 - µ2 = 75 versus Ha: µ1 - µ2 75
We are given
Data
Hypothesized Difference
75
Level of Significance
0.01
Population 1 Sample
Sample Size
592
Sample Mean
400
Sample Standard Deviation
55.0000
Population 2 Sample
Sample Size
592
Sample Mean
500
Sample Standard Deviation
85.0000
The test statistic formula for this test is given as below:
t = (X1bar – X2bar) / sqrt[(S1^2/N1)+(S2^2/N2)]
t = (400 – 500)/sqrt((55^2/592)+(85^2/592))
t = -24.03249832
df = 592+592 -2 = 1182
Level of significance = = 0.01
Critical values = -2.58 and 2.58
P-value = 0.0000
P-value < = 0.01
So, we reject the null hypothesis
There is insufficient evidence to conclude that results of ALZ and ILZ therapies are equivalent at 1% level of significance.
Data
Hypothesized Difference
75
Level of Significance
0.01
Population 1 Sample
Sample Size
592
Sample Mean
400
Sample Standard Deviation
55.0000
Population 2 Sample
Sample Size
592
Sample Mean
500
Sample Standard Deviation
85.0000
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