Clinical trial question Confidence Interval

Question

Data are collected in a clinical trial evaluating a new compound designed to improve wound healing in 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 in Table. Suppose that the clinician feels 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 placbo.
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.

Table:
Number of patients with percent reduction in Size of Wound
New compound n=125  None=4   1-25=11  25-50=37  51-75=32  76-100=41
Placebo      n=125  None=12  1-25=24  25-50=45  51-75=34  76-100=10

Also:

a. Generate a 95% Confidence Interval for the mean age among participants assigned to the placebo.
b. Generate a Confidence interval fro the difference in mean ages in participants assigned to the experimental versus the placebo groups.
c. Generate a 95% Confidence Interval for the difference in mean BMI in participants assigned to the experimental versus the placebo groups.

Answer 1

My hint for question a) to get you started is that 32+41=73% of those receiving the new compound have got more than a 50% reduction in the size of the wound (which is what is defined as "success") and hence 73% would be the point estimate of the percent success of patients receiving the new compound. To turn this point estimate into a confidence interval you need to somehow estimate the randomness associated with the 73%. 73% plus or minus what?

Say the real value happens to actually be 73%. If you did this experiment exactly the same again, would you get exactly 73%? Probably not. On average, what would you get? Use this thinking to think through how the confidence interval is generated - and I presume your teachers have given you some material to help with this too.