A method of testing for noninferiority followed by testing for superiority in an adaptive group sequential design is presented. The method permits a data-dependent increase in sample size without any inflation of type-1 error. Closed-form expressions for computing conditional power and the sample size required to achieve any desired conditional power are derived. A new statistical method for performing inference on the primary efficacy parameter is derived. The method is used to obtain the p-value, median-unbiased point estimate and confidence interval for the efficacy parameter. For normal endpoints with known variance, the coverage of the confidence interval is exact. In other settings, the coverage is exact for large samples. An illustrative example is provided in which the methods of testing and estimation are applied to an actual clinical trial of acute bacterial skin and skin-structure infection. The operating characteristics of the trial are obtained by simulation and demonstrate that the type-1 error is preserved, the point estimate is median unbiased, and the confidence interval provides exact coverage up to Monte Carlo accuracy.