Traditionally, when the primary endpoint is rejected at trial completion, secondary endpoints often are tested at the full alpha level in a pre-specified hierarchical order and the strategy controls the overall type I error rate. However, in a group sequential setting, this traditional hierarchical testing strategy may not control the overall type I error rate for the secondary endpoint in the strong sense [Hung et al. 2007, Glimm et al. 2010, Tamhane et al. 2010], and it was proposed that an alpha spending function also be specified for testing the secondary endpoint. A few hypothetical examples based on real life experiences will be used for the discussion of this topic, and it will be explored whether there is a less conservative approach to control the type I error rate for secondary endpoint. In addition, few other statistical considerations in the setting of a trial is stopped at an interim analysis will also be discussed.