Among the clinical and histopathological features, extrathyroidal extension (OR = 2.29, CI 95% 1.24–4.22, p = 0.008), tumoral infiltration of surgical margins (OR = 2.44, CI 95% 1.05–5.69, p = 0.04), the presence of lymph node metastases at diagnosis (OR = 4.00, CI 95% 1.65–9.73, p = 0.002), and high stimulated Tg levels in the context of RAI (OR = 1.03, CI 95% 1.01–1.05, p = 0.007) were identified as risk factors for one-year tumor relapse. This evidence concerns the gene TG and neoplasm.