Inclusion Criteria:

• HER2-positive disease, defined as immunohistochemistry (IHC) 3+ or amplification by fluorescent in situ hybridization (FISH) (HER2/chromosome 17 centromere [CEP17] ratio >= 2 or an average of >= 6 HER2 gene copies per nucleus) confirmed by Central Pathology Review (Mayo Clinic Rochester) prior to patient being registered to begin protocol therapy
  • NOTE: ductal carcinoma in situ (DCIS) components should not be counted in the determination of HER2 status
• Stage I-III breast cancer with the following criteria met:
  • If node-negative or if node status unknown (because it was not assessed), tumor must be > 2 cm (T2 or T3 tumor) or have higher-risk T1c disease (defined as tumor > 1 cm and estrogen receptor [ER]-negative and progesterone-receptor [PR] negative); if some ER/PR staining is present, ER and PR negative are defined as being positive in < 10% cells (per local pathology read)
  • If node-positive (N1-N3), T1mi, T1a, T1b, T1c, T2, or T3 tumors are eligible
    • Definition of node-negative disease (when node status known): if the patient has had a negative sentinel node biopsy and/or a negative axillary dissection, then the patient is determined to be node-negative; axillary nodes with single cells or tumor clusters =< 0.2 mm by either hematoxylin and eosin (H&E) or IHC will be considered node-negative; any axillary lymph node with tumor clusters between 0.02 and 0.2 cm is considered a micrometastasis; patients with a micrometastasis are eligible; an axillary dissection is not required to be performed in patients with a positive sentinel node and management of the axilla will be left up to the treating provider; in cases where the specific pathologic size of lymph node involvement is subject to interpretation, the principal investigator will make the final determination as to eligibility; in these special situations, the investigator must document this approval in the patient medical record
• ER/PR determination assays performed by IHC methods according to the local institution standard protocol
• Standard chemotherapy/trastuzumab declined by patient OR patient is deemed by physician for any reason to not be a candidate for standard therapy (i.e. patient and/or provider choose not to pursue standard trastuzumab-based chemotherapy regimen because of concerns related to toxicity or patient preference)
• For patients with bilateral or multifocal/multicentric breast cancers, one of the following criteria must be met to enroll: (1) each cancer individually meets criteria for enrollment (only ONE tumor has to undergo central confirmation for HER2), OR (2) at least one tumor meets eligibility (per tumor size/nodes/subtype outlined above) and the other foci in the ipsilateral or contralateral breast are also HER2-positive but are too small for enrollment (e.g., a patient is eligible if a cancer is T2N0 and HER2-positive in one breast, but the contralateral breast has a T1b HER2+ cancer that isn't eligible on its own, OR, (3) at least one tumor meets eligibility and the other foci in the ipsilateral or contralateral breast are HER2-negative and do not meet criteria for adjuvant chemotherapy per provider discretion (e.g. if a patient has a HER2-positive tumor meeting eligibility but also has a second, HER2-negative, small, node-negative, ER+, low grade cancer present, she is still eligible for enrollment); however, in the specific case that a second breast cancer is stage III and HER2-negative, that patient is excluded (because the second cancer is high-risk and likely will require non-HER2-directed therapy)
• All tumor removed by either a modified radical mastectomy or a segmental mastectomy (lumpectomy)
  • NOTE: management of axillary lymph nodes is up to the treating provider; however, all surgical margins should be clear of invasive cancer or DCIS (i.e., no tumor on ink); the local pathologist must document negative margins of resection in the pathology report; if all other margins are clear, a positive posterior (deep) margin is permitted, provided the surgeon documents that the excision was performed down to the pectoral fascia and all tumor has been removed; likewise, if all other margins are clear, a positive anterior (superficial; abutting skin) margin is permitted provided the surgeon documents that all tumor has been removed
• =< 90 days from the patient's most recent breast surgery for this breast cancer
• Eastern Cooperative Oncology Group (ECOG) performance status (PS) 0-2
• Baseline ejection fraction >= 50% by multi gated acquisition scan (MUGA) scan or echocardiogram performed =< 60 days prior to registration
• Absolute neutrophil count (ANC) >= 1500/mm^3
• Platelet count >= 100,000/mm^3
• Hemoglobin > 9.0 g/dL
• Total bilirubin =< 1.5 x upper limit of normal (ULN); if patient has known Gilbert's syndrome, direct bilirubin =< 2.0 x ULN
• Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) =< 2.5 x upper limit of normal (ULN)
• Alkaline phosphatase =< 2.5 x ULN
• International normalized ratio (INR) < 1.5 x ULN for institution unless patient is on planned therapy with anticoagulants (i.e., warfarin) with higher target planned; in those cases, INR up to 3.5 is acceptable
• Partial thromboplastin time (PTT) < 1.5 x ULN for institution unless patient is on planned therapy with heparin or heparin-like products
• Life expectancy > 5 years
• Willing to employ adequate and appropriate birth control if applicable
  • NOTE: This study is for patients aged 65 and older and most female patients will have entered menopause by this time; however patients should not become pregnant while on this study; pre-menopausal women need to use birth control while on this study and women should not breastfeed a baby while on this study; any man treated on this study will also need to use contraception if his partner is a premenopausal female; patients should check with their health care provider about what kind of birth control methods to use and how long to use them

• Negative urine or serum pregnancy test done =< 7 days prior to registration/randomization, for women of childbearing potential only

  • NOTE: in the rare case that a woman enrolling on study is of childbearing potential, a pregnancy test is required prior to enrollment on study
• Able to provide informed written consent
• Willing to return to consenting institution for follow-up (during the active monitoring phase of the study)
• Willing to provide blood samples for mandatory correlative research purposes

Exclusion Criteria:

• Evidence of metastatic disease
  • NOTE: patients will not require baseline staging positron emission tomography (PET) or computed tomography (CT) chest, abdomen, pelvis or bone scan to rule out metastatic disease prior to enrollment; any staging scans will be ordered at the treating provider's discretion; if metastatic disease is found on any staging studies done, patients will not be eligible for enrollment
• Locally advanced tumors at diagnosis (T4), including tumors fixed to the chest wall, peau d'orange, skin ulcerations/nodules, or clinical inflammatory changes (diffuse brawny cutaneous induration with an erysipeloid)
• Any T1a/T1b/T1c tumor that is node-negative/node-unknown AND ER OR PR positive
• Patients with stage III, HER2-negative cancer in the contralateral breast

• Positive hepatitis B (hepatitis B surface antigen and antibody) and/or hepatitis C (hepatitis C antibody test) as indicated by serologies conducted =< 3 months prior to starting study if liver function tests are outside of the normal institutional range

  • NOTE: patients with hepatitis B or C serologies indicating active infection without known active disease must meet the eligibility requirements for ALT, AST, total bilirubin, INR, PTT, and alkaline phosphatase on at least two consecutive occasions, separated by at least 1 week
• Active liver disease, for example, due to autoimmune hepatic disorder, or sclerosing cholangitis

• Significant cardiac disease or risk factors as indicated by MUGA or echocardiogram performed =< 60 days prior to registration

  • NOTE: patients are excluded from this study if there is a history of significant cardiac disease, cardiac risk factors or uncontrolled arrhythmias, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, including, but not limited to, the following:

    • Any prior myocardial infarction (asymptomatic changes on electrocardiogram [EKG] suggestive of old myocardial infarction [MI] is not an exclusion)
    • Documented congestive heart failure (CHF)
    • Current use of any therapy specifically for CHF
    • Current uncontrolled hypertension (diastolic > 100 mmHg or systolic > 200 mmHg)
    • Clinically significant pericardial effusion
• Co-morbid systemic illnesses or other severe concurrent disease which, in the judgment of the investigator, would make the patient inappropriate for entry into this study or interfere significantly with the proper assessment of safety and toxicity of the prescribed regimens
• Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection or psychiatric illness/social situations that would limit compliance with study requirements
• Currently receiving any other investigational agent which would be considered as a treatment for the primary neoplasm
• Concurrent second malignancy or past malignancy with > 30% estimated risk of relapse in next 5 years; EXCEPTIONS: non-melanotic skin cancer or carcinoma-in-situ of the cervix; NOTE: if there is a history or prior malignancy, patient must not be receiving active treatment for this malignancy cancer
• Any prior treatment with T-DM1 (trastuzumab emtansine) or any trastuzumab therapy
• Any neoadjuvant chemotherapy
• > 4 weeks of tamoxifen therapy, or other hormonal therapy, for adjuvant therapy for this malignancy
  • NOTE: if the patient has received < 4 weeks of such therapy but is still receiving it at the time of entry into the study, patient must temporarily stop the therapy; the therapy can re-start only after 12 weeks of T-DM1 has been administered
• History of exposure at any time to the following cumulative doses of anthracyclines:
  • Doxorubicin or liposomal doxorubicin > 500 mg/m^2
  • Epirubicin > 900 mg/m^2
  • Mitoxantrone >120 mg/m^2
  • Another anthracycline, or more than one anthracycline used in a cumulative dose exceeding the equivalent of doxorubicin 500 mg/m^2
• History of intolerance (including grade 3 or 4 infusion reactions) to murine proteins
• History of previous invasive breast cancer =< 5 years
  • NOTE: history of DCIS, lobular carcinoma in situ (LCIS) is allowed