MassHealth director Dan Tsai is moving on after more than six years running the state’s Medicaid program to join the Biden administration as deputy administrator for the Centers for Medicare and Medicaid Services. The Baker administration announced Tsai’s departure, effective June 29, on Monday. In his new role, the state’s longest-serving Medicaid chief in almost 20 years will take on the role of director for the Center for Medicaid and Children’s Health Insurance Program Services.