In　phase　II　clinical　trials　on　cancer,　it　is　of　great　interest　to　establish　the　efficacy　and　safety　of　a　new　treatment　simultaneously.　Existing　hypotheses　may　not　achieve　this　goal　effectively.　We　introduce　two　new　sets　of　hypotheses　that　consider　the　association　between　the　two　factors,　then　construct　the　optimal　two-stage　designs　for　the　hypotheses.　The　proposed　designs　strictly　control　the　maximum　type　I　error　rate　at　the　given　nominal　level　alpha,　maintain　the　minimum　power　at　least　the　given　I　-　beta,　and　have　the　smallest　expected　total　sample　size　under　the　null　hypothesis.　Furthermore,　an　algorithm　is　provided　to　compute　these　designs.　R-codes　are　given　in　the　Supplemental　Material.