Appointments No Treatment

SELECT 
  a.appointment_id, 
  a.patient_id, 
  a.appointment_date
FROM appointments a
LEFT JOIN treatments t ON a.appointment_id = t.appointment_id
WHERE t.treatment_id IS NULL AND a.status = 'completed';

Say you're using a LEFT JOIN to find appointments without a matching treatment. Filtering for treatment_id IS NULL isolates those cases. Checking the appointment status keeps the focus on visits that actually happened.