The following data are collected in a clinical trial evaluating a new compound d

Question

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 mesured and the data are shown below. Wound healing:% Reduction in Size of Wound

Suppose the clinicians feel that if the percent reduction in the size of the wound is greater than 50% then the treatment is a success.

a) Generate a 95% confidence interval for the percent success in patients receiving the new compound. b) Generate a 95% confidence interval for the difference in the percent success between the new compound and placebo. C) Generate a 95% confidence interval for the relative risk of treatment success between treatments. D) Generate a 95% confidence interval for the odds ratio of treatment success between treatments.

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

(a) For new compound mean success = [4 * 0 + 13* 11+ 38 * 37 + 63 * 32 + 88 * 41]/125 = 57.384

Variance = 705.4685 so standerd deviation = 26.56/sqrt(125) = 2.34755

95% confidence interval for the percent success in patients = ( Mean +- 1.96 * 2.34755)

1.96 is used because it is the Z value for the 95% interval = (57.384 +- 1.96 * 2.34755)

so 95 % CI = (62, 52.78)

(b) For new compound mean success = [12 * 0 + 13* 24 + 38 * 45 + 63 * 34 + 88 * 10]/125 = 40.352

Variance = 62.0921 so standerd deviation = 24.96/sqrt(125) = 2.2325

95% confidence interval for the percent success in patients = ( Mean +- 1.96 * 2.2325)

1.96 is used because it is the Z value for the 95% interval = ( 40.352 +- 1.96 *2.2325)

so 95 % CI = (44.72, 35.98)

(C) Relative Risk of success = Success with new compound / Success with placebo

So mean Relative risk = [0* 0.33 + 13* 0.46 + 38 * 0.82 + 63 * 0.94+ 88 * 4.10]/202 = 2.26

Standerd deiviation = 30.36/202 = 0.15

95% confidence interval for the percent success in patients = ( Mean +- 1.96 * 0.15)

1.96 is used because it is the Z value for the 95% interval = ( 2.26 +- 1.96 *0.15)

so 95 % CI = (2.554, 1.966)

this the relative risk of success which have a mean of 2.26

(d) Odd ratio = ad/bc

So mean odd ratio = [0* 0.31 + 13* 0.40 + 38 * 0.75 + 63 * 0.92+ 88 * 5.85]/202 = 3.00

Standerd deiviation = 36.81/202 = 0.189

95% confidence interval for the odd ratio in patients = ( Mean +- 1.96 * 0.189)

1.96 is used because it is the Z value for the 95% interval = ( 3.00+- 1.96 *0.189)

so 95 % CI = (3.37, 2.63)

this the odd ratio which have a mean of 3.00.

treatment none 1-25% 26-50% 51-75% 76-100% Mean Value of success 0 13 38 63 88 New compound (n=125) 4 11 37 32 41 Placebo (n=125) 12 24 45 34 10 Relative Risk 0.33 0.46 0.82 0.94 4.1 Odd ratio 0.31 0.40 0.75 0.92 5.85

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