# Sample size and power calculations for a randomized controlled trial

I need help with the power calculations to determine the sample size of a randomized clinical trial. This is a relatively simple trial with two arms: an intervention arm and a control arm. Patients in the intervention arm will receive a dietary supplement while patients in the control arm will receive a placebo. This is a longitudinal trial starting at time zero, with patient visits at 6 and 12 months. It is my hope that the supplement will reduce the patient's risk of developing obesity.

I know from previous reports that at the 6 month visit, 25% of the controls should have developed obesity. Also from previous reports, at the 12 month visit, cumulatively, 45% of the controls should have developed obesity! I think that in the best case scenario, the supplement will reduce the risk of getting obesity to only 2.5% among patients in the control arm.

My question: How many patients do I need in the intervention arm and how many do I need in the control arm to detect this difference? If I wanted to detect a smaller difference (perhaps a difference of at least 5% between the two groups), how would that change my calculation?

I've found some websites with calculators: http://www.epibiostat.ucsf.edu/biostat/sampsize.html#proportions http://www.stat.ubc.ca/~rollin/stats/ssize/b2.html

But I'm not sure how to input my data or which calculator to use. Any help would be greatly appreciated!

• Have you looked at the power analysis functions in R, e.g. power.prop.test()? – Jeremy Miles Mar 6 '15 at 18:40
• Did you get any answer? i want to know the formula for calculating sample size for a 3 arm randomized study. – user1327454 Aug 18 '15 at 13:45

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