Formulas are provided in the normal distribution case to correct the mean and variance of the sample mean from a two-stage phase II study in which a preferred dose is selected in the first stage, the second stage collects additional data with the selected dose, and then a non-superiority hypothesis is tested with the data from both stages.
Statistical Methodology | Statistical Theory
Levin, Bruce, "Formulas for Correcting the Mean and Variance of the Full-Data Sample Mean of the Primary Endpoint Under the Dose Selected at Stage One in a Two-Stage Trial with Selection Between Two Active Doses" (August 2004). Columbia University Biostatistics Technical Report Series. Working Paper 17.