Anastrozole and Letrozole After Surgery for the Treatment of Stage I-III Breast Cancer

Inclusion Criteria: * REGISTRATION-INCLUSION CRITERIA * Disease characteristics: * Histological confirmation of invasive breast carcinoma * Stage I-III breast cancer * Estrogen receptor (ER) positive disease according to American Society of Clinical Oncology (ASCO)/College of American Pathologists (CAP) guidelines as ER \>= 1% positive nuclear staining * Completion of all planned cancer treatments prior to registration: * Surgical resection of breast and nodal surgery; (NOTE: Reconstructive surgery does not have to be completed) * Adjuvant radiation therapy, if needed * Neoadjuvant and/or adjuvant chemotherapy, if needed * Post-menopausal defined as * Age \>= 60 and amenorrhea \> 12 consecutive months OR * Previous bilateral oophorectomy OR * Age \< 60 and amenorrhea \> 12 consecutive months and documented follicle stimulating hormone (FSH) level within post-menopausal range according to institutional standard * NOTE: Patients who did not meet these criteria at time of diagnosis and received pre-operative (neoadjuvant) or post-operative (adjuvant) chemotherapy will not be allowed to participate * Eastern Cooperative Oncology Group (ECOG) performance status (PS) 0, 1, or 2 * Hemoglobin \>= 8.0 g/dL (obtained =\< 14 days prior to registration) * Absolute neutrophil count (ANC) \>= 1500/mm\^3 (obtained =\< 14 days prior to registration) * Platelet count \>= 70,000/mm\^3 (obtained =\< 14 days prior to registration) * Total bilirubin =\< 1.5 x upper limi…