Afimoxifene in Reducing the Risk of Breast Cancer in Women With Mammographically Dense Breast

PRIMARY OBJECTIVES: I. To estimate and compare the percent change in mammographic breast density (using Cumulus software) from baseline to month 12 in women applying 4mg afimoxifene (4-hydroxytamoxifen \[4-OHT\]) gel per breast versus placebo. SECONDARY OBJECTIVES: I. To compare the Cumulus versus (vs.) Volpara breast density measurement methods to estimate percent change in mammographic breast density from baseline to month 12 in women applying 4mg of 4-OHT gel per breast vs. placebo. II. To compare the percentage of women who underwent a change in Breast Imaging Reporting and Data System (BIRADS) category, comparing pre-and post- treatment measurements, for recipients of active agent versus placebo. III. To estimate percentage of women with \>= 10% absolute decrease in quantitative mammographic density percentage between baseline and 12 months, comparing between treated group 4mg per breast 4-OHT gel to placebo. IV. To describe symptoms assessed by breast cancer prevention trial (BCPT) eight symptom scale (BESS) questionnaire and laboratory toxicity assessment (factor VIII \[F VIII\], Von Willebrand \[vWB\] factor, sex hormone-binding globulin \[SHBG\], lipid profile). V. To evaluate serum measurements of 4-OHT and related metabolite levels and factors related to tamoxifen exposures, such as insulin-like growth factor (IGF) pathway members, C-reactive protein (CRP), estradiol. VI. To evaluate tissue biomarkers (among women undergoing optional pre- and post-treatment biopsies): terminal duct lobular unit (TDLU) involution; collagen structural changes; SETER/PR index: estrogen related transcription, Ki-67, COX-2, p16, CD68. VII. To examine whether any reductions in mammographic density seen after 1 year of 4-OHT vs. placebo gel application persist at 24 months, one year after gel application has stopped. OUTLINE: Patients are randomized to 1 of 2 arms. ARM A: Patients apply placebo gel topically to each breast once daily (QD) for up to 52 weeks. ARM B: Patients apply afimoxifene gel topically to each breast QD for up to 52 weeks. After completion of study treatment, patients are followed up at 24 months.