I need to establish the efficacy of a test treatment (T) by means of an indirect comparison to placebo (P). Therefore a study of T vs. reference (R) will be performed, and there is 'historical' data for the comparison between R and P. The outcome measure of interest is a responder rate (i.e., higher rates indicate higher efficacy), and the treatments will be compared based on the rate difference.

At the end of the day there will be a confidence interval for the rate difference R-P (based on 'historical' data) and one for T-R (from a prospective trial), and these will be combined to obtain an indirect confidence interval for the rate difference T-P. Efficacy of T will be assumed if the lower bound of the T-P confidence interval falls above zero.

For the planning of the trial, how do I determine the lower bound of a T-R confidence interval that assures that the lower bound of the T-P interval is >0 when the R-P interval is already known (example: R-P = 0.2; 95% CI: 0.15 ... 0.25 - what is the smallest lower bound of the T-R CI that assures that the lower bound of the indirect T-P falls above zero?)?