Tamoxifen Citrate, Letrozole, Anastrozole, or Exemestane With or Without Chemotherapy in Treating Patients With Invasive RxPONDER Breast Cancer

Inclusion Criteria: * Patients must have a histologically confirmed diagnosis of node positive (1-3 nodes) invasive breast carcinoma with positive estrogen and/or progesterone receptor status, and negative HER-2 status; estrogen and progesterone receptor positivity must be assessed according to American Society of Clinical Oncology (ASCO)/College of American Pathologists (CAP) guidelines as either estrogen receptor (ER) or progesterone receptor (PR) \>= 1% positive nuclear staining; HER-2 test result negativity must be assessed as per ASCO/CAP 2013 guidelines using immunohistochemistry (IHC), in situ hybridization (ISH) or both; HER-2 is negative if a single test (or all tests) performed in a tumor specimen show: a) IHC negative (0 or 1+) or b) ISH negative using single probe or dual probe (average HER-2 copy number \< 4.0 signals per cell by single probe or HER-2/CEP ration \< 2.0 with an average copy number \< 4.0 signals per cell by dual probe); if HER-2 IHC is 2+, evaluation for gene amplification (ISH) must be performed and the ISH must be negative; ISH is not required if IHC is 0 or 1+; HER-2 equivocal is not eligible * Patients with multifocal, multicentric and synchronous bilateral breast cancers are allowed * Multifocal disease is defined as more than one invasive cancer \< 2 cm from the largest lesion within the same breast quadrant; (NOTE: the Oncotype DX® testing must be completed on the largest lesion) * Multicentric disease is defined as more than one invasive cancer \>= 2 cm from the largest lesion within the same breast quadrant or more than one lesion in different quadrants (NOTE: Oncotype DX® testing should be completed on all tumors and the determination for eligibility should be made on the highest recurrence score) * Synchronous bilateral disease is defined as invasive breast cancer with positive lymph nodes (axillary or intramammary) in at least one breast, diagnosed within 30 days of each other; (NOTE: the Oncotype DX® testing should be completed on both tumors and the tumor with the highest recurrence score should be used) * Patients will have undergone axillary staging by sentinel node biopsy or axillary lymph nodes dissection (ALND); patients must have at least one, but no more than three known positive lymph nodes (pN1a, pN1b or pN1c); patients with micrometastases as the only nodal involvement (pN1mi) are not eligible; patients with positive sentinel node are not required to undergo full axillary lymph node dissection; this is at the discretion of the treating physician; axillary node evaluation is to be performed per the standard of care at each institution * Patients with a prior diagnosis of contralateral ductal carcinoma in situ (DCIS) are eligible if they underwent a mastectomy or lumpectomy with whole breast radiation; prior partial breast irradiation, including brachytherapy, is not allowed; patients with a prior diagnosis of ipsilateral DCIS or invasive breast cancer who received radiation to that breast are not eligible * Patients must have had either breast-conserving surgery with planned radiation therapy or total mastectomy (with or without planned postmastectomy radiation); patients must have clear margins from both invasive breast cancer and DCIS (as per local institutional guidelines); lobular carcinoma in situ (LCIS) at the margins is allowed * Registration of patients who have not yet undergone Oncotype DX® screening must occur no later than 56 days after definitive surgery; (for all patients, Step 2 Registration must occur within 84 days after definitive surgery); if the Oncotype DX® Breast Cancer Assay has not been performed, patients must be willing to submit tissue samples for testing to determine the Recurrence Score value; a representative block or unstained sections from the representative block are sent directly to Genomic Health for Oncotype DX® Breast Cancer Assay which will be performed according to the standard commercial process * If the Oncotype DX® Recurrence Score is already known and is 25 or less, the patient must be registered to Step 2 immediately following Step 1 registration; if the Oncotype DX® Recurrence Score is already known and is greater than 25, the patient is ineligible * Patients must be females \>= 18 years of age. As the Oncotype DX® recurrence score has not been validated in men with breast cancer, men are not eligible for this study * Patients must have a complete history and physical examination within 28 days prior to registration * Patients must have a performance status of 0-2 by Zubrod criteria * Patients must be able to receive taxane and/or anthracycline based chemotherapy * Patients must not have received an aromatase inhibitor (AI) or a selective estrogen receptor modulator (SERM) such as tamoxifen or raloxifene within 5 years prior to registration * No other prior malignancy is allowed except for adequately treated basal cell (or squamous cell) skin cancer, in situ cervical cancer, or other cancer for which the patient has been disease-free for 5 years * The Quality of Life and Economic Substudy is permanently closed to accrual effective 12/1/12; patients who consented to QOL prior to 12/1/12 should continue to complete QOL forms per their expectation report; patients who are able to complete a questionnaire in English must be offered the opportunity to participate in the Quality of Life and Economic Substudy; (The Quality of Life and Economic Substudy is available to U.S. INSTITUTIONS ONLY); patients who are not able to complete a questionnaire in English are registered to S1007 without participating in the Quality of Life and Economic Substudy * Patients who consent to participate in the Quality of Life and Economic Substudy and who do not yet know the results of their Oncotype DX® screening must agree to complete the S1007 Health-Related Quality of Life Questionnaire: Enrollment between 14 days prior to and 7 days after Step 1 Registration * Patients who consent to participate in the Quality of Life and Economic Substudy and who do already know their Oncotype DX® Recurrence Score (and it is 25 or less) will proceed to Step 2 Registration without completing the S1007 Health-Related Quality of Life Questionnaire Enrollment Form (but will complete the S1007 Health-Related Quality of Life Questionnaire: Randomized Study Form) * Patients or their legally authorized representative must be informed of the investigational nature of this study and must sign and give written informed consent in accordance with institutional and federal guidelines; for Step 1 registration of patients who have not yet submitted specimens for the Oncotype DX Breast Cancer Assay, the appropriate consent form is the Step 1 Consent Form; for both Step 1 and Step 2 registration of patients whose Recurrence Score is already known and is 25 or less, the appropriate consent form is the Step 2 Consent Form * As a part of the Oncology Patient Enrollment Network (OPEN) registration process the treating institution's identity is provided in order to ensure that the current (within 365 days) date of institutional review board approval for this study has been entered in the system * STEP 2 REGISTRATION * Recurrence score (RS) by Oncotype DX® must be =\< 25 * Step 2 Registration must take place within 84 days after definitive surgery; patients must not have begun chemotherapy or endocrine therapy for their breast cancer prior to randomization * Patients randomized to either arm may also co-enroll in phase III trials that compare local therapies, or compare systemic therapies (such as chemotherapy, if randomized to Arm I of S1007) * The Quality of Life and Economic Substudy is permanently closed to accrual effective 12/1/12; patients at U.S. INSTITUTIONS who consent to participate in the Quality of Life and Economic Substudy must agree to complete the S1007 Health-Related Quality of Life Questionnaire: Randomized Study Form after Recurrence Score results and randomized treatment status are known but before treatment has been initiated * Patients or their legally authorized representative must be informed of the investigational nature of this study and must sign and give written informed consent in accordance with institutional and federal guidelines; for all patients the appropriate consent form for this registration is the Step 2 Consent * STEP 3 REGISTRATION CBALR TM Substudy * Patients must be disease-free, with no prior invasive recurrence at time of registration to Step 3 * Patients must be registered to Step 3 no more than 8 years after randomization (Step 2 Registration) and must agree to have samples drawn within 28 days after registration to Step 3 * Patients must agree to have blood samples collected at up to 3 timepoints: 1) within 28 days after registration to Step 3, 2) 2-3 years after time of registration to Step 3, and 3) At time of invasive recurrence (if applicable). Patients must also agree to have tissue submitted at time of invasive recurrence (if applicable) from the invasive recurrence biopsy (where tissue is available) Exclusion Criteria: * Patients must not have inflammatory breast cancer and must not have metastatic disease * Patients must not have begun chemotherapy or endocrine therapy for their breast cancer prior to registration * Patients must not require chronic treatment with systemic steroids (inhaled steroids are allowed) or other immunosuppressive agents * Patients must not be pregnant or nursing; women of reproductive potential must have agreed to use an effective contraceptive method; a woman is considered to be of "reproductive potential" if she has had menses at any time in the preceding 12 consecutive months; in addition to routine contraceptive methods, "effective contraception" also includes heterosexual celibacy and surgery intended to prevent pregnancy (or with a side-effect of pregnancy prevention) defined as a hysterectomy, bilateral oophorectomy or bilateral tubal ligation; however, if at any point a previously celibate patient chooses to become heterosexually active during the time period for use of contraceptive measures outlined in the protocol, he/she is responsible for beginning contraceptive measures