| This dissertation is focused on multiple hypotheses testing procedures under group sequential design, under which the data are accrued sequentially or periodically in time. We propose two stepwise procedures using the error spending function approach. The first procedure controls the Family-wise Error Rate (FWER), under the assumption that the test statistics follow normal distribution with known correlations. This procedure involves repeated application of a step-down procedure at each stage on the hypotheses that are not rejected in the previous stages. The second proposed procedure is a group sequential BH procedure (GSBH) controlling the False Discovery Rate (FDR), which is a natural extension of the original BH method from single to multiple stages under a group sequential design. Similar to the proposed step-down procedure controlling the FWER, a step-up procedure is applied on the active hypotheses at each stage in the GSBH procedure. This GSBH procedure is theoretically proved to control the FDR under some positive dependence condition. An adaptive version of GSBH procedure (ad.GSBH) is also introduced, which is proved to control the FDR under independence. Simulation studies are performed to investigate the performance of these three procedures. The simulation results show that these procedures are often powerful and provide more reduction of the expected sample sizes compared to their relevant competitors. |
