Although the results obtained from ECOG E5194 cohort 1 (criteria: mammographically detected low- or intermediate-grade DCIS, measuring less than 2.5 cm with margins ≥ 3 mm) and RTOG 9804 trial (the same enrolled clinicopathological features to cohort 1 of ECOG E5194 trial) demonstrated that the 7-year ipsilateral breast tumor recurrence (IBTR) ranged from 5.6% to 10.5% for low-risk ductal carcinoma in situ (DCIS) patients, the aforementioned two studies included a proportional patients who had young age and negative estrogen receptor (ER) status tumor. Previous studies and our studies revealed that age \< 40 years and ER-negative status in tumor were independent prognostic factor for recurrence of breast DCIS irrespective of tumor characteristics. The UK/ANZ randomized trial, enrolling high-risk and low-risk clinicopathologic features of DCIS, demonstrated that a benefit of tamoxifen in terms of reducing the IBTR is observed in the BCS alone group but not found in the BCS plus RT group. A recent published randomized trial showed that tamoxifen at the dose of 5 mg/day for 3 years. Based on the aforementioned results, we hypothesized that the administration of tamoxifen is not inferior than the prescription of RT in terms of reducing the IBTR for DCIS patients who had age more than 40 years, the pathological features meeting the ECOG E5194 cohort 1 criteria, and positive ER status in tumors. To approve the hypothesis, we will design a randomized non-inferiority trial to assess whether the effect of administration of tamoxfien (5 mg per day) for 10 years following BCS is not inferior in terms of reducing IBTR when comparing RT following BCS for patients who had low-risk clinicopathologic features (age more than 40 years and ECOG E5194 cohort 1 criteria) and positive-ER status of breast DCIS.