Interest in adaptive designs for confirmatory clinical trials has increased in the past few years. A particularly appealing application is the use of adaptive designs in combined phase II/III studies with treatment selection at interim. These studies start comparing several treatments with a control. One (or more) treatment(s) are then selected after the first stage based on the available information at an interim analysis, including interim data from the ongoing trial, external information and expert knowledge. Recruitment continues, but now only for the selected treatment(s) and the control, possibly in combination with a sample size reassessment. The final analysis of the selected treatment(s) include(s) the patients from both stages and is performed such that the overall type I error rate is strictly controlled, thus providing confirmatory evidence of efficacy at the final analysis. We describe two approaches to control the type I error rate in adaptive designs with sample size reassessment and/or treatment selection. The first method adjusts the critical value using a simulation based approach, which incorporates the number of patients at an interim analysis, the true response rates, the treatment selection rule, etc. We discuss the underlying assumptions of simulation based procedures and give several examples where the type I error control is lost if some of the assumptions are violated. The second method is an adaptive Bonferroni-Holm test procedure based on conditional error rates of the individual treatment-control comparisons. We show that this procedure controls the type I error rate, even if a deviation from a pre-planned adaptation rule or the time point of such a decision is necessary. Motivated by a real case study, a simulation study is conducted to compare the two methods with respect to power and type I error rate control, being aware that many further considerations are necessary when designing an adaptive design.