1.The following data are collected in a clinical trial evaluating a new compound
ID: 3131156 • Letter: 1
Question
1.The following data are collected in a clinical trial evaluating a new compound designed to improve wound healing in trauma patients. The new compound is compared against a placebo. After treatment for 5 days with the new compound or placebo, the extent of wound healing is measured and the data are shown below.
Wound Healing: % Reduction in Size of Wound
Treatment
None
1 – 25%
26 – 50%
51 – 75%
76 – 100%
New Compound (n = 125)
4
11
37
32
41
Placebo (n = 125)
12
24
45
34
10
Suppose that clinicians feel that if the percent reduction in the size of the wound is greater than 50% then the treatment is a success. Generate a 95% confidence interval for the percent success in patients receiving the new compound.
Wound Healing: % Reduction in Size of Wound
Treatment
None
1 – 25%
26 – 50%
51 – 75%
76 – 100%
New Compound (n = 125)
4
11
37
32
41
Placebo (n = 125)
12
24
45
34
10
Explanation / Answer
Confidence Interval For Proportion
CI = p ± Z a/2 Sqrt(p*(1-p)/n)))
x = Mean
n = Sample Size
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
Mean(x)= greater than 50% = 32+41 = 73
Sample Size(n)=125
Sample proportion = x/n =0.584
Confidence Interval = [ 0.584 ±Z a/2 ( Sqrt ( 0.584*0.416) /125)]
= [ 0.584 - 1.96* Sqrt(0.002) , 0.584 + 1.96* Sqrt(0.002) ]
= [ 0.498,0.67]
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