A patient could discontinue taking medication or simply discontinue the medication. Only a trial, or a subject's participation in it, can be terminated. Admission or entry already imply moving towards and so the into is superfluous. In some instances, it may be better to use the active voice and state that 'the subject entered the study'. If you must use a double negative, make sure you get it right.
Expiration is the phase of the respiratory cycle during which air is expelled from the lungs.