Having identified that the lack of replicability of results in earlier phases of clinical medical research stems largely from unattended selective inference, we offer a new hierarchical weighted false discovery rate controlling testing procedure alongside the single-level weighted procedure. These address the special structure of clinical research, where the comparisons of treatments involve both primary and secondary endpoints, by assigning weights that reflect the relative importance of the endpoints in the error being controlled. In the hierarchical method, the primary endpoints and a properly weighted intersection hypothesis that represents all secondary endpoints are tested. Should the intersection hypothesis be among the rejected, individual secondary endpoints are tested. We identify configurations where each of the two procedures has the advantage. Both offer higher power than competing hierarchical (gatekeeper) familywise error-rate controlling procedures being used for drug approval. By their design, the advantage of the proposed methods is the increased power to discover effects on secondary endpoints, without giving up the rigor of addressing their multiplicity.