Inclusion
Age 45 - 74
Postmenopausal female
Postmenopausal is defined as either
Prior removal of the ovaries, or if ovaries intact amenorrhea for \>= 12 months and not on any form of contraception, or
Amenorrhea for greater than 2 months with serum follicle-stimulating hormone (FSH) in postmenopausal range (\>= 25 IU/L). Women with ovaries and a prior hysterectomy or endometrial ablation \< age 55 must have a FSH \>= 25 IU/L. Women may be on vaginal low dose estrogen preparations for vaginal dryness. Women over age 50 with a levonorgestrel intrauterine device in place for 2 or more years and not planning removal in the next 6 month are also eligible if FSH \>= 25 IU/L
Note: FSH will be done at time of screening
Women with intact ovaries and uterus \< age 55 must have a negative pregnancy test prior to randomization
Overweight or obese (body mass index \[BMI\] \>= 25 kg/m\^2)
Note: BMI must be calculated within 28 days of randomization
Willing to undergo a fasting blood draw and non-fasting RPFNA with fixed and frozen aliquots sent to University of Kansas Medical Center (KUMC)
At increased risk of breast cancer per at least one of the following:
Personal medical history
History of atypical hyperplasia or lobular carcinoma in situ (LCIS) found on breast biopsy
History of unilateral ductal carcinoma in situ treated with unilateral mastectomy, lumpectomy, or local excision with or without radiation and this treatment was completed at least 3 months prior to the screening RPFNA
High mammographic density determined by one of the following:
Visual estimate of area of density (VAS) \> 50%,
Volpara (trademark) \>= 15% dense volume (Volpara d)
Breast Imaging Reporting and Data System (BIRADS) assessment = extremely dense (BIRADs D)
Genetic test result
Germline gene mutation in ATM, BARD1, BRCA2, CDH1, CHEK2, NF1, PALB2, PTEN, RAD51C, RAD51D, or STK11
Polygenic lifetime risk score \>= 2x average or 25%
Calculated risk based on standard models
Five-year Breast Cancer Risk Assessment Tool (BCRAT) (version 2.0) \>= 1.66%
Ten-year International Breast Cancer Intervention Study risk evaluation tool (IBIS) (version 8) \>= 3%
Ten-year relative risk IBIS (version 8) \>= 2X that for age group
Ten- year Breast Cancer Surveillance Consortium (version 2) \>= 3%
Family History
Breast cancer in a first or second degree relative (female or male) with onset under age 50. (First degree relative = parent, sibling, or child. Second degree relative = grandparent, uncle, aunt, nephew, niece, half-sibling, grandchild or first cousin)
Breast cancer in two or more first or second-degree relatives from either the maternal or paternal linage without regard to age
Bilateral breast cancer or breast and ovarian cancer in the same first or second degree relative without regard to age
Primary source documentation of risk is required and must be submitted to the lead academic organization (LAO) for review along with the eligibility checklist
Risk factor: Atypical hyperplasia or LCIS; Primary source document: Copy of pathology report or clinical note confirming the diagnosis
Risk factor: Ductal carcinoma in situ (DCIS) and treatment history; Primary source document: Copies of pathology report or clinic notes confirming the diagnosis, treatment plan and treatment end date(s)
Risk factor: Mammographic density; Primary source document: Copy of clinic note or mammogram report
Risk factor: Genetic; Primary source document: Copy of genetic test report
Risk factor: Calculated based on standard models; Primary source document: Copy of the calculation result
Total bilirubin =\< 1.5 x institutional upper limit of normal (ULN)
Note: Higher total bilirubin levels (=\< 3 mg/dL) can be allowed if due to known benign liver condition, i.e., Gilbert's syndrome
Results from prior laboratory testing within 180 days of randomization may be used
Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase \[SGOT\]) =\< 3.0 x institutional upper limit of normal
Results from prior laboratory testing within 180 days of randomization may be used
Alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 3.0 x institutional upper limit of normal
Results from prior laboratory testing within 180 days of randomization may be used
Human immunodeficiency virus (HIV)-infected patients on effective anti-retroviral therapy with undetectable viral load within 6 months are eligible for this trial
For patients with evidence of chronic hepatitis B virus (HBV) infection, the HBV viral load must be undetectable on suppressive therapy, if indicated
Patients with a history of hepatitis C virus (HCV) infection must have been treated and cured. For patients with HCV infection who are currently on treatment, they are eligible if they have an undetectable HCV viral load
Patients on chronic suppressive antiviral therapy for herpes simplex virus (HSV) are eligible
Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 (Karnofsky \>= 60%)
Women must have at least 1 unaffected untreated breast for fine needle aspiration. Women may have had prior unilateral breast radiation or mastectomy for DCIS
Ability to understand and the willingness to sign a written informed consent document
Most recent screening mammogram must be performed ≤ 12 months prior to RPFNA and must be reported as BIRAD 1 or 2. If BIRAD 0 then follow-up diagnostic imaging must be BIRAD 1 or 2 or cleared clinically with radiology recommendation of return to annual screening
Confirmation that baseline research blood was drawn fasting (\>= 10 hours), has been received in good condition at KUMC, and is archived for assessment of primary endpoint
Exclusion
Exclusions based on current or past conditions:
Bilateral breast implants (danger of implant puncture with RPFNA)
Prior invasive breast cancer
Prior invasive uterine cancer
Other prior invasive cancer and haven't completed cancer related therapy or with evidence of disease (other than non-melanoma skin cancer) within the past 2 years
Currently breastfeeding (concern that tamoxifen may be in breast milk) or nursing within past 12 months (concern about milk fistula with RPFNA)
Type I or type II diabetes mellitus requiring current pharmacologic treatment (including metformin, glucagon-like peptide 1 agonists, insulin, sulfonylurea)
Prior deep vein thrombosis, pulmonary embolus, or stroke
Prior gastric bypass surgery
History of chronic liver disease including NASH (nonalcoholic steatohepatitis) or cirrhosis
Pathogenic or likely pathogenic germline mutation in BRCA1 or TP53
Exclusions based on medications:
Current use of prescription anticoagulants such as Coumadin (warfarin), direct-acting oral anticoagulants such as Xarelto (rivaroxaban) or Eliquis (apixaban) or heparin
Women who would not be able to or do not wish to discontinue daily use of aspirin (81mg or higher) and aspirin containing products (81 mg or higher) at least 3 weeks prior to each RPFNA
Note: Women may resume daily use of aspirin and aspirin containing products 3 days after each RPFNA procedure
Current use of a levonorgestrel intrauterine device if in place less than 2 years or if there is planned removal within the next 6 months
Current use of hormone therapy (oral, transdermal, or injectable)
Note: Vaginal estrogen is allowed
Prior treatment with tamoxifen, aromatase inhibitor or selective estrogen receptor degrader for more than 2 months
Note: Women with \< 2 months of these drugs must be off for at least 6 months before they may begin biomarker screening tests
Greater than 1 gram daily of omega-3 fatty acid supplement within the last 6 months
Current use of prescription immunosuppressive drugs
Current use of CYP3A4 strong inducers rifampin or aminoglutethimide
Current use of or plans to initiate a glucagon-like peptide 1 agonist within the next 6 months
Current use of metformin for any indication
Participants may not be receiving any other investigational agents
History of allergic reactions attributed to compounds of similar chemical or biologic composition to tamoxifen or omega-3 fatty acid or generic Lovaza or compounds of similar chemical composition
Uncontrolled intercurrent illness or psychiatric illness/social situations that would limit compliance with study requirements