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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!

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    $\begingroup$ Have you looked at the power analysis functions in R, e.g. power.prop.test()? $\endgroup$ – Jeremy Miles Mar 6 '15 at 18:40
  • $\begingroup$ Did you get any answer? i want to know the formula for calculating sample size for a 3 arm randomized study. $\endgroup$ – user1327454 Aug 18 '15 at 13:45
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First off, I would like to suggest learning how to calculate power explicitly instead of using an online calculator. You would do this in a full statistical programming language, like R. Using this method, you can calculate the power for a huge myriad of possible scenarios that aren't covered by the typical calculator (like a 3-arm study). The accepted answer provided here offers an excellent description of how to perform this operation.

However, using an online calculator for a straightforward comparison of proportions seems reasonable. In a power calculation, you need to (typically) assume 3 variables and calculate the fourth. You want to calculate sample size, so you need to assume an alpha level, power, and effect size. Alpha and power are usually set at 0.05 and 0.80, respectively. That just leaves effect size. For proportions, your effect size is the two proportions in the control and supplement arms. For your first comparison, you want a power to detect the difference between 0.45 and 0.025 proportions. Using this calculator you linked, I get a total sample size of 29 (without continuity corrections). To change your assumptions, you can try 0.45 and 0.40, which brings it up to a whopping 3067 (detecting proportion differences near 0.50 is difficult). From here, you can change your assumptions as you see fit, like changing the ratio in each group or the needed power.

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This will be a superiority study? Then you will have to provide a superiority margin level. In this case the mentioned calc (http://statpages.info/proppowr.html) doesn't fit.

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    $\begingroup$ 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. $\endgroup$ – gung - Reinstate Monica Sep 20 '16 at 16:19
  • $\begingroup$ @gung But, Pavel did link to a better calculator, so he gave an answer but just didn't explain it properly. $\endgroup$ – Carl Sep 20 '16 at 17:27

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