There are two groups: control and experimental, mean difference is 10% between experimental group and control group [if there are X successes in control group then there are 1.1 * X successes in experimental group], significance level is 0.05, power (sensitivity = (1 - beta)) is 0.8. The number of patients in groups are equal. Which is the minimum number of patients in group?
The known formulas for sample size include standard deviation (which is unknown in this case), so we can't apply computations directly. Can we estimate the SD with the "minimum number of patients" condition? Or we need to choose other way?
It appears that you are trying to estimate power for a binary (dichotomous) outcome using the methods designed for a continuous outcome (i.e., one that produces means and standard deviations). The power in your situation will be affected by the base-rate, that is, the success rate in the control condition. A 10% difference around a base-rate of 50% will require a smaller sample than a 10% difference around a base-rate of 5%. The additional information you need to solve for sample size is the base-rate, not the standard deviation. You also need to be applying the method for a binary outcome.