This clinical trial evaluates deoxyribonucleic acid (DNA) methylation signatures in diagnosing and managing thyroid nodules. The purpose of this research is to develop a new test for thyroid cancer. This test will use needle biopsies (small collections of tissue with a needle) from the thyroid to determine whether the participant has a malignant (cancer) or benign (not showing cancer) thyroid tumor. The information learned from this trial may help develop a more accurate test so that patients do not have unnecessary surgeries for nodules that are thought to be suspicious but are actually benign.