# 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()? Mar 6, 2015 at 18:40
• Did you get any answer? i want to know the formula for calculating sample size for a 3 arm randomized study. Aug 18, 2015 at 13:45

• Welcome to the site, @PavelNesmiyanov. Was this intended as an answer to the OP's question, a comment requesting clarification from the OP or one of the answerers, or a new question of your own? Please only use the "Your Answer" field to provide answers to the original question. You will be able to comment anywhere when your reputation is >50. If you have a new question, click the gray ASK QUESTION at the top of the page & ask it there, then we can help you properly. Since you're new here, you may want to take our tour, which has information for new users. Sep 20, 2016 at 16:19