ATEMPT 2.0: Adjuvant T-DM1 vs TH

This is a randomized phase II adjuvant study for women and men with Stage I HER2-positive invasive breast cancer. Participants will be randomized into one of two treatment arms in this study and receive: * Arm 1: trastuzumab-emtansine (T-DM1, Kadcyla) and trastuzumab SC (Herceptin Hylecta) * Arm 2: paclitaxel and trastuzumab SC (Herceptin Hylecta) This research study is looking to see if the study drug T-DM1 followed by trastuzumab SC will have less side-effects than traditional HER2-positive breast cancer treatment of trastuzumab and paclitaxel.The study is also looking to learn about the long-term benefits and disease-free survival of participants who are treated with T-DM1 followed by trastuzumab SC. T-DM1 is an antibody-drug conjugate; it is made up of an antibody (trastuzumab) linked to a cytotoxic drug, DM1 (chemotherapy). T-DM1 functions as a targeted cancer therapy because it targets HER2-positive breast cancer cells directly, limiting exposure of the rest of the body to chemotherapy. More specifically, the trastuzumab in T-DM1 first binds to the HER2 protein on the surface of the breast cancer cells and the DM1 then enters the cells and can cause them to die, preventing tumor growth. The FDA (the U.S. Food and Drug Administration) has not approved T-DM1 for use on its own in patients with stage I, II, or III breast cancer. However, it has been approved for use in (a) advanced or metastatic, previously treated breast cancer and (b) in some patients receiving postoperative treatment after preoperative chemotherapy and surgery have been completed. Trastuzumab SC is a subcutaneous form of trastuzumab.Trastuzumab is a monoclonal antibody, which are disease-fighting proteins made by cloned immune cells. Paclitaxel and trastuzumab are considered a standard-of-care regimen in early breast cancer. Trastuzumab is FDA-approved to be administered as an IV (intravenous) or subcutaneous (muscular injection). The research study procedures include screening for eligibility and study treatment including laboratory evaluations and follow up visits. Participants will receive study treatment for a year in total and will be followed for 5 years after treatment. It is expected that about 500 people will take part in this research study. Genentech is supporting this research study by providing funding for the study and supplying trastuzumab-emtansine (T-DM1) and trastuzumab SC (subcutaneous).